A 40-N and a 70-N force act concurrently. (e) Find the magnitude of the resultant force when the angle between them is Answer.

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1 1 A 40-N and a 70-N force act concurrently. (a) Find the magnitude of the resultant force when the angle between them is (b) Find the magnitude of the resultant force when the angle between them is (c) Find the magnitude of the resultant force when the angle between them is (d) Find the magnitude of the resultant force when the angle between them is (e) Find the magnitude of the resultant force when the angle between them is Find the magnitude and direction of the resultant of a 60 N force that acts at an angle of 45 0 clockwise from the +Y axis, a 20 N force that acts at an angle of 90 0 from the +Y axis, and a 40 N force that acts at an angle of clockwise from the +Y axis. 68 N at 24 0 clockwise from the +Y axis (a) 110 N (b) 107 N (c) 96 N (d) 81 N (e) 30 N 5 Which of the figure's six arrangements correctly show the vector addition of forces F 1 and F 2 to yield the third vector, which is meant to represent their net force F net? 2 Two 15-N forces act concurrently on point P. (a) Find the magnitude of their resultant when the angle between them is (b) Find the magnitude of their resultant when the angle between them is (c) Find the magnitude of their resultant when the angle between them is (d) Find the magnitude of their resultant when the angle between them is (e) Find the magnitude of their resultant when the angle between them is The figure shows overhead views of four situations in which two forces accelerate the same block across a frictionless floor. (a) Rank the situations according to the magnitudes of the net force on the block, greatest first. (b) Rank the situations according to the magnitudes of the acceleration of the block, greatest first. (a) 30 N (b) 29 N (c) 21 N (d) 15 N (e) 0 N 3 Joanne pulls on a trunk with a 12-N force. Bev pulls at right angles to Joanne. How hard must Bev pull to make the resultant force on the trunk 13 N? 5 N

2 7 In the overhead view of a 2.0 kg cookie tin is accelerated at 3.0 m/s 2 in the direction over a frictionless horizontal surface. The acceleration is caused by three horizontal forces, only two of which are shown: F 1 of magnitude 10 N and F 2 of magnitude 20 N. What is the third force F 3 in unit-vector notation and in magnitude-angle notation? 9 Your sense of vertical depends on visual clues and on the vestibular system located in your inner ear. That system contains tiny hair cells in a fluid. When you hold your head upright, the hairs are vertically in line with the gravitational force Fg on you and the system signals your brain that your head is upright. When you tilt your head backward by some angle?, the hairs are bent and the system signals your brain about the tilt. The hairs are also bent when you are accelerated forward by an applied horizontal force F app. The signal sent to your brain then indicates, erroneously, that your head is tilted back, to be in line with an extension through the vector sum F sum = Fg + F app as shown in the figure. However, the erroneous signal is ignored when visual clues clearly indicate no tilt, such as when you are accelerated in a car. 8 In a two-dimensional tug-of-war, Alex, Betty, and Charles pull horizontally on an automobile tire at the angles shown in the overhead view of the figure. The tire remains stationary in spite of the three pulls. Alex pulls with force F A of magnitude 220 N, and Charles pulls with force F c of magnitude 170 N. The direction of F c is not given. What is the magnitude of Betty's force F B?. A pilot being hurled along the deck of an aircraft carrier at night has almost no visual clues. The illusion of tilt is strong and very convincing, with the result that the pilot feels as though the plane leaves the deck headed sharply upward. Without proper training, a pilot will attempt to level the plane by bringing its nose sharply down, sending the plane into the ocean. Suppose that, starting from rest, a pilot undergoes constant 10 In the figure a block B of mass M = 15.0 kg hangs by a cord from a knot K of mass m K which hangs from a ceiling by means of two other cords. The cords have negligible mass, and the magnitude of the gravitational force on the knot is negligible compared to the gravitational force on the block. What are the tensions in the three cords?

