What is the weight of newtons and the mass in kilograms of a 5.0 lb bag of sugar. Note: 1 newton =.225 lbs.

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1 1 2 What is the weight of newtons and the mass in kilograms of a 5.0 lb bag of sugar. Note: 1 newton =.225 lbs N 2.27 kg What is the weight of newtons and the mass in kilograms of a 240-lb. fullback. Note: 1 newton =.225 lbs. 6 An interstellar ship has a mass of 1.20 x 10 6 kg and is initially at rest relative to a star system. (a) What constant acceleration is needed to bring the ship up to a speed of 0.10c (where c is the speed of light, 3.0 x 10 8 m/s) relative to the star system in 3.0 days? (b) What is that acceleration in g units? (c) What force is required for the acceleration? (d) If the engines are shut down when 0.10c is reached (the speed then remains constant), how long does the ship take (start to finish) to journey 5.0 light-months, the distance that light travels in 5.0 months? N 109 kg An electron travels in a straight line from the cathode of a vacuum tube to its anode, which is exactly 1.5 cm away. It starts with zero speed and reaches the anode with a speed of 6.0 x 10 6 m/s. (a) Assume constant acceleration and compute the force on the electron. Take the electron's mass to be 9.11 x kg. This force is electrical in origin (b) Calculate the weight of the electron. 7 (a) 115 m/s 2 (b) 11.8 g (c) 1.38 x 10 8 N (d) 4.2 y x 10 9 seconds Why does a child in a wagon seem to fall backward when you give the wagon a sharp pull? Inertia (a) 1.64 x N (b) F grav = 8.9 x N 8 Whiplash sometimes results from an automobile accident when the victim's car is struck violently from the rear. Explain why the head of the victim seems to be thrown backward in this situation. Is it really? 4 A 75 kg space ranger is about to take a trip. (a) Compute the weight of a 75 kg space ranger on Earth. (b) Compute the weight of a 75 kg space ranger on Mars, where g = 3.8 m/s 2. (c) Compute the weight of a 75 kg space ranger in interplanetary space, where g = 0. (d) What is the ranger's mass at each location? 9 A person wearing a cast on an arm or a leg expenences extra fatigue. Explain this on the basis of Newton's first and second laws. (a) 735 N (b) 285 N (c) 0 (d) 75 kg 10 Why do you push harder on the pedals of a bicycle when first starting out than when moving at constant speed? 5 A certain particle has a weight of 22 N at a point where g = 9.8 m/s 2. (a) What is its weight at a point where g = 4.9 m/s 2? (b) What is its mass at a point where g = 4.9 m/s 2? (c) What is its weight if it is moved to a point in space where g = 0? (d) What is its mass if it is moved to a point in space where g = 0? 11 overcoming the inertia of the book Why is the stopping distance of a truck much shorter than for a train going the same speed? The truck has less inertia then the train (a) 11 N (b) 2.2 kg (c) 0 (d) 2.2kg 12 At the surface of a certain planet, the gravitational acceleration g has a magnitude of 12.0 m/s 2. A 3.0-kg brass ball is transported to this planet. (a) What is the mass of the brass ball on the Earth. (b) What is the mass of the brass ball on the planet.

2 13 14 Driving down the road you hit the brakes suddenly. As a result, your body moves toward the front of the car. Explain, using Newton's laws. The force exerted on the car by the brakes causes it to slow down, but your body continues to move forward with the same velocity (due to inertia) until the seat belt exerts a force on it to decrease its speed. A ball is rolling with a velocity of 20 cm/sec and no outside force acts on it. (a) Draw a free body diagram of the situation. (b) What will be its velocity after 5 seconds? (b) 20 cm/sec A force of 5 Newtons gives a mass m 1 an acceleration of 8 m/s 2, and a mass m 2 an acceleration of 24 m/s 2. (a) Draw a free body diagram of each situation (b) Draw a free body diagram of the situation if the two masses were fastened together. (c) What acceleration would it give the two when they are fastened together? (b) (d) You re new motorcycle weighs 2450 N. (a) Draw the free body diagram of this situation (b) What is its mass in kilograms? 15 It takes a net force of 50 N to give a body an acceleration of 10 m/sec 2. (a) Draw a free body diagram of the situation. (b) What is the mass of the body? (b) 5.0 kg 21 (b) 250 kg You place a 7.50-kg television set on a spring scale. The scale reads 78.4 N, (a) Draw a of the forces on the television (b) Draw a of the forces on the scale. (c) What is the acceleration of gravity at that location? (b) (c) 10.5 m/s 2, down 16 A shot-putter exerts a net force of 140 N on a shot just before it is released from his hand. The shot has an observed acceleration of 19 m/s 2. (a) Draw a free body diagram of the situation. (b) What is the mass of the shot? (b) 7.3 kg 22 What is the mass of an object that weighs 490 Newtons? 50 kg 17 A racing car undergoes a uniform acceleration of 4.00 m/s 2. A net force causing the acceleration is 3.00 x 10 3 N. (a) Draw a free body diagram of the situation. (b) What is the mass of the car? 23 A 2.26 kg book is dropped from a height of 1.5 m. (a) Draw a of the forces on the falling book. (b) What is its acceleration? (c) What is its weight in Newton s? (b) 750 kg (b) 9.81 m/s 2 (c) 22.2 N 18 A 1,850 kg car is moving to the right at a constant velocity of 1.44 m/s. (a) Draw a free body diagram of the situation. (b) What is the net force on the car? (c) Draw a free body diagram of the situation if the car is moving to the left. (d) What would be the net force on the car if it were moving to the left? (b) zero, as long as the speed is constant (c) (d) zero

3 24 An electron travels in a straight line from the cathode of a vacuum tube to its anode, which is exactly 1.5 cm away. It starts with zero speed and reaches the anode with a speed of 6.0 x 10 6 m/s. (a) Draw a of the situation and the forces on the electron. (b) Assume constant acceleration and compute the force on the electron. Take the electron's mass to be 9.11 x kg. This force is electrical in origin (c) Calculate the weight of the electron. 28 A car has a mass of 1600 kg. A braking force of 500 N is applied to the car while it is in motion. (a) Draw a of the forces on the car. (b) What is the direction and magnitude of the acceleration it produces? (b) m/s 2 25 (b) 1.1 x N (c) F grav =8.9 x N Use the data in the table (a) Draw a position-time graph (b) Draw a velocity-time graph (c) What would you predict for the average velocity during the eighth time interval if the puck continued to be pulled by the stretched loop? (d) Does the object have a constant acceleration? (e) Is a constant force applied to the object during the eight time inerval? 29 A 65-kg swimmer steps horizontally off a 10-m tower. The swimmer comes to a stop 2 m below the surface of the water. (a) Draw a free body diagram of the swimmer in free fall. (b) Find the swimmer's velocity just before he hits the water. (c) Draw the free body diagram of the forces on the swimmer as he enters the water. (d) Find the net force exerted by the water on the swimmer as he comes to rest below the surface of the water. (a) (b) 14 m/s, (c) (d) 3185 N 30 A net external force is required to give a 25 kg suitcase an acceleration of 2.2 m/s 2 to the right? (a) Draw a free-body diagram of the forces on the suitcase. (b) What is the magnitude and direction of the net external force on the suitcase? (b) 55 N 26 (a) graph (b) graph (c) (d) (e) A body is pulled across a smooth horizontal surface by a spring loop that is kept stretched by a constant amount. It is found that the body is accelerated at 15 cm/s 2. (a) Draw a free body diagram of the forces on the body (b) The body is pulled by two loops, each just like the first loop, side by side and stretched by that same amount. Draw a free body diagram of the new situation. (c) What will be the acceleration of the body when it is pulled by the two loops? (b) (c) 30 cm/s 2 31 Together a motorbike and rider have a mass of 275 kg. The motorbike is slowed down with an acceleration of m/s 2. (a) Draw a free body diagram of the forces on the motorbike. (b) What is the net force on the motorbike? (c) Describe the direction of this force and the meaning of the negative sign. (b) x 10 3 N (c) The negative sign of the acceleration showing down the motor bike tells us that the motor bike has a velocity in the positive direction. The negative sign on the force indicates that it is directed opposite to the motor bike velocity. 27 Is it possible to have motion in the absence of a net force? Explain. Yes, objects can move at constant speed.

