PHYSICS AC NEWTON S LAWS HOMEWORK Ans. Key

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1 1 PHYSICS AC NEWTON S LAWS HOMEWORK Ans. Key BASIC CONCEPTS OF MASS VS. WEIGHT VS. VOLUME VS. DENSITY MULTIPLE CHOICE: You have one kilogram of feathers and one kilogram of lead. Which has more: 1. c. mass? 3. c. weight? a. feathers b. lead a. feathers b. lead Ans. One kilogram is one kilogram. The amount of mass/matter is the same in both cases. Since weight is just mass times gravity, the weight will be the same too. Pb 2. a. volume? 4. b. density? a. feathers b. lead a. feathers b. lead Ans. to get a kilogram of feathers, you have to get a bunch of feathers together and they will occupy a lot of space (which is what volume measures). Lead is much more compact than the feathers so any amount/mass of lead is more dense than any amount/mass of feathers. MULTIPLE CHOICE: You have one liter of water and one liter mercury. Which has more: 5. b. mass? 7. b. weight? a. water b. mercury a. water b. mercury Ans. a liter of mercury, which is more dense than water, will have more mass than a liter of water. Density is mass per unit volume. Since the volume is the same in both (one liter), we have to inspect the mass. The mass of mercury in a space of one liter would be much greater than the mass of water in the space of one liter. 6. c. volume? 8. b._ density? a. water b. mercury a. water b. mercury Ans. a liter of mercury occupies the same space as a liter of water. As mentioned before, the density of mercury is much greater than the density of water. The molecules are much closer together per unit volume.

2 2 MULTIPLE CHOICE: You have the dough for a loaf of bread and you put it in the oven where it bakes. What happens to each of the following after baking? 9. c._ mass? 11. c. weight? a. bigger b. smaller a. bigger b. smaller Ans. The mass will not change by the law of conservation of mass. The weight will not change because the weight is simply mass times a constant, gravity. 10. a. volume? 12. b. density? a. bigger b. smaller a. bigger b. smaller Ans. Since the particles of bread will vibrate further apart from each other, the dough will occupy more and more space as it gets heated, thus its volume increases. Since the mass is not changing but the volume is increasing, the density will decrease. Density is mass per unit volume. If the denominator gets bigger, the density gets smaller (density and volume are inversely proportional). 13. If you have the mass of something (say 10 kg) and you want to find its weight, how do you do it? Show your work. To go from mass to weight, multiply by 9.8 = mg = 10 kg 9.8 m/s 2 = 98 N. 14. If you have weight of something (say 10 N) and want to find its mass, how do you do it? Show your work. To go from weight to mass, divide by 9.8 = mg 10 N = m 9.8 m/s kg = m. NEWTON S FIRST LAW 1. State Newton s First Law: An object will stay at rest or move in a straight line at constant velocity unless acted upon by an external force. 2. Give an example of Newton s First Law at work for an object at rest: A rock will not move of its own. It needs a force to overcome its inertia. 3. Give an example of Newton s First Law at work for an object in motion: A satellite in space will continue moving in a straight line through space without need for fuel or a force to keep it going. If the gravitational attraction of a planet acts upon it, it will begin to accelerate positively or negatively and stop moving at a constant velocity. 4. MULTIPLE CHOICE: a. The more mass an object has the inertia it has. a. more b. less c. inertia is independent of mass

3 Rear deck 3 5. In terms of Newton s First Law, why is it dangerous to have sharp things lying in the rear deck of the car below the back window? In a frontal accident, the loose objects will fly forward because they will continue to move at the same velocity they were moving at before the collision occurred according to Newton s First Law. These objects can hit the back of the heads of the passengers and cause serious and even fatal damage if they are pointed. 6. a. What causes your neck to whiplash in a car when you are hit from behind? b. How does the seat head rest help prevent whiplash? The whiplash obeys Newton s First Law. Your neck is like a hinge made by vertebrae. When your car get hit from the back, your body moves forward because it is in contact with the seat which is firmly screwed to the car body and has no choice but to move forward. Your head and neck, on the other hand, are free to swing back in the absence of a head rest to stop them. The whiplash stems from the fact that your head and neck want to remain at rest (according to Newton s First Law) even though the rest of your body is forced to move forward. 7. An F-18 Hornet of mass 3900 kg is flying at constant velocity in the air. Its thrusters are providing 500,000 N of thrust to the plane. What s the plane s acceleration (in m/s 2 )? Trick Question: The acceleration is zero because the jet fighter is moving at CONSTANT VELOCITY. 8. An aircraft carrier of mass 250,000,000 kg is moving at a constant speed of 15 m/s. If its engine is providing 260,000,000 N of force to the propellers, how much is the force of water resistance (in N)? _The water resistance force must be equal and opposite to the force provided by the engine if the ship is MOVING AT CONSTANT VELOCITY and is not accelerating. There can be no net force acting on the ship, according to Newton s First Law_ 9. You are an astronaut at zero gravity. Two objects in front of you look identical but one of them has more mass than the other. What simple thing could you do to find out which one has more mass? You can shake the two objects back and forth in your hands. The object that requires more force to move back and forth will have more inertia and thus more mass.