3 11 Use the figure to answer the following questions. (a) What are the magnitudes of the force 'f on the block from the cord and the normal force FN on the block from the plane? (b) We now cut the cord. Does the block accelerate as it slides down the inclined plane? If so, what is its acceleration? 14 Four forces act on a hot air balloon, shown from the side in the figure below. Find the magnitude and direction of the net (resultant) force on the balloon. 12 In the figure, horizontal force F is applied to a block on a ramp. (a) Is the component of F that is perpendicular to the ramp F cos θ or F sin θ. (b) Does the presence of F increase or decrease the normal force on the block from the ramp? 4305 N 15 0 above the 5210 N force 15 A dog pulls on a pillow with a force of 5 N at an angle of 37 0 above the horizontal. (a) Draw a free body diagram of the forces on the pillow (b) Find the x and y components of this force. 13 The forces acting on a sailboat are 390 N north and 180 N east. If the boat (including crew) has a mass of 270 kg, (a) Draw a free body diagram of the forces on the sailboat. (b) What are the magnitude and direction of its acceleration? (c) What is the net force on the sailboat (a) Drawing (b) 4 N Horizontal 3 N Vertical (b) 1.6 m/s north of east or 24 0 east of north (c) 429 N 65 0 north of east or 24 0 east of North

4 16 Two forces are applied to a car in an effort to accelerate it, as shown in the figure below. (a) What is the net (resultant) force of these two forces? (b) If the car has a mass of 3200 kg, what acceleration does it have? Disregard friction. 19 A man is pulling on his 20 kg dog with a force of 70.0 N directed at an angle of above the horizontal. (a) Draw a free body diagram of the forces on the dog. (b) Find the x component of this force. (c) Find the y component of this force. (d) Find the normal force on the dog. (a) Drawing (b) 60.6 N (c) 35.0 N (d) N (a) 780 N to the right of forward (b) 0.24 m/s to the right of forward 20 A crate is pulled to the right with a force of 85 N, to the left with a force of 115 N, upward with a force of 565 N, and downward with a force of 236 N. (a) Draw a free body diagram of the forces on the crate. (b) Find the net external force in the x direction. (c) Find the net external force in the y direction. (d) Find the magnitude and direction of the net external force on the crate. 17 Three forces act simultaneously on point J. One force is 10.0 N north; the second is 15.0 N west; the third is 15.0 N east of north. Determine the magnitude and direction of the net (resultant) force. (a) (b) -3.0 x 10 1 N left (c) 329 N up (d) 3.3 x 10 2 N clockwise from the positive x-axis 24.2 N, Find the magnitude and direction of the net (resultant force) of a 60 N force that acts at an angle of 45 0 clockwise from the +Y axis, a 20 N force that acts at an angle of 90 0 from the +Y axis, and a 40 N force that acts at an angle of clockwise from the +Y axis. 21 Use trig to solve the following problems. (a) Find q if tan q = (b) Find q if sin q = (c) Find q if cos q = (d) Find q if tan q = (e) Find q if sin q = (f) Find q if cos q = N at 24 0 clockwise from the +Y axis (a) q = (b) q = (c) q = (d) q = (e) q = (f) q =

5 22 Use trig to solve the following problems. (a) Find the tan (b) Find the sin (c) Find the cos (d) Find the tan 58 0 (e) Find the sin 40 0 (f) Find the cos Solve for all sides and all angles for the following right triangles. (a) 0.53 (b) 1.00 (c) 1.00 (d) 1.6 (c) 0.64 (f) 0.33 hyp 9.65 adj 5.1 angle opp 5.1 angle Solve for all sides and all angles for the following right triangles. 26 Solve for all sides and all angles for the following right triangles. 24 hypothesis 4.7 adj 2.5 angle 32 0 Solve for all sides and all angles for the following right triangles. Missing side 9.62 adj 7.0 side angle 54 0 opp 7.0 side A right triangle has two sides A and B. (a) If tan q = A/B which side of the triangle is longer if the tangent is greater than one? (b) If tan q = A/B which side of the triangle is longer if the tangent is less than one? (c) If tan q = A/B what does it mean if the tangent equals one? adj 9.4 opp 7.61 angle 51 0 (a) side A; (b) side B; (c) Side A = side B they have the same length.