4 32 A certain force F 0 gives an object an acceleration of 6 x 10 6 m/s 2 Another force gives the same object an acceleration of 9 x 10 6 m/s 2. (a) Draw a free body diagram of the forces on the object for each of the situations described above. (b) What is the magnitude of the second force? (c) The two forces act together in the same direction. Draw a free diagram of the new situation. (d) What is the acceleration of the object if the two forces act together on the object in the same direction? (e) The two forces act together in the opposit direction. Draw a free diagram of the new situation. (f) What is the acceleration of the object if the two forces act in opposite directions on the object? 35 The rock shown below is sliding across the floor at a constant speed without friction. Draw a free body diagram of the forces acting on the rock. (b) F 2 = 1.5F 0 (c) (d) 15 x 10 6 m/s 2 (e) (f) 3 x 10 6 m/s 2 in the direction of F The rock shown below is falling toward the earth Draw the free body diagram for the falling rock. 33 The Ice puck shown below has a mass of 0.50 kg, F 2 = 10 N, and F 1 = 6 N? (a) Draw a free body diagram of the forces on the ice puck shown above. (b) What is the acceleration of the puck? 37 The rock shown below is falling toward the earth Draw the free body diagram for the falling rock. (b) 34 A block of mass 8.0 kg, starting from rest, is pulled along a horizontal tabletop by a constant force of 2.0 N. It is found that this body moves a distance of 3.0 m in 6.0 sec. (a) Draw a of the forces on the block. (b) What is the acceleration of the body? (c) What is the ratio of the applied force to the mass? (d) Since your answer to part (c) is not equal to that to part (b) (at least, it shouldn't be), what conclusions can you draw about this motion? Give numerical results, if possible. (b) (c) (d) 38 A young girl slides down a rope. As she slides faster and faster she tightens her grip, increasing the force exerted on her by the rope. What happens when this force is equal in magnitude to her weight? Explain. When the magnitude of the force exerted on the girl by the rope equals the magnitude of her weight, the net force acting on her is zero. As a result, she moves with constant velocity.

5 39 Give the direction of the net force acting on each of the following objects. If the net force is zero, state "zero." (a) A car accelerating northward from a stop light. (b) A car traveling southward and slowing down. (c) A car traveling westward with constant speed. (d) A skydiver parachuting downward with constant speed. (e) A baseball during its flight from pitcher to catcher (ignoring air resistance). 45 A 42.0-kg parachutist lands moving straight downward with a speed of 3.85 m/s. (a) If the parachutist comes to rest with constant acceleration over a distance of m, what force does the ground exert on her? (b) If the parachutist comes to rest over a shorter distance, is the force exerted by the ground greater than, less than, or the same as in part (a)? 40 (a) northward; (b) northward; (c) zero; (d) zero; (e) downward. On a planet far, far away, an astronaut picks up a rock. The rock has a mass of 5.00 kg, and on this particular planet its weight is 40.0 N. If the astronaut exerts an upward force of 46.2 N on the rock, what is its acceleration? 46 Integrate Problem Driving home from school one day, you spot a ball rolling out into the street (see figure). You brake for 1.20 s, slowing your 950-kg car from 16.0 m/s to 9.50 m/s. (a) What was the average force exerted on your car during braking? (b) How far did you travel while braking? 41 In a grocery store, you push a 12.5-kg shopping cart with a force of 14.0 N. If the cart starts at rest, how far does it move in 3.00 s? 42 You are pulling your little sister on her sled across an icy (frictionless) surface. When you exert a constant horizontal force of 110 N, the sled has an acceleration of 2 m/s 2. If the sled has a mass of 7.0 kg, what is the mass of your little sister? 47 A 747 jetliner lands and begins to slow to a stop as it moves along the runway. Its mass is 3.5 x 10 5 kg its speed is 27.0 m/s, and the net braking force is 4.3 x 10 5 N (a) What is its speed 7.50 s later? (b) How far has it traveled in this time? 43 A 0.53-kg billiard ball is given a speed of 12 m/s during a time interval of 4.0 ms. What force acted on the ball? 44 A 92-kg water skier floating in a lake is pulled from rest to a speed of 12 m/s in a distance of 25 m. What is the net force exerted on the skier, assuming his acceleration is constant? 48 A 64-kg parent and a 16-kg child meet at the center of an ice rink. They place their hands together and push. (a) Is the force experienced by the child more than, less than, or the same as the force experienced by the parent? (b) Is the acceleration of the child more than, less than, or the same as the acceleration of the parent? Explain. (c) If the acceleration of the child is 2.6 m/s 2 in magnitude, what is the magnitude of the parent's acceleration? Integrate Problem

6 49 In a tennis serve, a kg ball can be accelerated from rest to 35 m/s over a distance of 0.80 m. Find the average force exerted by the racket on the ball during the serve. 55 An apple of mass falls out of a tree from a height (a) What is the magnitude of the force of gravity, mg, acting on the apple? (b) What is the apple's speed, v, just before it lands? (c) Show that the force of gravity times the height, mgh, is equal to 1/2 mv 2. Be sure to show that the dimensions are in agreement as well as the numerical values A 40.0-kg swimmer with an initial speed of 1.75 m/s decides to coast until she comes to rest. If she slows with constant acceleration and stops after coasting 2.00 m, what was the force exerted on her by the water? NASA plans to test a new type of rocket, a Variable Specific Impulse Magnetoplasma Rocket (VASIMR), in A VASIMR can produce 1200 N of thrust (force) when in operation. A VASIMR has a mass of 2.2 x 10 5 N (a) What acceleration will it experience? Assume that the only force acting on the rocket is its own thrust. (b) Over what distance must the rocket accelerate from rest to achieve a speed of 9500 m/s? (c) When the rocket has covered one-half the acceleration distance found in part (b), is its average speed 1/2, 1/3, or 1/4 its average speed during the second half of the acceleration distance? Explain Paleontologists estimate that if a Tyrannosaurus Rex were to trip and fall, it would have experienced a force of approximately 260,000 N acting on its torso when it hit the ground. Assume the torso has a mass of 3800 kg, (a) Find the magnitude of the torso's upward acceleration as it comes to rest. (For comparison, humans lose consciousness with an acceleration of about 7g.) (b) Assuming the torso is in free fall for a distance 1.46 m as it falls to the ground, how much time is required for the torso to come to rest once it contacts the ground? Biological A 0.15-kg baseball is moving at 43 m/s toward home plate when it is hit with the bat. The ball is in contact with the bat for s, and leaves the bat at 25 m/s directly away from home plate. Determine the average force exerted by the bat on the ball. Integrate Problem 52 At the local grocery store, you push a 14.5-kg shopping cart. You stop for a moment to add a bag of dog food to your cart. With a force of 12.0 N, you accelerate the cart from rest through a distance of 2.29 m in 3.00 s. What was the mass of the dog food? 58 While waiting at the airport for your flight to leave, you observe some of the jets as they take off. With your watch you find that it takes about 35 seconds for a plane to go from rest to takeoff speed. In addition, you estimate that the distance required is about 1.0 km. (a) If the mass of a jet is 1.7 x 10 5 m/s 2 what force is needed for takeoff? (b) Describe the strategy you used to solve part (a). 53 On an aircraft carrier, a jet can be catapulted from 0 to 155 mi/h in 2.00 s. If the average force exerted by the catapult is 5.10 x 10 6 N what is the mass of the jet? Integrate Problem 54 An archer shoots a kg arrow at a target with a speed of 43 m/s. When it hits the target, it penetrates to a depth of m. (a) What was the average force exerted by the target on the arrow? (b) If the mass of the arrow is doubled, and the force exerted by the target remains the same, how does the penetration depth change? Explain. 59 The figure here shows two horizontal forces acting on a block on a frictionless floor. A third horizontal force F 3 also acts on the block. (a) What is the magnitude and direction of F 3 when the block is stationary? (b) What is the magnitude and direction of F 3 when the block is moving to the left with a constant speed of 5 m/s? Note: Show the net force and the observed acceleration Integrate Problem (a) 2 N, leftward (b) 2 N, leftward

7 60 The figure shows a block sitting on a table. (a) Is the magnitude of the normal force F N greater than, less than, or equal to mg if the block and table are in an elevator moving upward at constant speed? (b) Is the magnitude of the normal force F N greater than, less than, or equal to mg if the block and table are in an elevator moving upward at increasing speed? 63 There are two horizontal forces on the 2.0 kg box in the overhead view of the figure but only one (of magnitude F 1 = 20 N) is shown. The box moves along the x axis. Draw a for each of the following values for the acceleration a, of the box and find the second force in unit-vector notation: (a) 10 m/s 2 (b) 20 m/s 2 (c) 0, (d) -10 m/s 2 (e) - 20 m/s 2 (a) 0 (b) (20 N) i (c) (-20 N) i (d) (-40 N) i (e) (-60 N) i 61 (a) equal (b) greater The figure shows the same bread box in four situations where horizontal forces are applied. Rank the situations according to the magnitude of the box's acceleration, greatest first. 64 A 500 kg rocket sled can be accelerated at a constant rate from rest to 1600 km/h in 1.8 s. (a) Make a vector drawing of the situation. (b) What is the magnitude of the required net force? 1.2 x 10 5 N 65 A car traveling at 53 km/h hits a bridge abutment. A passenger in the car moves forward a distance of 65 cm (with respect to the road) while being brought to rest by an inflated air bag. What magnitude of force (assumed constant) acts on the passenger's upper torso, which has a mass of 41 kg? 6.8 x 10 3 N 62 a, then b, c, and d tie A vertical force F is applied to a block of mass m that lies on a floor. (a) What happens to the magnitude of the normal force F N on the block from the floor as magnitude F is increased from zero if force F is downward? (b) What happens to the magnitude of the normal force F N on the block from the floor as magnitude F is increased from zero if force F is upward? 66 A firefighter who weighs 712 N slides down a vertical pole with an acceleration of 3.00 m/s 2, directed downward. (a) What is the magnitude of the vertical force on the firefighter from the pole? (b) What is the direction (up or down) of the vertical force on the firefighter from the pole? (c) What is the magnitude of the vertical force of the pole on the firefighter? (d) What is the direction of the vertical force of the pole on the firefighter? (a) increases from mg (b) decreases from mg to zero (a) 494 N (b) up (c) 494 N (d) down