4 4 NEWTON S SECOND LAW DIRECTIONS: Draw all the real forces (as vectors) acting on the block shown in each of the situations. The number of vectors to be drawn are in parentheses. 1. (2 vectors) A block at rest on a table FN 2. (3) A block being accelerated to the right. No friction is present. FN 3. (4) A block moving to the right at constant velocity. Friction is present. FN Fx Ff Fx 4. (3) A block at rest with another block on top of it 5. (4) A block with a book leaning against it. The block is not moving. Friction is present. 6. (3) A block on an inclined plane. The block is not sliding. Friction is present. FN FN FN1 FN Ff Fp Ff 7. (4) A block on an inclined plane being pulled up the plane. Friction is present. FN T 8. (3) A block at the bottom of an inclined plane butted up against a wall. FN1 9. (2) A block falling through the air at terminal velocity FF FN2 Ff 10. (2) A block hanging from the ceiling by a rope. T 11. (3) A block hanging from the ceiling by a rope and with a weight pulling it down. T1 12. (3) A block hanging from the ceiling by two ropes at angles. T1 T2 T2

5 5 OVER EASY MATH FORMULA BANK a = F or F = m a x = ±vxot ± m ½at2 a = v t = v f v i t f t i Newton s Second Law. Where a is the acceleration ((in m/s 2 ), F is the force (in N), and m is the mass (in kg) FNET = m a = Fx Ff Net force. Equals the pushing/pulling force (in N) one way minus the frictional force (in N) the other way. Distance travelled in a horizontal direction. Where x is the distance (in meters), v xo is initial horizontal velocity (in m/s), t is time (in sec), and a is acceleration (in m/s 2 ) Acceleration as the slope of velocity. Where a is the acceleration (in m/s 2 ), v f is the final velocity (in m/s), v i is the initial velocity (in m/s), and t is the time (in s) = m g FW = FN and Ff = Fx Ff = FN The force of weight. Where g is the acceleration (in m/s 2 ) due to gravity, F w is the force of weight (in N), and m is the mass (in kg) Equilibrium. The force of weight (F W) equals the normal force (F N) and the force of friction (F f) equals the pulling force (F x) in a simple equilibrium situation on a horizontal surface. F N F f F W F x Frictional Force. The Frictional force (F f) on a block on a flat surface or inclined plane is equal to the coefficient of friction ( ) times the Normal Force (F N) F f F N Refer to the figure at right to answer the questions following. Assume gravity is 10 m/s 2. Assume the strings are massless 40 N_ 1. What is the block s weight (in N)? Ans. G.IVEN(S): g = 10 m/s 2, m = 4 kg U. KNOWN: weight = E. QUATION: = m g S. OLVE: = m g S. UBSTITUTE: = 4 kg 10 m/s 2 = 40 N 4 kg 40 N 2. If an equilibrium situation exists, how much total force (in N) must there be in the upwards direction? Ans. The sum of the forces F = 0 for equilibrium to exist. If the weight is 40 N downwards, the force upwards must also be 40 N