6 28 A heavy box is pulled across a wooden floor with a rope. The rope makes an angle of 60 0 with the floor. A force of 75 N is exerted on the rope. What is the component of the force parallel to the floor? 31 A 3.00 kg ball is dropped from the roof of a building m high. While the ball is falling to Earth, a horizontal wind exerts a constant force of 12.0 N on it. (a) Draw the free body diagram. (b) How long does it take the ball to hit the ground? (c) How far from the building does the ball hit the ground? (d) What is its speed and angle when it hits the ground? (e) With what force and angle will the ball hit the ground? 29 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock rising in a parabolic trajectory. Good review problem of projectile motion (a) (b) 72.0 m (c) 6.00 s (d) 63.6 m/s (e) N Find the vertical and horizontal components of a force of 50 N that is directed 50 0 above the horizontal N vert 32.2 N. horiz 30 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock at the top of a parabolic trajectory. 33 A 110-N force and a 55-N force both act on an object point P. The 110-N force acts at The 55-N force act at 0 0. What is the magnitude and direction of the resultant force? 122 N 63 0

7 34 Two men and a boy are pulling a boat along a canal. The two men pull with forces F 1 and F 2 whose magnitudes and directions are indicated in the figure. (a) Find the magnitude and direction of the smallest force which the boy could exert to keep the boat in the middle of the canal. (b) If the boat has a mass of 400 kg what is the net force on the boat (c) What is the observed acceleration of the boat 36 Two ropes are pulling on a log. Find the net (resultant) force on the log if F 1 is pulled with 12 N of force at 10 0 and F 2 is changed to 14.0 N at N Three people are pulling on a tree. The first person pulls with 15 N at ; the second with 16 N at ; the third with 11 N at What is the magnitude and direction of the net (resultant) force on the tree? (Hard) (a) 186 N 90 0 from the bank on the 320 N side (b) 477 N (c) 1.19 m/s N Two men wish to pull down a tree by means of a rope fastened near the top. If they use only one rope the tree will come down on top of them. To prevent this, they tie two ropes 10 meters long to the same point and stand on the ground 10.0 meters apart when they pull. If each pulls with a force of 300 newtons, what is the net force exerted by the ropes on the tree? 35 A gardener pushes a 10 kg lawn mower by applying a force of 150 N along the handle. (a) Draw a free body diagram (b) Find the horizontal component of this force when the lawn mower handle makes an angle of (c) Find the horizontal component of this force when the lawn mower handle makes an angle of 45 0 (d) Find the horizontal component of this force when the lawn mower handle makes an angle of 60 o with the horizontal. (a) (b) 130 N (c) 106 N (d) 75.0 N newtons Three people attempt to haul a heavy sign to the roof of a building by means of three ropes attached to the sign. Person A stands directly above the sign and pulls straight up on a rope. Person B and Person C stand on either side of person A. Their ropes form 30 degree angles with Person A's rope. A force of 100 newtons is applied on each rope. What is the net upward force acting on the sign? 278 Newtons

8 40 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock tied to a rope and pulled so that the rock accelerates horizontally at 2g. No air friction 43 Beth, a construction worker, attempts to pull a stake out of the ground by pulling on a rope that is attached to the stake. The rope makes an angle of with the horizontal. Beth exerts a force of 125 N on the rope. (a) Draw a free body diagram of the forces on the stake (b) What is the magnitude of the upward component of the force acting on the stake? (a) Drawing (b)108 N 41 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock tied to a rope and pulled so that the rock moves horizontally at constant velocity. Note: There must be air friction in this case. 44 A 40-kg crate is pulled across the ice with a rope. A force of 100 N is applied at an angle of 30 o with the horizontal. (a) Draw the free body diagram (b) Calculate the upward force the rope exerts on the ice block as it is pulled. (c) Calculate the normal force on the crate. (d) Calculate the net force on the box (e) What is the observed accleration of the ice block? (class) (a) picture (b) 50 N (c) 342 N, up Refer to Problems and Solutions Manual for diagram (d) 86.6 N (e) 2.2 m/s 2 42 Dan applies a force of 92 N on a heavy box of mass 37 kg by using a rope held at an angle of 45 0 with the horizontal. (a) Draw the free body diagram (b What are the vertical and horizontal components of the 92- N force? (c) Calculate the normal force on the crate. (d) Calculate the net force on the box 45 Joe pushes on the handle of a 10-kg lawn spreader. The handle makes a 45 0 angle with the horizontal. Joe wishes to accelerate the spreader from rest to 1.39 m/s in 1.5 s. (a) Draw a free body diagram. (b) What is the normal force on the spreader? (c) What force must Joe apply to the handle? Neglect friction. (class) (a) (b) F h = 65 N; (a) (b) 107.2N (c) 13 N F v = 65 N (c) (d)