8 67 A car that weighs 1.30 x 10 4 N is initially moving at 40 km/h when the brakes are applied and the car is brought to a stop in 15 m. Assume the force that stops the car is constant. (a) Draw a vector diagram of the forces on the box (b) Find the magnitude of that force. (c) Find the time required for the change in speed. (d) If the initial speed is doubled, and the car experiences the same force during the braking, by what factor is the stopping distance multiplied? (e) If the initial speed is doubled, and the car experiences the same force during the braking, by what factor is the stopping time multiplied? (There could be a lesson here about the danger of driving at high speeds.) (b) 5.5 kn (c) 2.7 s (d) 4.0 (e) A motorcycle of weight 2.0 kn accelerates from 0 to 88.5 km/h in 6.0 s. (a) What is the magnitude of the constant acceleration? (b) What is the magnitude of the net force causing the acceleration? (a) 4.1 m/s 2 (b) 836 N In a laboratory experiment, an initially stationary electron (mass = 9.11 x kg) undergoes a constant acceleration through 1.5 cm, reaching a speed of 6.0 x 10 6 m/s at the end of that distance. (a) What is the magnitude of the force accelerating the electron? (b) What is the electron's weight? 68 A nucleus that captures a stray neutron must bring the neutron to a stop within the diameter of the nucleus by means of the strong force. That force, which "glues" the nucleus together, is approximately zero outside the nucleus. Suppose that a stray neutron with an initial speed of 1.4 x 10 7 m/s is just barely captured by a nucleus with diameter d = 1.0 x m. Assuming the strong force on the neutron is constant, find the magnitude of that force. The neutron's mass is 1.67 x kg. 73 (a) 1.1 x N (b) 8.9 x N When an automobile weighing 17.0 kn accelerates at 3.66 m/s 2, what is the magnitude of the net force on it? 6.35 x 10 2 N 16 N A certain force gives an object of mass m 1 an acceleration of 12.0 m/s 2 and an object of mass m 2 an acceleration of 3.30 m/s 2. (a) What acceleration would the force give to an object of mass m 2 - m 1? (b) What acceleration would the force give to an object of mass m 2 + m 1? (a) 4.6 m/s 2 (b) 2.6 m/s 2 An 80 kg man drops to a concrete patio from a window 0.50 m above the patio. He neglects to bend his knees on landing, taking 2.0 cm to stop. (a) What is his average acceleration from when his feet first touch the patio to when he stops? (b) What is the magnitude of the average stopping force exerted on him by the patio? What net force is required to bring a 1500-kg car to rest from a speed of 100 km/h within a distance of 55 m? A friend has given you a truly special 10-kg box of chocolates as a reward for your fine showing in the physics final. The box is resting on the smooth (frictionless) horizontal surface of a table (figure a). (a) Determine the weight of the box and the normal force acting on it. (b) Now your friend pushes down on the box with a force of 40 N, as in figure b. Again determine the normal force acting on the box. (c) If your friend pulls upward on the box with a force of 40 N (figure c), what now is the normal force on the box? (a) 245 m/s 2 (b) 20.4 kn (a) N (b) -138 N (c) 58 N

9 76 A hockey puck is sliding freely across a flat horizontal ice surface that is essentially frictionless. Which of the sketches in the figure is the correct free-body diagram for this puck? 83 An exceptional standing jump would raise a person 0.80 m off the ground. To do this, what force must a 60-kg person exert against the ground? Assume the person crouches a distance of 0.20 m prior to jumping, and thus the upward force has this distance to act over before he leaves the ground. 77 B The force of gravity on a 2-kg rock is twice as great as that on a 1-kg rock. Why then doesn't the heavier rock fall faster? 84 A person jumps from the roof of a house 4.0-m high. When he strikes the ground, he bends his knees so that his torso decelerates over an approximate distance of 0.70 m. The mass of his torso (excluding legs) is 50 kg, (a) Find his velocity just before his feet strike the ground (b) Find the average force exerted on his torso by his legs during deceleration. 78 What force is needed to accelerate a child on a sled (total mass = 70.0 kg) at a rate of 1.45 m/s 2? 85 The 100-m dash can be run by the best sprinters in 10.0 s. A 60-kg sprinter accelerates uniformly for the first 30 m to reach her top speed, which she maintains for the remaining 70 m. (a) What is the horizontal component of force exerted on her feet by the ground during acceleration? (b) What is the speed of the sprinter over the last 70 m of the race (i.e., her top speed)? 79 A net force of 255 N accelerates a bike and rider at 3.20 m/s 2. What is the mass of the bike and rider? 86 the following questions: (a) Sketch the free-body diagram of a baseball at the moment it is hit by the bat. (b) Sketch the free-body diagram of a baseball after it has left the bat and is flying toward the outfield. 80 What average force is needed to accelerate a 7.00 gram pellet from rest to 500 m/s over a distance of m along the barrel of a rifle? 81 A kg baseball traveling 30.0 m/s strikes the catcher's mitt, which, in bringing the ball to rest, recoils backward 11.0 cm. What was the average force applied by the ball on the glove? 87 A person has a reasonable chance of surviving an automobile crash if the deceleration is no more than 30 g's. (a) Calculate the force on a 70-kg person accelerating at this rate. (b) What distance is traveled if brought to rest at this rate from 90 km/h? 82 What is the average force exerted by a shot-putter on a 7.0-kg shot if the shot is moved through a distance of 2.8 m and is released with a speed of 13 m/s? 88 A car has a mass of 1.50 x 10 3 kg. The car is accelerated at 4.5 m/s 2 to the east? (a) Draw a free body diagram of the situation (b) What is the net external force? (b) 6,750 N east

10 89 A 1.5 kg ball pushed with a force of 13.5 N accelerates to the left. (a) Draw a free body diagram of the situation (b) What is the acceleration of the ball? 94 A body with a mass of 0.5 kg is accelerated at 4 m/sec 2. (a) Draw a free body diagram of the situation. (b) How large a force is acting? 90 (b) 9.0 m/s 2 to the left A 6.0 kg object undergoes an acceleration of 2.0 m/s 2 (a) Draw a free body diagram of the situation (b) What is the magnitude of the net external force acting on it? (c) This same force is applied to a 4.0 kg object. Draw a free body diagram of the new situation. (d) What acceleration is produced? (a) (b) 12 N (c) (d) 3.0 m/s 2 95 (b) 2 N A tow rope is used to pull a 1,750-kg car, giving it an acceleration of 1.35 m/s 2. (a) Draw a free body diagram of the forces on the car. (b) What is the net force on the car? (b) 2,362.5 N in the direction of the acceleration 91 A kg baseball is thrown straight upward with an initial speed of 20.0 m/s as it just leaves your hand. (a) Draw a free body diagram of the situation (b) Draw a free body diagram of the forces on the ball when it reaches half its maximum height? (c) What is the force on the ball when it reaches half its maximum height? (d) Draw a free body diagram of the forces on the ball when it reaches its peak? (e) What is the force on the ball when it reaches its peak? (Disregard air resistance.) 96 An air-track glider can move along an x axis that ties along the air track. The figure gives the glider's velocity component v, as a function of time t, as a force with component F x acts on the glider. For each lettered time interval, determine whether F x is positive, negative, or zero and whether it is constant, increasing, or decreasing. (a) (b) (c) N (d) (e) N 92 A 5.5 kg watermelon is pushed across a table. The acceleration of the watermelon is 4.2 m/s 2 to the right. (a) Draw a free body diagram of the situation. (b) Find the net external force exerted on the watermelon. A positive and constant; B zero and constant; C Negative D zero and constant; E positive and increasing F positive and decreasing (b) 23 N to the right 93 A net external force gives a mass of 25 kg an acceleration of 20 m/s 2? (a) Draw a free body diagram of the situation. (b) Find the net external force exerted on the watermelon. (b) 5.0 x 10 2 N