6 6 20 N 3. What is the vertical component of upwards force (in N) provided by one of the spring scales? Ans. Two scales means they are holding the weight equally. Just divide by N 4. If a third spring scale is inserted, how much of the weight (in N) of the 4-kg mass does each spring scale now hold up? Ans. Three scales means they are holding the weight equally. Just divide by 3. 4 kg Gravity on the moon is 1/6 th the gravity on Planet Earth. If you weigh 200 N on the moon 5. m = kg what is your mass (in kg)? Ans. G.IVEN(S): gm = (1/6)gE =(1/6) 9.8 m/s 2 = 1.63 m/s 2, FWM = 200 N U. KNOWN: Weight = FWE E. QUATION: = m g S. OLVE: = m g F w = m g 200 N S. UBSTITUTE: = m kg m/s 6. E = N how much do your weigh (in N) on the earth? Ans. G.IVEN(S): g = 9.8 m/s 2, m= kg U. KNOWN: Weight = FWE E. QUATION: = m g S. OLVE: = m g S. UBSTITUTE: E = m ge E = kg 9.8 m/s 2 = N kg what is your mass (in kg) on the moon? Ans. TRICK QUESTION: The mass is the same anywhere. What changes is the weight from place to place depending on gravity m/s 2 = gt_ what is the acceleration due to gravity (in m/s 2 ) on Planet Tupac if your weight there is 1500 N? Ans. G.IVEN(S): T = 1500 N, m= kg U. KNOWN: g = gt E. QUATION: T = m gt S. OLVE: T = m gt F wt m S. UBSTITUTE: F w m = gt = gt 1500 N kg = gt m/s2 = gt

7 7 A 5-kg block is being pulled along a horizontal surface at a constant velocity by a force of 50 N. Friction is present. Assume gravity is 9.8 m/s What is the weight (in N) of the block? 49 N Ans. G.IVEN(S): g = 9.8 m/s 2, m= 5 kg U. KNOWN: Weight = FW E. QUATION: = m g S. OLVE: = m g S. UBSTITUTE: = 5 kg 9.8 m/s 2 = 49 N 5-kg Fx = 25 N 10. What is the Normal Force (in N) on the block? 49 N Ans. According to your formula bank above, the force of weight equals the normal force in an equilibrium situation on a horizontal surface. FW = FN 11. If the block is moving at a constant velocity, what is the acceleration (in m/s 2 ) of the 5-kg block? 0 m/s 2 Ans. By definition, if something is moving at constant velocity, it is NOT accelerating. 12. What must be the frictional force (Ff) acting on the block (in N)? Ff =25 N Ans. According to your formula bank above, in order for there to be no acceleration, the forces to the left must equal the forces to the right. Equilibrium exists. This means that the force of friction equals the horizontal pulling force: Ff = Fx 13. What is the coefficient of friction,, between the block and the surface it rests on? _0.51= Ans. G.IVEN(S): g = 9.8 m/s 2, m= 5 kg, FN = 49 N, Ff =25 N U. KNOWN: coefficient of friction = E. QUATION: Ff = FN S. OLVE: Ff = FN F f = F N 25 N S. UBSTITUTE: = 0.51= 49 N

8 8 Anastacia pulls horizontally on a loaded 120-kg wagon so that its velocity goes from 0 m/s to 4 m/s in 0.5 seconds. Assume gravity is 9.8 m/s 2, friction is present, and that the coefficient of friction between the wagon wheels and the ground is = What is the acceleration (in m/s 2 ) of the wagon? 8 m/s 2 Ans. G.IVEN(S): vi = 0 m/s, vf = 4 m/s, time, t = 0.5 sec U. KNOWN: acceleration = a E. QUATION: a = v t = v f v i t f t i S. OLVE: a = v f v i S. UBSTITUTE: a = 4 m s t f t i 0 m s 0.5 s 0 s a = 8 m/s How far (in m) would the wagon move in 5 seconds? 100 m Ans. G.IVEN(S): a = 8 m/s 2 U. KNOWN: distance = x E. QUATION: x = 1 2 at2 S. OLVE: x = 1 2 at2 S. UBSTITUTE: x = 1 2 at2 = 1 2 (8 m s 2)(5 s)2 = 100 m 16. What is the weight (in N) of the wagon? = 1176 N Ans. G.IVEN(S): g = 9.8 m/s 2, m= 120 kg U. KNOWN: Weight = FW E. QUATION: = m g S. OLVE: = m g S. UBSTITUTE: = 120 kg 9.8 m/s 2 = 1176 N 17. What is the Normal Force (in N) on the wagon (assuming Anastacia is pulling horizontally)? FN = 1176 N Ans. According to your formula bank above, the force of weight equals the normal force in an equilibrium situation on a horizontal surface. FW = FN 18. How much frictional force (in N) is acting on the wagon? N Ans. G.IVEN(S): FN = 1176 N, = 0.6 U. KNOWN: Force of Friction = Ff E. QUATION: Ff = FN S. OLVE: Ff = FN S. UBSTITUTE: Ff = (0.6) (1176 N) = N