9 46 A water skier is towed by a speedboat. The skier moves to one side of the boat in such a way that the tow rope forms an angle of 55 o with the direction of the boat. The tension on the rope is 350 N. What would be the tension on the rope if the skier were directly behind the boat? 200 N 48 A student pulls a 125 kg box across a floor by means of a rope making an angle of 60 0 with the horizontal. He applies a 60 N force on the rope (a) What is the component of the force in the horizontal direction? (b) What is the component of the force in the vertical direction? (c) What is the normal force on the box? (d) If the angle of the rope is reduced to 30 0 and the same force applied, what will now be the magnitudes of the horizontal, vertical components and the normal force on the box? 47 Wendy pushes a 15 kg lawn spreader across a lawn by applying a force of 95 N along the handle that makes an angle of with the horizontal. (a) Draw a free body diagram. (b) What are the horizontal and vertical components of the force? (c) What is the normal force on the spreader? (d) The handle is lowered so it makes an angle of with the horizontal. Now what are the horizontal and vertical components of the force? (e) What is the new normal force on the spreader? (a) H= 30 N (b) V= 52 N (c) N (d) Hcomp. 52 N Vcomp 30 N Fnormal (a) (b) horizontal = 48 N, vertical = 82 N (c) (d) horizontal = 82 N, vertical = 48 N (e) 49 A block of mass 8.0 kg, starting from rest, is pulled along a frictionlesshorizontal tabletop by a constant force of 2.0 Newtons at an angle of 35 0 from the horizontal. (a) Draw a picture of the situation. (b) What is the net force on the block? (c) What is the acceleration of the body? (a) picture (b) 1.63 N (c).168 m/s 2 50 A 5.5 kg watermelon is pushed across a table at an angle of 47 0 from the horizontal. 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. (c) What is the applied force on the watermelon?

10 51 A tow rope at a 50 0 angle with the ground is used to pull a 1,750-kg car, giving it an acceleration of 1.35 m/s 2. (assume frictionless) (a) Draw a free body diagram of the situation. (b) What is the net force on the car? (c) What is the force applied to the rope? 55 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 105 N and 92 N downward and at an angle of 15 0 to the horizontal. (a) Draw a free body diagram of the forces on the block (b) What is the acceleration of the block? 52 (a) picture (b) 2,362.5 N in the direction of the acceleration (c) 3675 N You give to a 24.3 kg box a push at an angle of 20 0 with the horizontal and a force of 85.5 N. (a) Draw a free body diagram of the motion. (b) What is the net force on the car? (b) What is the acceleration of the car? 56 Two people pull on a 208 kg boat. If they pull in the same and at an angle of 35 0 to the water, 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 to the left. (a) Draw a free body diagram for each situation. (b) What is the magnitude of the force exerted by each person on the boat? Hard 53 A 5-kg object is pulled along a frictionless horizontal surface by a force of 10 N at 15 0 from the horizontal. (a) Draw a free body diagram of the situation. (b) What is the net force on the block? (c) What is the observed acceleration of the block? (d) If the object is at rest at t = 0, how fast is it moving after 3 s? (e) How far does it travel from t = 0 to t = 3 s? 57 A 3.5 kg block is pushed along a horizontal floor by a force F = 15 N that makes an angle θ = 40 degrees with the horizontal, as shown in the figure below. The coefficient of kinetic friction between the block and the floor is (a) Calculate the frictional force exerted on the block (b) Calculate the acceleration of the block. (a) picture (b) 9.66 N (c) 1.93 m/s 2 (d) 5.79 m/s (e) Two lifeguards pull on ropes attached to a raft. Each lifeguard pulls his rope at an angle of 20 0 to the water. 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 to the left. (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.) (class) (a) 11.0 N (b) 0.14 m/s 2