11 97 A 100 kg crate sits on the floor of a freight elevator that starts from rest on the ground floor of a building at time t = 0 and rises to the top floor during an 8.0 s interval. The speed of the elevator as a function of time is shown in the figure. (a) What is the magnitude F ele of the force on the crate from the elevator floor at t = 1.8 s? (b) What is the direction (up or down) of the force on the crate from the elevator floor at t = 1.8 s? (c) What is F ele at t 4.4 s? (d) What is the direction at t 4.4 s? (e) What is F ele at t = 6.8 s? (f) What is the direction at t = 6.8 s? 99 The diagram show the motion of a 2000 kg motor bike during a six second time interval. (a) What is the observed acceleration during 1-6 second time interval? (b) What is the Net Force during the 1-6 second time interval? (a) 7 m/s 2 (b) 14,000 N (a) 1060 N (b) up (c) 9.8 x 10 2 N (d) up (e) 843 N (f) up 100 The graph shows the motion of a 75 kg runner moving during an eight second interval. (a) What is the observed acceleration during 1-6 second time interval? (b) What is the Net Force during the 1-6 second time interval? 98 The figure shows the motion of a 20 kg ball. (a) Calculate the net force during the 0-5 second time interval? (b) Calculate the net force during the 5-10 second time interval? (c) Calculate the net force during the second time interval? (d) Calculate the net force during the second time interval? (e) Calculate the net force during the second time interval? (a).5 m/s 2 (b) 37.5 N (a) 1200 N (b) 0 N (c) -40 N (d) 0 N (e) -80 N

12 101 The graph shows the motion of a 5 kg object during a twelve second time interval (a) Calculate the net force during the 0-4 second time interval? (b) Calculate the net force during the 4-8 second time interval? (c) Calculate the net force during the 8-12 second time interval? 104 The graph shows the motion of an object. Draw a force-time graph of the object s motion. 105 The graph to the left shows the motion of an object. Draw a force-time graph of the object s motion. (a) 0 N (b) 75 N (c) -125 N 102 The graph to the left shows the motion of an object. Draw a force-time graph of the object s motion. 106 The graph to the left shows the motion of 2500 kg rocket. (a) Describe the net force applied to the rocket during each time interval. (b) Draw a force time graph. 103 The graph to the left shows the motion of an object. Draw a force-time graph of the object s motion.

13 107 A block is pulled along a horizontal surface by 2, 4, 6, and 8 parallel bands of rubber. All bands are alike and each is stretched the same length in each experiment. The graph shows the resulting accelerations plotted versus the number of bands. (a) What can you conclude from the fact that the plot yields a straight line? (b) What does the intercept of the graph with the horizontal axis measure? (c) Can you use the graph to predict the acceleration of the block produced by stretching one rubber band by the standard amount? (d) Suppose you repeat the experiment, changing only the surface on which the block is pulled. How will the new graph relate to the old one? 109 The graph shows the motion of an object. Draw a force-time graph of the object s motion. 110 The graph to the left shows the motion of a 150 g object. (a) Describe the net force applied to the object during each time interval (b) Draw a force time graph. (a) There is a variable acceleration and a variable force (b) A minimum force is needed to overcome friction or some other resisting force (c) Yes Look at the differences between the slopes of the lines (d) Changes only the x-intercept and and y-intercept. 108 The graph to the left shows the motion of a 50 kg object. Draw a force-time graph of the object s motion. (a) Describe the net force applied to the object during each time interval. (b) Draw a force time graph. 111 (a) (b) graph The graph shows the velocity, along a straight line, of an object of mass 2 kg, as a function of time. (a) Describe how the force is applied to the object. (b) Plot a graph of the net force as a function of time. (a) (b) graph (a) (b) graph

14 112 The figure below shows a plot of the speed of a person's body during a chin-up. All motion is vertical and the mass of the person (excluding the arms) is 64.0 kg. Find the magnitude of the average net force exerted on the body by the arms at 0.50 s intervals. 114 A velocity-time graph of a 2 kg toy train is shown in the figure to the left. (a) Describe the net force applied to the train during each time interval (b) Draw a force time graph. 0.0 to 0.5 = 13 N 0.5 to 1.0 = 13 N 1.0 to 1.5 = 0.0 N 1.5 to 2.0 = -26 N (a) (b) graph 113 The figure to the left shows the position x versus time t of a particle moving in one dimension. During what time intervals is there net force acting on the particle? Give the direction (+ or -) of the net force during these time intervals. 115 The figure to the left is the velocity-time graph of a 20 kg object. (a) Describe the net force applied to the object during each time interval (b) Draw a force time graph. From t = 2 s to t = 6 s, the force is negative; from t = 6 s to t = 8 s, the force is positive. The force is zero at other times. 116 (a) (b) graph The velocity-versus-time graph for a shuttle bus moving along a straight path is shown in the figure to the left. (a) Describe the net force applied to the shuttle bus during each time interval (b) Draw a force time graph. (a) (b) graph

15 117 The velocity-time graph for a 5 gram object moving along a straight path is shown in the figure to the left. Find the net force during the time intervals 0.0 s to 5.0 s, 5.0 s to 15.0 s, and 0.0 s to 20.0 s. 120 The velocity-time graph to the left describes a familiar motion of a car traveling during rush-hour traffic. (a) Describe the net force applied to the car during each time interval (b) Draw a force time graph. 118 The velocity-time graph to the left describes a familiar motion of a car traveling during rush-hour traffic. (a) Describe the net force applied to the car during each time interval (b) Draw a force time graph. 121 (a) (b) graph A net force of 9000 N is used to stop a 1500 kg car traveling at 20 m/s. (a) Draw a free body diagram of the situation. (b) What is the observed acceleration of the car? (c) What braking distance is needed to bring the car to a halt? (b) -6 m/s 2 (c) 33 m 122 You give to a 24.3 kg box a push with a force of 85.5 N. (a) Draw a free body diagram of the motion. (b) What is the acceleration of the car? 119 (a) (b) graph The velocity-time graph to the left describes a familiar motion of a car traveling during rush-hour traffic. (a) Describe the net force applied to the car during each time interval (b) Draw a force time graph. 123 (b) 3.52 m/s A force of 15 N is applied to an object of mass m. The object moves in a straight line, with its speed increasing by 10 m/s every 2 s. (a) Draw a free body diagram of the situation. (b) Find the mass m. (b) 3 kg 124 A single net force of 10 N acts on an object of mass m. The particle starts from rest and travels in a straight line a distance of 18 m in 6 s. (a) Draw a free body diagram of the situation (b) What is the observed acceleration of the particle? (c) Find its mass m. (a) (b) graph (b) 1 m/s 2 (c) 10 kg

16 125 David Purley, a racing driver, survived deceleration from 173 km/h to 0.0 km/h over a distance of m when his car crashed. Assume that Purley's mass is 70.0 kg. (a) Draw a free body diagram of the forces on David Purley as he crashed into the wall. (b) What is the observed acceleration on David Purley? (c) What is the magnitude of the average force acting on David Purley during the crash? (d) What is David Purley s weight? (e) Compare the crash force to Purley's weight. 129 After a day of testing race cars, you decide to take your own 1550-kg car onto the test track. While moving down the track at 10 m/s, you suddenly accelerate to 30 m/s in 10 s. (a) Draw a free body diagram of the above situation. (b) What is the average net force that you have applied to the car during the 10-s interval? (b) 3.1 x 10 3 N (b) m/s 2 (c) x 10 5 N (d) 6.87 x 10 2 N (e) 178 times 130 Pulling up on a rope, you lift a 4.25-kg bucket of water from a well with an acceleration of 1.80 m/s 2. What is the tension in the rope? s 126 A 7.5 kg bowling ball initially at rest is dropped from the top of an 11 m building. It hits the ground 1.5 s later. (a) Draw a free body diagram of the situation (b) What is the acceleration of the bowling ball? (c) Find the net external force on the falling ball. (b) -9.8 m/s 2 (c) N 131 Illinois Jones is being pulled from a snake pit with a rope that breaks if the tension in it exceeds 755 N. (a) If Illinois Jones has a mass of 70.0 kg and the snake pit is 3.40 m deep, what is the minimum time necessary to pull our intrepid explorer from the pit? (b) Explain why the rope breaks if Jones is pulled from the pit in less time than that calculated. s 127 A truck driver slams on the brakes and skids to a stop through a displacement x. (a) Draw a free body diagram of the above situation. (b) If the truck had double the mass, find the truck s "skidding distance" in terms of x. (c) If the initial velocity of the truck were halved, what would be the truck's "skidding distance" in terms of x? 132 Integrated Problem The tension at which a fishing line snaps is commonly called the line's "strength." What minimum strength is needed for a line that is to stop a salmon of weight 85 N in 11 cm if the fish is initially drifting at 2.8 m/s? Assume a constant deceleration. (b) x (c) (1/4) x 128 A block of mass 3.0 kg is moving along a smooth horizontal surface with a velocity v o at an instant of time t = 0. A force of 18 newtons is applied to this body opposite to the direction of its motion. The force slows the block down to half its original velocity while it moves 9.0 m. (a) Draw a free body diagram of the situation. (b) How long does it take for this to occur? (c) What is v 0? x 10 2 N How much tension must a rope withstand if it is used to accelerate a 1300-kg car horizontally at 0.80 m/s 2? Ignore friction N How much tension must a rope withstand if it is used to accelerate a 1300-kg car vertically at 0.80 m/s 2? Ignore friction. (b) (c) 135 A 75-kg petty thief wants to escape from a third story jail window. Unfortunately, a makeshift rope made of sheets tied together can support a mass of only 50 kg. How might the thief use this "rope" to escape? Give quantitative answer.

