HW #9

1. 33. Many auto passengers suffer neck injuries when struck by cars from behind. How does NL of I apply? Why headrests? • The body is accelerated forward with the seat, but the head remains (behind) at its current velocity until an unbalanced force pulls it forward (which is the neck, which can cause whiplash if forceful enough). • Headrests provide the unbalanced force needed to accelerate the head with the body.

2. 31. Consider two rotating bicycle wheels, one filled with air and the other with water. Which would be more difficult to stop rotating? Explain. • The bicycle wheel filled with water would be the more difficult wheel to stop rotating because it has the greater amount of rotational inertia or resistance to change its rotational motion.

3. HW #9

4. Chapter 3Newton’s First Law of Motion Pages 42-44 (21, 22, 23, 26, 27, 31, 35-37, 43, 46-49)

5. 21 21. a. Greatest to least resistance to change in motion BACD b. Greatest to least weight BACD c. greatest to least normal support BACD

6. 22 22. a. Greatest to least force required to keep them going A=B=C (no force) b. Greatest to least force required to stop them in the same time interval CBA W =mg w = 50 kg x 9.8 m/s2 weight = 490 N or 500 N

7. 26 1 N = ? lb 1 N x 1 lb/4.45 N = 0.2 lb

8. 27 w = mg 300 N = m x 9.8 m/s2 300 N / 9.8 m/s2 = 30.6 kg or 31 kg (rounded)

9. 31. • NO FORCE IS REQUIRED TO KEEP AN OBJECT MOVING IF NO OTHER FORCES ARE ACTING ON IT. INERTIA

10. 35. Suppose you place a ball in the middle of a wagon that is at rest and then abruptly pull the wagon forward. Describe the motion of the ball relative to the ground. • Except for some change in motion due to friction between the wagon and ball, the will be no motion of the ball relative to the ground; but relative to the wagon, the ball will appear to move toward the back.

11. 36. To pull a wagon across a lawn at a constant velocity, you have to exert a steady force. Does this contradict Newton’s first law? • No. The key is net force. Your steady force is balancing the rolling friction, which means that the net force = 0, which means dynamic equilibrium, which means constant velocity, which means no acceleration. Removing friction would allow the wagon to continue moving at the same velocity without any more pull force.

12. 37. When a junked car is crushed into a compact cube, does its mass change? Its volume? Its weight? • Mass remains unchanged. • Volume is reduced. • Weight remains unchanged (no change in position within the gravitational field so no change in gravitational force)

13. 43. The head of a hammer is loose and you wish to tighten it by banging it against the top of a workbench. Why is it better to hold the hammer with the handle down as shown rather than with the head down? • The handle stops when it hits the bench, but the relatively massive head tends to keep moving towards the handle and tightens.

14. 46-49 • 46. Normal Force (equal to and opposite of weight) • 47. Weight and tension forces in equilibrium • 48. Weight and tension, with tension force greater than weight. Upward acceleration • 49. Weight only with a slight amount of air resistance.

15. Chapter 6.1-6.4Newton’s 2nd law of Motion Pages 99-102 (1, 3-6, 8, 11, 22, 24, 25, 34, 37, 40)

16. 1. What causes acceleration? • Unbalanced forces. • 3. Is acceleration directly proportional to mass, or is it inversely proportional to mass? • Acceleration is inversely proportional to mass. • 4. If two quantities are inversely proportional to each other, does that mean as one increase the other increases also? • No, it means the opposite (as one increases, the other decreases)

17. 5. If the net force acting on a sliding block is tripled, what happens to the acceleration? • The acceleration also triples. It’s a direct relationship! • 6. If the mass of a sliding block is tripled at the same time the net force on it is tripled, how does the resulting acceleration compare with the original acceleration? • The resulting and original acceleration do not change. They are the same. 10N/1kg = 10 m/s2 and so does 30 N/3kg.

18. 8. Suppose you exert a push on a crate that rests on a level floor, and it doesn’t move. How much friction acts compared to with your push? • The same magnitude as your push, but oppositely directed. • 11. When do you produce more pressure on the ground, standing or lying down? • Standing. Same force, less area of application, more pressure!

19. 22. • A) D, A=B=C • B) A=C, B=D • 24. C,D,B, A • 25. Fnet = ma, so a = Fnet/m; 200 N/40 kg = 5 m/s2 • 34. A car moves forward as the brakes are applied. During braking, the velocity and acceleration of the car are in opposite directions. Agree or disagree? • Agree! • 37. When you lift the lineman, the force of friction is reduced, making it easier to move the lineman.

20. 40. A common saying goes” It’s not the fall the hurts you; it’s the sudden stop.” Translate this into Newton’s laws of motion. • By a = F/m • A sudden stop means a very large acceleration (change in motion!). Seeing that the mass stays constant, the force, being directly proportional to acceleration, would also increase greatly.

21. Chapter 7.1-7.4Newton’s 3nd law of Motion Pages 118-122 (1, 3, 7, 8, 20, 24, 29, 36, 39, 40)

22. Chapter 7, pg 118-123 • 1. Can an action force exist without a reaction force? • No. • 3. When you walk along a floor, what pushes you? • The floor! You push on the floor, and the floor pushes back on you with equal and opposite force. • 7. If the world pulls you downward against your chair, what is the reaction force? • The reaction force is the chair pulling upwards on the Earth.

23. Chapter 7, pg 118-123 • 8. When a cannon is fired, are the forces on the cannonball and on the cannon equal in magnitude? Are the accelerations of the two equal? • Forces are equal in magnitude, but acceleration is unequal; • 9. When a cannon is fired, why does the cannonball and the cannon have very different accelerations? • Equal forces on two different masses produce two different accelerations (the cannonball is more greatly accelerated than the cannon)

24. Chapter 7, pg 118-123 • 20. Fill ins: inertia, acceleration, action and reaction • 24. When you rub your hands together, can you push harder on one hand than the other? • No. Each hand pushes equally on the other. • 25. Your weight is the result of the gravitational force of the Earth on your body. What is the corresponding reaction force? • Your body pulling on the Earth with equal and opposite force.

25. Chapter 7, pg 118-123 • 29. Why is it easier to walk on a carpeted floor than on a smooth, polished floor? • One can exert a greater force on carpet than on a polished floor because of the greater friction. This, in turn, provides a greater reaction force to provide traction for walking. • 36. The impact force is the same for both. The car has less mass (thus, less inertia) than the van, so the acceleration for the car is greater than for the van.

26. Chapter 7, pg 118-123 • 39. Consider two carts, one twice as massive as the other, that fly apart when squeezed together. When released, how fast does the heavier cart roll compared to the lighter cart? • The heavier cart rolls twice as slow (it is twice the mass, so given the same force, it has half the acceleration) • 40. What force propels a rocket when it is in a vacuum (a place with no matter)? • The action force is the rocket pushing on the exhaust gases, so the reaction force is the gases pushing on the rocket with equal force in the opposite direction. Recoil reaction!