11 58 A 5-kg block is held at rest against a vertical wall by a horizontal force of 100 N. (a) What is the frictional force exerted by the wall on the block? (b) What is the minimum horizontal force needed to prevent the block from falling if the coefficient of friction between the wall and the block is µ s = 0.40? 61 Two students are sliding a 225 kg sofa at a constant speed across the floor. The students carry the sofa, each exert a force equal to half the weight of the sofa. (a) Which would be an improvement over sliding the sofa (b) What other changes could be made to make moving the sofa easier without lifting it off the floor? Change the angles or put the sofa on rollers 59 (a) N (b) 123 N A box of mass m rests on a horizontal table. The box is pulled by a massless rope with a force F at an angle? as shown in the figure below. The coefficient of static friction is 0.6. The minimum value of the force needed to move the box depends on the angle?. (a) Discuss qualitatively how you would expect this force to depend on?. (b) Compute the force for the angles? = 0, 10, 20, 30, 40, 50, and 60 and make a plot of F versus? for mg = 400 N. From your plot, at what angle is it most efficient to apply the force to move the box? A box of books weighing 325 N moves with a constant velocity across the floor when it is pushed with a force of 425 N exerted downward at an angle of below the horizontal. Find? k between the box and the floor A student moves a box of books down the hall by pulling on a rope attached to the box. The student pulls with a force of 185 N at an angle of 25 0 above the horizontal. The box has a mass of 35 kg, and µ k between box and floor is Find the acceleration of the box. 2.7 m/s 2 (a) The force initially decreases with 0 since the upward component of F will decrease the normal force exerted by the table, Fn. As q increases further, however, the forward component of F decreases so much that F must become larger again in order to move the box. (b) F = msmg/(cos q + ms sin q). F is a minimum near 3P. 64 A clerk moves a box of cans down an aisle by pulling on a rope attached to the box. The clerk pulls with a force of N at an angle of with the horizontal. The box has a mass of 35.0 kg, and the coefficient of kinetic friction between box and floor is Find the acceleration of the box. 60 A student moves a box of books by attaching a rope to the box and pulling with a force of N at an angle of The box of books has a mass of 20.0 kg and the coefficient of kinetic friction between the bottom of the box and the sidewalk is Find the acceleration of the box 1.4 m/s 1.24 m/s 2 to the right

12 65 A 4.00 kg block is pushed along the ceiling with a constant applied force of 85.0 N that acts at an angle of with the horizontal, as in the figure below. The block accelerates to the right at 6.00 m/s. Determine the coefficient of kinetic friction between the block and the ceiling. 68 Rachel pulls her 18-kg suitcase at a constant speed by pulling on a handle that makes an angle A with the horizontal. The frictional force on the suitcase is 27 N and Rachel exerts a 43- N force on the handle. (a) What angle does the handle make with the horizontal? (b) What is the normal force exerted on the suitcase? (a) 51 0 (b) 143 N, up (challenge) Suppose you put a wooden block against a wall and push horizontally to keep it from falling. Draw a diagram showing the forces on the block and the causes of those forces. Pay special attention to the normal force and the weight of the block. Are they in the same direction? Are they equal? 66 Block B in the figure below weights 160 lb. (= 710 N). The coefficient of static friction between block and table is Find the maximum weight of block A for which the system will be in equilibrium. Weight down, friction up; force of your hand onto wall; (normal) force of wallout. Normal force is perpendicualr to the weight. Weight is equal (and opposite to friction force, which is the coefficient of friction times the normal force. 70 Two students are sliding a 225 kg sofa at a constant speed across the floor. One student pulls with a force of 225 N at an angle of 13 0 above the horizontal. The other student pushes with a force of 250 N at an angle of 23 0 below the horizontal. What is the coefficient of kinetic friction between the sofa and the floor? 40 lb. 177 N 67 A brick layer applies a force of 100 N to each of two handles of a wheelbarrow. Its mass is 20 kg and it is loaded with 30 bricks, each of mass 1.5 kg. The handles of the wheelbarrow are 30 0 from the horizontal and the coefficient of friction is What initial acceleration is given the wheelbarrow? A person applies a 220 N force at 25 0 to the horizontal to push 55 kg crate across a level floor. If the coefficient of kinetic friction is (a) Draw a picture of the horizontal (b) What is the magnitude of the frictional force? (c) What is the acceleration of the crate? 0.71 m/s (a) (b) (c)