17 A fisherman in a boat is using a "10-lb test" fishing line. This means that the line can exert a force of 44 N without breaking (1 lb = 4.4 N). (a) How heavy a fish can the fisherman catch if he pulls the fish up vertically at constant speed? (b) How heavy a fish can he catch if the fish occasionally accelerates at 3.0 m/s 2 downward? In the figure, the 10 kg block is attached to spring balances calibrated in Newton s. The system is accelerated upward at the pulley with an acceleration of 5 m/s 2. (a) Draw the free body diagram of the forces on the block. (b) Give the readings of the balance assuming that the strings are massless 140 You need to lower a bundle of old roofing material weighing 100 N to the ground with a rope that will snap if the tension in it exceeds 87 N. (a) Draw a free body diagram of the forces on the bundle of roofing material. (b) What is the net force on on the bundle? (c) What is the observed acceleration on the bundle? (d) How can you avoid snapping the rope during the descent if you use only one line? (e) If the descent is 20 m and you just barely avoid snapping the rope, with what speed will the bundle hit the ground? (b) -13 N (c) m/s 2 (d) lower (e) 7.13 m/s 141 A 75 kg person escapes from a burning building by jumping from a window 25 m above a catching net. Assume that air resistance exerts a 95 N force on the person during the fall. (a) Draw the free body diagram of the forces on the person as he is falling. (b) What is the net force on the falling body (c) What is the observed acceleration of the falling body (d) Determine the person's velocity just before he hits the net. (b) 74 N (b) (c) (d) m/s 138 Imagine a landing craft approaching the surface of Callisto, one of Jupiter s moons. If the engine provides an upward force (thrust) of 3260 N, the craft descends at a constant speed: If the engine provide only 2200 N, the craft accelerates downward at 0.39 m/s 2. (a) Draw a free body diagram for the forces on the landing craft for both situations. (b) What is the weight of the landing craft in the vicinity of Callisto's surface? (c) What is the mass of the craft? (d) What is the free fall acceleration near the surface of Callisto? 142 The parachute on a race car that weighs 8,820 N opens at the end of a quarter-mile run when the car is traveling 35 m/s. (a) Draw the free body diagram of the forces on the car as the parachute opens. (b) What total retarding force must be supplied by the parachute to stop the car in a distance of 1100 m? (b) -5.0 x 10 2 N (b) 3260 N (c) 2.7 x 10 3 kg (d) -1.2 m/s The rock shown below is suspended by a cord. Draw a free body diagram of the forces on the rock. 139 A spaceship lifts off vertically from the moon, where the freefall acceleration is 1.6 m/s 2. An astronaut in the spaceship has an upward acceleration of 1.0 m/s 2 as it lifts off. (a) Draw a free body diagram of the forces on the an astronaut in the spaceship. (b) What is the force of the spaceship on the astronaut who weighs 735 N on Earth? (b) 195 N

18 144 In a modified "tug-of-war" game, two people pull in opposite directions, not on a rope, but on a 25-kg block resting on a smooth surface. The participants exert forces of 90 N and 92 N. (a) Draw a free body diagram of the forces on the block (b) What is the acceleration of the block? 148 Two people pull on a 208 kg boat. If they pull in the same direction the boat has an acceleration of 1.52 m/s 2. If they pull in opposite directions, the boat has an acceleration of m/s 2. (a) Draw a free body diagram for each situation. (b) What is the magnitude of the force exerted by each person on the boat? 145 (b) 0.08 m/s 2 A vertical force T is exerted on a 5-kg body near the surface of the earth, as shown in the figure below. For each of the following situations draw the free body diagram before you find the acceleration. (a) Find the acceleration of the body if T = 5 N. (b) Find the acceleration of the body if T = 10 N. (c) Find the acceleration of the body if T = 100 N. Ft 149 (b) 104 N 211 N A boat moves through the water with two forces acting on it. One is a 2.10 x 10 3 N forward push by the motor, and the other is a 1.80 x 10 3 N resistive force due to the water. (a) Draw the free body diagram of the forces on the motor. (b) What is the net force on the boat? (c) What is the acceleration of the 1200 kg boat? (d) If it starts from rest, how far will it move in 10.0 s? (e) What will its velocity be at the end of this time interval? Fg (b) 300 N (c) 0.25 m/s 2 (d) 12.5 m (e) 2.5 m/s (a) a = m/s 2 (b) a = m/s 2 (c) a = 10.2 m/s The rock shown below is accelerated upward at 9,8 m/s 2. Draw a free body diagram of the forces on the rock.(ignore friction) 146 A 1000-kg load is being moved by a crane. For each situation draw a free body diagram before you solve the problem. (a) Find the tension in the cable that supports the load as it is accelerated upward at 2 m/s 2. (b) Find the tension in the cable that supports the load as it is lifted at constant speed. (c) Find the tension in the cable that supports the load as it moves upward but its speed decreases by 2 m/s in each second. (a) 11,810 N (b) 9810 N (c) T = 7810 N 147 Space-shuttle astronauts accelerate 35 m/s 2 during takeoff. (a) Draw the free body diagram of the forces on an astronaut seated in the space shuttle. (b) What upward force does a 75 kg astronaut experience during an acceleration of this magnitude? (b) 3360 N 151 A very thin boron rod with a cross-section of 0.10 mm x 0.10 mm can sustain a force of 57 N. Assume the rod is used to pull a block along a smooth horizontal surface. Draw a free body diagram of the forces on the block for each of the following situations before you solve the problem. (a) If the maximum force accelerates the block by 0.25 m/s 2, find the mass of the block. (b) If a second force of 24 N is applied in the direction opposite the 57 N force, what would be the new acceleration of the block? 2.3 x 10 2 kg (b) 0.14 m/s 2

19 152 When the click beetle jumps in the air, its net acceleration upward can be as large as times the acceleration due to gravity. (An acceleration this large would instantly kill any human being.) A beetle has a mass of mg. (a) Draw a free body diagram of the force exerted on the beetle at the beginning of a jump. (b) Calculate the force exerted by the beetle on the ground at the beginning of the jump with gravity taken into account. (c) Calculate the force with gravity neglected. (d) Why are the answers so close? Use m/s 2 as the value for free 156 A rubber ball weighs 49 N. (a) What is the mass of the ball? (b) What is the acceleration of the ball if an upward force of 69 N is applied? (before solving part b draw a free body diagram of the forces on the ball) (a) 5.0 kg (b) 4.0 m/s 2 (b) x 10-1 N (c) x 10-1 N (d) 157 A small weather rocket weighs 14.7 N. (a) What is its mass? (b) The rocket is carried up by a balloon is released from the balloon and fired, and its engine exerts an upward force of 10.2 N. Draw a free body diagram of the situation. (c) What is the acceleration of the rocket? 153 A 0.5 mm wire made of carbon and manganese can just barely support the weight of a 70.0 kg person. Suppose this wire is used to lift a 45.0 kg load. (a) Draw a free body diagram of the forces on the person described in the two situations above. (b) What maximum upward acceleration can be achieved without breaking the wire? (a) 1.50 kg (b) (c) m/s (b) 5.5 m/s 2 The whale shark is the largest type of fish in the world. Its mass can be as large as 2.0 x 10 4 kg, which is the equivalent mass of three average adult elephants. Suppose a crane lifts a net with a 2.0 x 10 4 kg shark off the ground. The net is steadily accelerated from rest over an interval of 0.80 s until the net reaches a speed of 1.0 m/s. (a) Draw a free body diagram of the forces on the whale shark. (b) Calculate the tension in the cable pulling the net. 158 A person fishing hooks a 2.0-kg fish on a line that can only sustain a maximum of 38 N of force before breaking. At one point while reeling in the bass, it fights back with a force of 40 N. (a) Draw a free body diagram of the forces on the fish. (b) What is the minimum acceleration with which you must play out the line during this time in order to keep the line from breaking? (a) Picture (b) -1 m/s 2 (b) 2.21 x 10 5 N 159 The rock shown below is accelerated downward at 19.6 m/s 2. Draw a free body diagram of the forces on the rock (Ignore friction). 155 The instruments attached to a weather balloon have a mass of 5.0 kg. The balloon is released and exerts an upward force of 98 N on the instruments. (a) Draw a free body diagram of the forces on the weather instruments from the balloon. (b) What is the acceleration of the balloon and instruments? (c) After the balloon has accelerated for 10 seconds, the instruments are released. Draw a free body diagram of this situation (d) What is the velocity of the instruments at the moment of their released? (d) What net force acts on the instruments at their release? (e) When does the direction of instruments velocity first become downward? (a) Picture (b) 9.8 m/s 2, up; (c) 98 m/s, up; (d) -49 N, down; (e) 10 s 160 A 4500-kg helicopter accelerates upward at 2 m/s 2. (a) Draw a free body diagram of the forces on the helicopter. (b) What lift force is exerted by the air on the propellers? (a) Picture (b) 5.3 x 10 4 N