9 9 19. What is the net (resultant) force (in N) acting on the wagon? 960 N Ans. G.IVEN(S): m = 120 kg, a = 8 m/s 2 U. KNOWN: Net Force = FNET E. QUATION: FNET = m a S. OLVE: FNET = m a S. UBSTITUTE: FNET = 120 kg (8 m/s 2 ) = 960 N 20. What is the force (in N) applied by Anastacia to the wagon handle to get the net force in Probl. 19? N = Fx Ans. G.IVEN(S): FNET = 960 N, Ff = N U. KNOWN: Pulling Force = Fx E. QUATION: FNET = FX Ff S. OLVE: FNET + Ff = FX S. UBSTITUTE: 960 N = FX N = Fx

10 10 NEWTON S THIRD LAW My Third Law states that for every action, there is an equal and opposite reaction. When I shoot a rifle, the rifle recoils backwards while the bullet goes forwards. QUESTION: Why does the bullet move forward and the rifle backwards? If they are equal and opposite, don t the forces cancel each other out, then? ANSWER: The key is to realize that even though the forces are equal and opposite, they are acting on different objects. One force acts on the rifle and so it moves backwards. The other force acts on the bullet so it moves forward. If the forces acted ON THE SAME object, they would cancel out, but they don t._ A person is log rolling (see figure) in a river. 1. What is the action? _the force of the person on the log pushing backwards 2. What is the reaction? _ the force of the log on the person pushing forwards A person is running on Planet Earth. 3. What is the action? _ the force of the person on the earth pushing backwards 4. What is the reaction? _ the force of the earth on the person pushing forwards 5. How come we can clearly see the effects of the action in the log rolling but no so when the person is running on Planet Earth? _The earth is so big and massive that the acceleration that it undergoes because of our pushing on it is almost negligible and definitely not visible to the naked eye. The log, on the other hand, has a small mass and its acceleration backwards is easily noticed. 6. If you put a rubber band between your thumb and forefinger and stretch, which of the two fingers pulls harder? Explain The action and reaction forces are equal since the rubber band pulls back on our fingers with the same amount of force that we apply to it. No we might feel as if our forefinger is applying more force because it gets tired more easily than the thumb. But that is just because the thumb is built stronger than the forefinger. The forces are the same.

11 11 7. A hammer strikes a nail, knocking it into a piece of wood. a. How does the force on the hammer by the nail compare to the force on the nail by the hammer? _By Newton s Third Law, the forces are equal_. b. What does the force on the hammer by the nail make the hammer do? _The force on the hammer by the nail makes it shiver in our hands but barely slows it down (deceleration)_. c. What does the force on the nail by the hammer make the nail do? The force on the nail by the hammer makes it accelerate into the wood because of its small mass. 8. An action hero hits 10 people in a movie with his fist and nothing happens to him. According to Newton s Third Law, every time he hits somebody with a certain amount of force the person s face or body hits the action hero s fist back with the same amount of force. The action hero s knuckles would be a bloody mess after hitting ten people. 9. A speeding truck makes impact with a bug that splatters on the windshield. Because of the sudden force on the unfortunate bug, it undergoes a sudden fatal deceleration a. Is the corresponding force that the bug exerts on the windshield greater, less than, or the same as that of the bug? greater than less than the same as By Newton s Third Law b. Is the deceleration of the two objects the same? Why or why not? Not at all. The bug undergoes a massive deceleration because of its small mass in comparison to the massive truck. The truck s change in velocity (deceleration) is practically negligible and couldn t be picked up even by the most sensitive instruments. 10. When you jump upwards, the world really does recoil downward. Why can t you notice the motion of the earth? Explain. The earth really gets pushed downwards but you can t notice it because of the earth s massive size in relation to you (also, there might be somebody else jumping on the other side of the earth at the same time). 11. We know that the earth pulls on the moon with a force. Does the moon also pull on the earth? If so, which pull is stronger? Explain: The earth and moon each pull on each other with the same amount of force. Because of the earth s larger mass compared to the moon, however, we perceive the rotation of the moon around the earth and not vice-versa. It is kind of like a big person swinging a small person around in a horizontal circle by the arms. Both the big person and the small person are rotating but we notice the spinning of the smaller person more.

12 12. Identify the action and reaction forces in the case of an object falling without air resistance It might seem as if there is no reaction force here but there is. As the object falls to the ground, it is actually attracting the ground to itself as well. The earth is so large and massive, however, that we don t notice it accelerating towards us. The action force is the force of the earth on the object attracting it and the reaction force is the force of the object on the earth attracting it. 12