13 72 In 1988, a 3,500 kg telephone constructed by a Dutch telecommunications company was demonstrated in the Netherlands. Suppose this phone is towed horizontally by a force equal to 8,800 N and pulled at a 15 0 angle. Given that the coefficient of kinetic friction is 0.12; calculate the magnitude of the net acceleration of the telephone. 76 A box weighing 600 N is pushed along a horizontal floor at constant velocity with a force of 250 N at 30 0 to the floor. What is the coefficient of kinetic friction between the box and the floor? 1.42 m/s 2 77 If you use a force of 30.0 N pulled at 12 0 to the horizontal to slide a 12.0-kg wooden crate across a floor at a constant velocity, what is the coefficient of sliding friction between crate and floor? A blue whale with a mass of 1.90 x 10 5 kg was caught in What minimum force pulled at an angle 10 0 would be needed to pull the whale at a constant velocity along a horizontal ramp if the coefficient of kinetic friction between the ramp's surface and the whale were 0.160? Cleopatra's Needle, an obelisk given by the Egyptian government to Great Britain in the late nineteenth century, is more than 20 m tall and has a mass of roughly 1.89 x 10 5 kg. Suppose the monument is lowered onto its side and dragged horizontally to a new location. Given that the magnitude of the acceleration of the monument is m/s 2 and the coefficient of kinetic friction is 0.100, calculate the magnitude of the force applied at 10 0 that must be applied to the monument in order to move it A sled of mass 50 kg is pulled along snow-covered, flat ground using a rope attached to the sled and tied at 40 0 to the horizontal. The static friction coefficient is 0.30, and the sliding friction coefficient is (a) What does the sled weigh? (b) What force given to the rope will be needed to start the sled moving? (c) What force given to the rope is needed to keep the sled moving at a constant velocity? (d) Once moving, what total force given to the rope must be applied to the sled to accelerate it 3.0 m/s 2? 75 Isaac Newton developed the laws of mechanics. Brian Newton put those laws into application when he ran a marathon in about 8.5 h while carrying a bag containing 51 kg of coal. (By doing this, he set a strange but impressive world record in 1983.) Suppose Brian Newton wants to remove the bag from the finish line. He drags the bag with a force of 280 N at If the coefficient of kinetic friction between the bag and the pavement is 0.16, what is the magnitude of the net acceleration of the bag? A 200-kg crate is pushed with a force of 800 N downward at If the coefficient of friction is 0.20, calculate the acceleration of the crate m/s 2 A force of 30 N accelerates a 9.0-kg wagon at 2.0 m/s 2 along the sidewalk when it is applied to the handle at (a) How large is the frictional force? (b) What is the coefficient of friction? 2.92 m/s 2

14 81 In order to drag a 100-kg log along the ground at constant velocity, you have to pull on it with a force of 400 N at an angle of 35 0 from the horizontal. (a) Draw a free body diagram of the situation. (b) What is the resistive force exerted by the ground? (c) What force must you exert if you want to give the log an acceleration of 2 m/s 2? 84 A box is held in position by a cable along a smooth incline shown in the figure below. If? = 60 0 and m = 50 kg. (a) Draw a free body diagram of the situation (b) Find the tension in the cable (c) Find the normal force exerted by the incline. 82 The largest flowers in the world are the Rafflesia Arnoldii, found in Malaysia. A single flower is almost a meter across and has a mass up to 11.0 kg. Suppose you cut off a single flower and drag it along with a force of 42.0 N and at an angle of If the flower's velocity is constant, what is the coefficient of kinetic friction between the flower and the ground? (a) Picture (b) F T = 425N (c) F n = 245N 83 A giant crane in Washington, D. C., was tested by lifting a load with a mass of x 10 6 kg. (a) Draw a free body diagram of the forces on the load. (b) Find the force needed to lift the load with an observed acceleration of m/s 2. (c) The same force is applied to pull the load up a smooth slope that makes a angle with the horizontal,. Draw a free body diagram of the forces on the load described in the new situation (d)what would be the observed acceleration on the load in the new situation? 85 A block is projected up a frictionless inclined plane with initial speed 3.5 m/s. The angle of incline is (a) Draw a free body diagram of the forces on the block. (b) How far up the plane does it go? (c) How long does it take to get there? (d) What is its speed when it gets back-to the bottom (a) picture (b) 6.67 x 10 7 N (c) picture (d) 25.2m/s 2 (a) picture (b) 1.25 m (c).714 sec (d) 3.5 m/s since no friction 86 A horizontal force of 100 N pushes a 12-kg block up a frictionless incline that makes an angle of 25 0 with the horizontal. (a) What is the normal force that the incline exerts on the block? (b) What is the acceleration of the block? (Hard) (a) 149 N (b) 3.41 m/s 2