20 161 The maximum force a grocery sack can withstand and not rip is 250 N. 20 kg of groceries are lifted from the floor to the table with an acceleration of 5 m/s 2. (a) Draw a free body diagram of the forces on the grocery sack (b) Will the sack hold? 165 Draw a free body diagram of the forces acting on the balloon shown in the below. (b) No, the sack will rip. 162 A rocket weighs 196 Newton s. (a) What is the mass of a rocket (b) What force in excess of the weight of the rocket is needed to accelerate it upward at 4.0 m/sec? Before solving draw a free body diagram of the situation. (c) What is the total upward force that must be exerted on the rocket to give it this acceleration? (a) 20.0 kg (b) 80 Newton s (c) 276 Newton s 166 Draw a free body diagram of the forces acting on the space shuttle as it blasts off and begins to accelerate upward. 163 Imagine a spider with mass 7.0 x 10-5 kg moving downward on its thread. The thread exerts a force that results in a net upward force on the spider of 1.2 x 10-4 N. (a) Draw a free body diagram of the forces on the spider. (b) What is the acceleration of the spider? (c) Explain the sign of the velocity and describe in words how the thread changes the velocity of the spider. (b) +1.7 m/s 2 (c) The upward force being given as a positive number means that the downward motion of the spider is represented as a negative velocity. The positive acceleration is opposed to this negative velocity and gives rise to a slowing of the spider. 167 In the figure below, the 10 kg block is attached to spring balances calibrated in Newton s. (a) Draw the free body diagram of the forces on the block (b) Give the readings of the balance assuming that the strings are massless? 164 A Fireman weighing 90 N. slides down a vertical pole with an average acceleration of 3 m/s 2. (a) Draw a free body diagram of the forces on the firefighter. (b) What is the magnitude and direction of the vertical force exerted by the pole on the firefighter? (c) What is the magnitude and direction of the vertical forces exerted on the pole by the firefighter? (a) Picture (b) 110 lb. up 490 N (c) 110 lb. down 711 N (b) 98.1 N

21 A spaceship lifts off vertically from the moon, where the freefall acceleration is 1.6 m/s 2. An astronaut in the spaceship has an upward acceleration of 1.0 m/s 2 as it lifts off. (a) Draw a free body diagram of the forces on the an astronaut in the spaceship. (b) What is the force of the spaceship on the astronaut who weighs 735 N on Earth? (b) 195 N Two lifeguards pull on ropes attached to a raft. If they pull in the same direction, the raft experiences a net external force of 334 N to the right. If they pull in opposite directions, the raft experiences a net external force of 105 N. (a) Draw a free-body diagram representing the raft for each situation. (b) Find the force exerted by each lifeguard on the raft. (Disregard any other forces acting on the raft.) (b) 114 N; 220 N A small sports car collides head-on with a massive truck. (a) Which vehicle experiences the greater impact force? (b) Which vehicle experiences the greater acceleration? Explain. both experience the same impact force; the sports car experiences the larger acceleration because it has a smaller mass and acceleration is inversely proportional to mass Earth is attracted to an object with a force equal to and opposite the force Earth exerts on the object. Explain why Earth's acceleration is not equal to and opposite that of the object. because Earth has a very large mass A 3-kg box rests on a 7-kg box that rests on a horizontal table. (a) Draw a diagram showing the forces acting on the 3- kg box and indicate each reaction force. (b) Do the same for the forces acting on the 7-kg box. 170 A 5.0 kg bucket of water is raised from a well by a rope. The upward acceleration of the bucket is 23.0 m/s 2. (a) Draw a free body diagram of the forces on the bucket (b) What is the net force on the bucket? (c) Find the force exerted by the rope on the bucket of water. (b) 115 N (c) 164 N 175 (b) When you drop a 0.40-kg apple, Earth exerts a force on it that accelerates it at 9.8 m/s 2 toward Earth's surface. According to Newton's third law, the apple must exert an equal and opposite force on Earth. If the mass of Earth is 5.98 x 10 24, what's the magnitude of Earth's acceleration? 6.6 x m/s In the figure below, the 10 kg block is attached to spring balances calibrated in Newton s. (a) Draw the free body diagram of the forces on the block. (b) Give the readings of each balance assuming that the strings are massless 176 A chair is pushed forward with a force of 185 N, the force of Earth on the chair is 155 N downward, and the floor exerts a force of 155 N upward on the chair. Draw a free-body diagram of the forces on the chair. (a) force of 185 N points forward, 155 N downward, 155 N upward 177 In 1994, a Bulgarian athlete named Minchev lifted a mass of kg. By comparison, his own mass was only 54.0 kg. Estimate the force acting on each of his feet at the moment he was pulling the barbell up with an upward acceleration of 1.00 m/s 2. Assume that the downward force on each foot is the same. (b) N 1.12 x 10 3 N

22 178 Suppose Joe, who weighs 625 N, stands on a bathroom scale calibrated in Newton s. (a) What force would the scale exert on Joe? In what direction? (b) If Joe now holds a 50-N cat in his arms, what force would the scale exert on him? (c) After Joe puts down the cat, his father comes up behind him and lifts upward on his elbows with a 72-N force. What force does the scale now exert on Joe? (a) 625 N upward (b) 675 N upward (c) 553 N; upward 182 Riding in an elevator moving upward with constant speed, you begin a game of darts. Do you have to adjust your aim, compared to the way you play darts normally? Explain. No adjustment is necessary because you -ire moving with constant velocity If you throw an object in the elevator it falls with the same downward acceleration relative to you as it would if you were to throw it while standing on the surface of the Earth. 179 The rock shown below is acted on by one or more forces. All are drawn in a vertical plane, and friction is negligible except when noted. Draw the free body diagram for the rock. 183 Riding in an elevator moving with a constant upward acceleration, you begin a game of darts. Do you have to adjust your aim, compared to the way you play darts normally? Explain. Yes. In the upwardly accelerating elevator it is as if you are playing a game of darts on a planet with a greater acceleration of gravity. Therefore, you must aim higher than you would if the elevator were moving upward with constant speed. 180 A 3.46 kg briefcase is sitting at rest on a level floor. (a) Draw a free body diagram of the forces on the briefcase. (b) What is its observed acceleration? (c) What is its weight in Newton s? (d) What is it s normal force? You pull upward on a stuffed suitcase with a force of 115 N, and it accelerates upward at m/s 2. (a) What is the mass of the suitcase? (b) What is the weight of the suitcase? (a) 10.9 kg (b) 107 N Suppose a rocket launches with an acceleration of 32 m/s 2. What is the apparent weight of an 85-kg astronaut aboard this rocket? 181 (b) zero (c) 33.9 N (d) 33.9 N The rock shown below is acted on by one or more forces. All are drawn in a vertical plane, and friction is negligible except when noted. Draw the free body diagram for the rock k N At the bow of a ship on a stormy sea, a crewman conducts an experiment by standing on a bathroom scale. In calm waters, the scale reads 810 N. During the storm, the crewman finds a maximum reading of 1000 N and a minimum reading of 614 N. (a) Find the maximum upward acceleration (b) Find the maximum downward acceleration experienced by the crewman. (a) 2.3 m/s 2 (b) 2.4 m/s 2

23 187 When you lift a bowling ball with a force of 82 N, the ball accelerates upward with an acceleration a. If you lift with a force of 92 N, the ball's acceleration is 2a. (a) Find the weight of the bowling ball. (b) Find the acceleration a. 191 An 80 kg man is parachuting and experiencing a downward acceleration of 2.5 m/s 2. The mass of the parachute is 5.0 kg (a) What is the value of the upward force exerted on the parachute by the air? (b) What is the value of the downward force exerted by the man on the parachute? (a) 72 N (b) 1.4 m/s 2 Your groceries are in a bag with paper handles. The handles will tear off if a force greater than 51.0 N is applied to them. (a) What is the greatest mass of groceries that can be lifted safely with this bag, given that the bag is raised with constant speed. (b) What is the greatest mass of groceries that can be lifted safely with this bag, given that the bag is raised with an acceleration of 1.35 m/s 2. (a) 5.20 kg (b) 4.57 kg Responding to an alarm, a 92-kg fireman slides down a pole to the ground floor, 3.2 m below. The fireman starts at rest and lands with a speed of 4.0 m/s. (a) Find the force exerted on the fireman by the pole. (b) Find the force exerted on the fireman when the landing speed is 2.0 m/s. (c) If the landing speed is half that in part (a), is the force exerted on the fireman doubled? Explain. Integrate Problem (a) 660 N (b) 840 N (c) No An object is hung from a spring balance attached to the ceiling of an elevator. the balance reads 65 N when the elevator is standing still. (a) What is the reading when the elevator is moving upward with a constant speed of 7.4 m/s? (b) What is the reading of the balance when the elevator is moving upward with a speed of 7.6 m/s while decelerating at a rate of 2.4 m/s 2? My Solution (a) 620 N (b) 784 N Imagine a landing craft approaching the surface of Callisto, one of Jupiter"s moons. If the engine provides an upward force (thrust) of 3260 N, the craft descends at a constant speed: if the engine provide only 2200 N, the craft accelerates downward at 0.39 m/s 2. (a) What is the weight of the landing craft in the vicinity of Callisto's surface? (b) What is the mass of the craft? (c) What is the free fall acceleration near the surface of Callisto? My Solution (a) 3260 N (b) 2.7 x 10 3 kg (c) -1.2 m/s2 In the figure, a passenger of mass m = 72.2 kg stands on a platform scale in an elevator cab. We are concerned with the scale readings when the cab is stationary and when it is moving up or down. (a) Find a general solution for the scale reading, whatever the vertical motion of the cab. (b) What does the scale read if the cab is stationary or moving upward at a constant 0.50 m/s? (c) What does the scale read if the cab accelerates upward at 3.20 m/s 2 and downward at 3.20 m/s 2. (d) During the upward acceleration in part (c), what is the magnitude of the net force on the passenger, and what is the magnitude ap,,ab of his acceleration as measured in the frame of the cab? Does F net = ma p,cab? My Solution (a) 65 N (b) 49 N (a) F N =m(a g +A) (b) 708 (c) 477N (d) 231 N