15 87 A 65-kg girl weighs herself by standing on a scale mounted on a skateboard that is rolling down an incline as shown in the picture. Assume there is no friction so that the force exerted by the incline on the skateboard is perpendicular to the incline. What is the reading on the scale if θ = 30 0? 90 A laundry basket has a mass of 5.5 kg, find the magnitude of the normal force on a ramp inclined 12 0 above the horizontal 53 N 91 A 40.0 kg wagon is towed up a hill inclined at with respect to the horizontal. The tow rope is parallel to the incline and exerts a force of 140 N on the wagon. Assume that the wagon starts from rest at the bottom of the hill, and disregard friction. (a) How fast is the wagon going after moving 30.0 m up the hill? (b) How fast is the wagon going after moving 80.0 m up the hill? 552 N 88 A 2.0 kg mass starts from rest at the top of an inclined plane 85 cm long and slides down to the bottom in 0.50 s. What net force acts on the mass along the incline? (a) 4.9 m/s (b) 8.0 m/s 13.6 N 92 Suppose a 3.00 x 10 2 N force is used to pull an exceptionally large elephant with a mass of 1.22 x 10 4 kg up a frictionless slope. What is the maximum angle that the slope can make with the horizontal if the task is to be completed? 89 A block with a mass of 5.0 kg is held in equilibrium on an incline of angle θ = by the horizontal force, F, as shown in the figure. (a) Find the magnitude of F. (b) Find the normal force exerted by the incline on the block. (challenge) degrees The largest squash ever grown had a mass of 409 kg. Suppose you want to push a squash with this mass up a smooth frictonless ramp that is 6.00 m long and that makes a angle with the horizontal. You push the squash with a force of 2080 N. (a) Calculate the net force exerted on the squash (b) Calculate the observed acceleration of the squash (c) Calculate the time it will it take to reach the top of the ramp (a) 28 N (b) 56 N (a) 76 N (b).19 m/s 2 (c) 8.2 s

16 94 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock. 97 A 3.00 kg block starts from rest at the top of a incline and slides 2.00 m down the incline in 1.50 s. (a) Find the acceleration of the block. (b) Find the coefficient of kinetic friction between the block and the incline. (c) Find the frictional force acting on the block. (d) Find the speed of the block after it has slid a distance of 2.00 m. (a) 1.78 m/s 2 (b) 0.37 (c) 9.4 N (d) 2.67 m/s 95 The rock shown below is acted on by one or more forces.. Draw the free body diagram for the rock. 98 The coefficient of static friction between the 3.00 kg crate and the incline of the figure shown below is What is the minimum force, F N that must be applied to the crate perpendicular to the incline to prevent the crate from sliding down the incline? 96 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock. Sliding without friction. (challenge) 32.1 N 99 The most massive car ever built was the official car of the General Secretary of the Communist Party in the former Soviet Union. The car had a mass of 3,335 kg. Suppose this car is moving down a slope when the driver applies the brakes. The wheels stop rotating, and the car slides, decelerating at a rate of 6.00 m/s 2. (a) Calculate the force of kinetic friction acting on the car as it decelerates. (b) Determine the coefficient of kinetic friction. 25,682 N 0.798

17 100 Walter Arfeuille of Belgium lifted a kg load off the ground using his teeth. Suppose Arfeuille can hold three times that mass on a slope using the same force. What is the coefficient of static friction between the load and the slope? A 5.0 kg block on an inclined plane is acted upon by a horizontal force of 50 N shown in the figure below. The coefficient of friction between block and plane is (a) What is the acceleration of the block if it is moved up the plane? (b) How far up the plane will the block go if it has an initial upward speed of 4.0 m/s? (c) What happens to the block after it reaches the highest point? 101 In 1994, a 3.00 x 10 3 kg pancake was cooked, and flipped, in Manchester, England. (a) If the pancake is placed on a surface that is inclined with respect to the horizontal, what must the coefficient of kinetic friction be in order for the pancake to slide down the surface with a constant velocity? (b) What would be the frictional force acting on the pancake? x 10 4 N The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock. Static friction prevents sliding. 104 (class Problem) (a) m/s 2 (b) 3.83 m (c) stops The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock. Sliding with friction.