24 194 In the figure, what does the scale read if the elevator cable breaks so that the cab falls freely; that is, what is the apparent weight of the passenger in free fall? 199 A 50 kg passenger rides in an elevator cab that starts from rest on the ground floor of a building at t = 0 and rises to the top floor during a 10 s interval. The cab's acceleration as a function of the time is shown in the figure, where positive values of the acceleration mean that it is directed upward. (a) What is the magnitude of the maximum force on the passenger from the floor? (b) What is the direction (up or down) of the maximum force on the passenger from the floor? (c) What is the magnitude of the minimum force on the passenger from the floor? (d) What is the direction of the minimum force on the passenger from the floor? (e) What is the magnitude of the maximum force on the floor from the passenger? (f) What is the direction of the maximum force on the floor from the passenger? An elevator cab and its load have a combined mass of 1600 kg. Find the tension in the supporting cable when the cab, originally moving downward at 12 m/s, is brought to rest with constant acceleration in a distance of 42 m x 10 4 N A lamp hangs vertically from a cord in a descending elevator that decelerates at 2.4 m/s 2. (a) If the tension in the cord is 89 N, what is the lamp's mass? (b) What is the cord's tension when the elevator ascends with an upward acceleration of 2.4 m/s 2? (a) 7.3 kg (b) 89 N 200 (a) 590 N, (b) up (c) 340 N, (d) up (e) 590 N (f) down A rocket and its payload have a total mass of 5.0 x 10 4 kg. (a) How large is the force produced by the engine (the thrust) when the rocket is "hovering" over the launchpad just after ignition? (b) How large is the force produced by the engine (the thrust) when the rocket is accelerating upward at 20 m/s 2.? 197 An elevator cab is pulled upward by a cable. The cab and its single occupant have a combined mass of 2000 kg. When that occupant drops a coin, its acceleration relative to the cab is 8.00 m/s 2 downward. What is the tension in the cable? 201 (a) 4.9 x 10 5 N (b) 1.5 x 10 6 N A 10-kg bucket is lowered by a rope in which there is 30 N of tension. What is the acceleration of the bucket? 16.0 kn 198 A hot-air baloon of mass M is descending vertically with downward acceleration of magnitude a. How much mass (ballast) must be thrown out to give the balloon an upward acceleration of magnitude a? Assume that the upward force from the air (the lift) does not change because of the decrease in mass m/s 2 The cable supporting a 1500-kg elevator has a maximum strength of 21,750 N. What maximum upward acceleration can it give the elevator without breaking? 2Ma/(a + g)

25 203 An elevator in a tall building is allowed to reach a maximum speed of 4.0 m/s going down. What must the tension be in the cable to stop this elevator over a distance of 3.0 m if the elevator has a mass of 1200 kg including occupants? 207 A 60-kg house painter stands on a 15-kg aluminum platform. A rope attached to the platform and passing over an overhead pulley allows the painter to raise herself and the platform. (a) To get started, she accelerates herself and the platform at a rate of 0.8 m/s 2. With what force must she pull on the rope? (b) When her speed reaches 1 m/s, she pulls such that she and the platform go up at a constant speed. What force must she exert on the rope? (Ignore the mass of the rope.) 204 A 75.0-kg person stands on a scale in an elevator. (a) What does the scale read (in kg) when the elevator is at rest? (b) What does the scale read (in kg) when the elevator is climbing at a constant speed of 3.0 m/s? (c) What does the scale read (in kg) when the elevator is falling at 3.0 m/s? (d) What does the scale read (in kg) when the elevator is accelerating upward at 3.0 m/s 2? (e) What does the scale read (in kg) when the elevator is accelerating downward at 3.0 m/s 2? (a) 398 N (b) 368 N 205 A 17.0-kg monkey hangs from a cord suspended from the ceiling of an elevator. The cord can withstand a tension of 220 N and breaks as the elevator accelerates. What was the elevator's minimum acceleration (magnitude and direction)? 3 17 m/s 2 upward 208 A student has to escape from his girlfriend's dormitory through a window that is 15.0 m above the ground. He has a heavy 20- m-long rope, but it will break when the tension exceeds 360 N and he weighs 600 N. The student will be injured if he hits the ground with a speed greater than 10 m/s. (a) Show that he cannot safely slide down the rope. (b) Find a strategy using the rope that will permit the student to reach the ground safely. 206 A man stands on a scale in an elevator that has an upward acceleration a. The scale reads 960 N. When he picks up a 20 kg box, the scale reads 1200 N. Find the mass of the man, his weight, and the acceleration a. m = 80 kg, W = 785 N = 176 lb., a = 2.19 m/s 2 (a) The forces acting on the student are T - W ma, where upward is positive and m ( ) kg. Assuming the maximum tension, T 360 N, a = _ 3.92 m/s 2. This downward acceleration continues for 15 m, resulting in a speed given by (2a x)1/2 = 10.8 m/s, which is too great for safety. (b) The student can double up the rope, landing with a s~ of 9.9 m/s. 209 An elevator weighing 3500 kg. is pulled upward by a cable with an acceleration of 1.00 m/s 2. (a) Draw a free body diagram of this situation. (b) What is the tension in the cable? (c) The elevator is decelerating at a rate of 1.00 m/s 2 but is still moving upward. Draw a free body diagram of this situation (d) What is the tension in the elevator cable? (b) 37,885 N (c) (d) 30, 8300 N.

26 A student stands on a bathroom scale in an elevator at rest on the 64th floor of a building. The scale reads 836 N. (a) As the elevator moves up, the scale reading increases to 935 N, then decreases back to 836 N. Draw a free body diagram which explains this situation (b) Find the acceleration of the elevator. (c) As the elevator approaches the 74th floor, the scale reading drops as low as 782 N. Draw a free body diagram which explains this situation (d) What is the acceleration of the elevator? (e) Using your results from parts a and b, explain which change in velocity, starting or stopping, would take the longer time. (f) Draw the set of free body diagram which shows the elevator moving down (g) Explain the changes in the scale you would expect on the ride back down. (b) 1.2 m/s 2 ; (c) (d) m/s 2 ; (e) stopping, lower acceleration; (f) (g) scale reads less than 836 N, reads 836 N, then reads more than 836 N A lamp hangs vertically from a cord in a descending elevator that decelerates at 2.4 m/s 2. (a) Draw a free body diagram of this situation. (b) If the tension in the cord is 89 N, what is the lamp's mass? (c) The elevator ascends with an upward acceleration of 2.4 m/s 2. Draw a free body diagram of the new situation. (d) What is the tension in the cord? A person weighing 490 N stands on a scale in an elevator. Draw a free body diagram for each situation. (a) What does the scale read when the elevator is at rest? (b) What is the reading on the scale when the elevator rises at a constant velocity? (c) The rising elevator slows down at 2.2 m/s 2 as it reaches the desired floor. What does the scale read? (d) The elevator descends, accelerating at 2.7 m/s 2. What does the scale read? (e) What does the scale read when the elevator descends at a constant velocity? (f) Suppose the cable snapped and the elevator fell freely. What would the scale read? (a) 490 N (b) 490 N (c) 3.8 x 10 2 N (d) 3.6 x 10 2 N (e) 490 N (f) 0 A 60-kg girl weighs herself by standing on a scale in an elevator. Draw a free body diagram for each situation. (a) What does the scale read when the elevator is descending at a constant rate of 10 m/s, (b) What does the scale read when the elevator is accelerating downward at 2 m/s 2, and (c) What does the scale read when the elevator is ascending at 10 m/s but its speed is decreasing by 2 m/s in each second? (a) 588 N (b) 468 N (c) 468 N (b) 7.29 kg (c) (d) 89 N 215 When a 9.00-kg mass is placed on top of a vertical spring, the spring compresses 4.50 cm. Find the force constant of the spring. 212 Safety engineers estimate that an elevator can hold 20 persons of 75-kg average mass. The elevator itself has a mass of 500 kg. Tensile strength tests show that the cable supporting the elevator can tolerate a maximum force of 2.96 x 10 4 N. (a) Draw a free body diagram of the situation (b) What is the greatest acceleration that the elevator's motor can produce without breaking the cable? s (b) 5 m/s 2

27 216 A weight is suspended by a spring balance connected to the ceiling (a) Draw the forces on the block (b) Draw the forces on the wall (c) Draw the forces on the spring balance 219 A vertical spring of force constant 400 N/m is attached to a 10- kg block resting on a horizontal surface so that the spring exerts an upward force on the block. The spring is stretched by 10 cm. (a) Draw a free body diagram of the situation (make sure you draw your accurately). (b) What force does the spring exert on the block? (c) What is the force that the surface exerts on the block? (b) 40 N (c) 58.1 N 220 A weight is suspended by a spring balance connected to the ceiling. A person applies an downward force on the block. (a) Draw the forces on the block (b) Draw the forces on the wall (c) Draw the forces on the spring balance (b) (c) 217 A block is placed on a spring whose spring constant is 2.0 N/cm and compresses the spring 10 cm. (a) Draw a free body diagram. (b) What is the weight of the block? (c) What is the mass of the block? (b) 20 N (c) 2.04 kg 218 A weight is suspended by a spring balance connected to the ceiling. A person applies an upward force on the block. (a) Draw the forces on the block (b) Draw the forces on the wall (c) Draw the forces on the spring balance 221 (b (c) A 6-kg box slides on a frictionless horizontal surface. It is pulled by a horizontal spring with force constant of 800 N/m. (a) Draw a free body diagram of the forces on the box. (b) If the spring is stretched 4 cm from its equilibrium position, what is the acceleration of the box? (b) 5.33 m/s A piece cut from a bicycle inner tube is stretched to a total length of 0.7 m long when it carries a load of 25 N. The force constant k is 300 N/m. (a) How far did the rubber tube stretch when 75 Newton s of force were added? (b) What was the original length of the tube when no load was present. (Hint: You need to find the change in x - draw all three s) (b) (c) (a).25 (b).616 m

28 223 If a mass of 0.55 kg attached to a vertical spring stretches the spring 2.0 cm from its equilibrium position (a) Draw a of the forces on the spring (b) What is the spring constant? 228 A load of 45 N attached to a spring that is hanging vertically stretches the spring m. What is the spring constant? 3.2 x 10 2 N/m (b) 270 N/m 224 A crate weighing 76 N is attached to a spring (k = 450 N/m). (a) Draw a of the forces on the weight. (b) How much displacement is caused by the weight of this crate? 229 A pinball machine uses a spring that is compressed 4.0 cm to launch a ball. If the spring constant is 13 N/m, what is the force on the ball at the moment the spring is released? 0.52 N 225 (b) m A spring of k = 1962 N/m loses its elasticity if stretched more than 50.0 cm. Suppose the spring described above is replaced with a spring that stretches 36 cm from its equilibrium position. (a) What is the spring constant in this case? (b) Is the second spring stiffer or less stiff than the first spring? 230 In an arcade game, a 0.12 kg disk is shot across a frictionless horizontal surface by being compressed against a spring and then released. If the spring has a spring constant of 230 N/m and is compressed from its equilibrium position by 6.0 cm, what is the magnitude of the spring force on the disk at the moment it is released? 14 N (a) 2725 N/m (b) more stiff 231 Janet wants to find the spring constant of a given spring, so she hangs the spring vertically and attaches a 0.40 kg mass to the spring's other end. If the spring stretches 3.0 cm from its equilibrium position, what is the spring constant? 226 The rock shown below is acted on by one or more forces. All are drawn in a vertical plane, and friction is negligible except when noted. Draw the free body diagram for the rock. Suspended from a spring. Pulled downward slightly and released. No friction N/m In preparing to shoot an arrow, an archer pulls a bow string back 0.40 m by exerting a force that increases uniformly from 0 to 230 N. What is the equivalent spring constant of the bow? 575 N/m 233 A child's toy consists of a piece of plastic attached to a spring, as shown in the figure. The spring is compressed against the floor a distance of 2.0 cm and released. If the spring constant is 85 N/m, what is the magnitude of the spring force acting on the toy at the moment it is released? 227 A slingshot consists of a light leather cup attached between two rubber bands. (a) If it takes a force of 32 N to stretch the bands 1.2 cm, what is the equivalent spring constant of the rubber bands? (b) How much force is required to pull the cup of this slingshot 3.0 cm from its equilibrium position? 1.7 N (a) 2.7 x 10 3 N/m (b) 79.8 N

29 234 A spring of k = 1962 N/m loses its elasticity if stretched more than 50.0 cm. What is the mass of the heaviest object the spring can support without being damaged? 1.00 x 10 2 kg 240 The largest tigers, and therefore the largest members of the cat family, are the Siberian tigers. Male Siberian tigers are reported to have an average mass of about 389 kg. By contrast, a variety of very small cats that is native to India have an average adult mass of only 1.5 kg. Suppose this small cat is placed on a spring scale, causing the spring to be extended from its equilibrium position by 1.2 mm. How far would the spring be extended if a typical male Siberian tiger were placed on the same scale? 235 The pygmy shrew has an average mass of 2.0 g. How many shrews of average mass must be placed on a spring scale with a spring constant of 24 N/m to produce 4.0 cm compression? 0.31 m pygmy sherews The largest meteorite of lunar origin reportedly has a mass of 19 g. If the meteorite produces a compression of 2.24 mm when placed on a spring scale, what is the spring constant of the spring? 241 The largest known crab is a giant spider crab that had a mass of 18.6 kg. The distance from the end of one of this crab's claws to the end of the other claw measured about 3.7 m. If this particular giant spider crab were hung from an elastic band so that the elongation of the band was equal to the crab's claw span, what would be the spring constant of the elastic band? 49 N/m 83 N/m 237 Rising 348 m above the ground, La Gran Piedra in Cuba is the tallest rock on Earth. Suppose an elastic band 2.00 x 10 2 m long hangs vertically off the top of La Gran Piedra. If the band's spring constant is 25.0 N/m, how large must a mass be if, when it is attached to the band, it causes the band to stretch all the way to the ground? 242 The CN Tower in Toronto, Canada, is 553 m tall, making it the world's tallest free-standing structure. Suppose an unusually long bungee cord is attached to the top of the CN Tower. The equilibrium length of the cord is equal to one-third the height of the tower. When a test mass of 70.0 kg is attached, the cord stretches to a length that equals two-thirds of the tower's height. From this information, determine the spring constant of the bungee cord. 377 kg 3.87 N/m 238 In 1952, a great rainfall hit the island of Reunion in the Indian Ocean. In less than 24 h, 187 kg of rain fell on each square meter of soil. If a 187 kg mass is placed on a spring scale and the platform of the scale is compressed 12.0 cm before it reaches equilibrium, what is the spring constant of the spring? 243 A net force of 55 N acts due west on an object. What added single force on the object produces equilibrium? 55 N due East 1.53 x 10 4 N/m 239 The largest ruby in the world may be found in New York. This ruby is 109 mm long, 91 mm wide, and 58 mm thick, making its volume about 575 cm 3. (By comparison, the world's largest diamond, the Star of Africa, has a volume of just over 30 cm 3.) If this ruby is attached to a vertically hanging spring with a spring constant of 2.00 x 10 2 N/m so that the spring is stretched 15.8 cm, what is the mass of the jewel? 244 The rock shown below is acted on by one or more forces. All are drawn in a vertical plane, and friction is negligible except when noted. Draw the free body diagram for the rock. Suspended from a spring. Instantaneously at rest at the top of its travel kg

30 245 A spring is 6 cm long. When it is suspended vertically and a 200 g mass is hung from its lower end, its length increases to 7.5 cm. (a) What is the constant of the spring? (b) What is the tension in the spring if it is stretched to 8.7 cm? 250 The rock shown below is acted on by one or more forces. All are drawn in a vertical plane, and friction is negligible except when noted. Draw the free body diagram for the rock. Suspended from a spring. Pulled downward slightly and released. No friction. (a) 1.34 N/cm (b) 3.35 N 246 A spring which obeys Hooke's law is stretched 4 cm by a force of 6 N. (a) What is the value of k, the spring constant? (b) How much will the spring be stretched by a force of 1.5 N? (a) 1.5 N/cm (b) 1 cm 247 The rock shown below is acted on by one or more forces. All are drawn in a vertical plane, and friction is negligible except when noted. Draw the free body diagram for the rock. Suspended from a spring. Moving upward through the equilibrium position. No friction. 251 The rock shown below is acted on by one or more forces. All are drawn in a vertical plane, and friction is negligible except when noted. Draw the free body diagram for the rock. Suspended from a spring. Instantaneously at rest at the top of its travel. 248 the following questions. (a) What are the dimensions of Hooke's constant? (b) What are the dimensions of the spring constant? (c) What are the dimensions of the force constant? 252 The rock shown below is acted on by one or more forces. All are drawn in a vertical plane, and friction is negligible except when noted. Draw the free body diagram for the rock. Suspended from a spring. Moving downward through the equilibrium position. No friction. (a) N/cm (b) N/cm (c) N/cm 249 A 250 g block is placed on top of a vertical spring with a spring constant k =2.5 N/cm. How much is the spring compressed? 980 c