18 105 You slide a 325-N trunk up a inclined plane with a constant velocity by exerting a force of 211 N parallel to the inclined plane. (a) What is the component of the trunk's weight parallel to the plane? (b) What is the sum of your applied force, friction, and the parallel component of the trunk's weight? Why? (c) What is the size and direction of the friction force? (d) What is the coefficient of friction? 109 A weight of 50.0 newtons is hung from the center of a stretched horizontal wire 10.0 m long. It causes the wire to sag 1.0 meter at its center. What is the force exerted by each half of the wire supporting the weight? (Hint: make a scale diagram of the wire with the weight hung from it.) 125 N (a) 111 N; (b) zero, constant velocity; (c) 100 N, down plane; (d) A person weighs 612 N. If the person sits in the middle of a hammock that is 3.0 m long and sags 1.0 m below the points of support, what force would be exerted by each of the two hammock ropes? 106 A 91 kg refrigerator is placed on a ramp. The refrigerator begins to slide when the ramp is raised to an angle of What is the coefficient of static friction? 460 N on each side A bell ringer decides to use a bowling ball to ring the bell. He hangs the 7.3-kg ball from the end of a 2.0 m long rope. He attaches another rope to the ball to pull the ball back, and pulls it horizontally until the ball has moved 0.60 m away from the vertical. How much force must he apply? 107 Two forces act on an object. A 36-N force acts at A 48-N force acts at What would be the magnitude and direction of their equilibrant? 22 N 60 N An electric sign weighing 200 newtons is supported by two slanting cables. Each cable is attached to the same point of the sign and makes a 45 0 angle with the horizontal. What is the force exerted by the sign along each of its cables? 108 Five forces act on an object: the first, 60 N at 90 0 ; the second, 40 N at 0 0 ; the third, 80 N at ; the fourth, 40 N at ; and the fifth, 50 N at What is the magnitude and direction of a sixth force that produces equilibrium of the object? 141 N. 34 N, A street lamp weighs 150 N. It is supported equally by two wires that form an angle of with each other. (a) What is the tension of each of these wires? (b) If the angle is changed to 90 0, What is the new tension on the string? (a) 150 newtons in each wire (b) 106 newtons in each wire

19 114 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock. 117 A sphere of mass 3.0 x 10-4 kg is suspended from a cord. A steady horizontal breeze pushes the sphere so that the cord makes an angle of 37 degrees with the vertical when at rest. (a) Draw a free body diagram. (b) Find the magnitude of the push. (c) Find the tension in the cord. (a) (b) 2.22 x 10-3 N (c) 3.69 x 10-3 N 115 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock. 118 The largest toad ever caught had a mass of 2.65 kg. Suppose a toad with this mass is placed on a metal plate that is attached to two cables, as shown in the figure below. If the plate is pulled upward so that it has an observed acceleration of 2.55 m/s 2, what is the tension in the cables? 116 The rock shown below is acted on by one or more forces. Draw the free body diagram for the rock. 23 N -23 N 119 A traffic light is supported by two cables that are apart. Each cable exerts a force of 150 newtons on the light. (a) Draw a free body diagram (b) How much does the light weigh? (Think of the weight of the light, the downward force, as the eqilibriant.) (a) (b) net (resultant) 102 newtons 70 0 equilibriant 102 newtons down

20 120 Joe wishes to hang a sign weighing 750 N so that cable A attached to the store makes a angle as shown in the figure below. Cable B is attached to an adjoining building. Calculate the necessary tension in cable B. 433 N, right 121 You have to push with a force of 200 N downward at 25 0 to the horizontal slide a refrigerator across a floor at constant velocity. What is the force of friction acting on the refrigerator?

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