Chapter 2

Exercises

2. A massive cleaver is more effective in chopping vegetables because its greater mass contributes to greater tendency to keep moving as the cleaver chops through the vegetables.

4. A stone will fall vertically if released from rest. If the stone is dropped from the top of the mast of a moving ship, the horizontal motion is not changed when the stone is dropped. Like Exercise 5 in Chapter 3, the path of the stone will be parabolic as seen from a frame of reference at rest on shore. If air resistance is not a factor, and the ship doesn't accelerate while the stone falls, it will move as far horizontally as the ship moves in the same time, and hit the same place below that it would hit if the ship were at anchor. From the frame of reference of the moving ship, the stone falls in a vertical straight line path.

6. The first of the three questions in this exercise is similar to Exercise 5. If the ball is shot while the train is moving at constant velocity (constant speed in a straight line), its horizontal motion before, during, and after being fired is the same as that of the train; so the ball falls back into the chimney as it would have if the train were at rest. But if the train accelerates, the ball will miss, because the ball's horizontal speed will match the train speed as the ball is fired&emdash;but the train continues to gain speed while the ball is in the air, so the chimney has advanced in front of the ball by the time it falls back to the train (or it falls in front of the chimney if the acceleration is negative&emdash;slowing down). On a circular track, the ball would also miss the chimney, for the ball will move along a tangent to the track while the train turns away from this tangent. So the ball returns to the chimney in the first case, which is a different answer to the second and third cases because of the change in motion (acceleration).

8. Ten kilograms weighs 98 N on the earth (weight = mass * gravity). On the moon the weight would be 1/6 of 98 N = 16.3 N. The mass be 10 kg everywhere.

9. Mass in kilograms is weight in pounds divided by 2.2 (if we are at the earth's surface). One's weight in newtons is found by multiplying one's weight in pounds by 9.8/2.2. For example, if you weigh 100 pounds, your mass is 100/2.2 = 45.45 kg. Your weight in newtons is 100 (9.8/2.2) = 445.5 N. Once mass is determined, find weight by using the defining relationship, Weight = mass * gravity.

11. If an object has no acceleration, we can conclude that no net force acts on it. There may be any number of impressed forces, but if the object does not accelerate their resultant will be zero.

12. Acceleration and velocity are quite different concepts; while it is true net force and acceleration will always be in the same direction, it does not follow that net force and velocity will always be in the same direction. One example to the contrary will defend this; namely anything that decelerates, such as a car that slows to a stop by friction. The friction force is in a direction opposite to the car's velocity.

14. The scale will read half her weight, [In this way, the net force (upward pull of left rope + upward pull of right rope -weight) = 0.]

15. In the left figure, Harry is supported by two strands of rope that share his weight (like the little girl in the previous exercise). So each strand supports only 250 N, below the breaking point. Total force up supplied by ropes equals weight acting downward, giving a net force of zero and no acceleration. In the right figure, Harry is now supported by one strand, which for Harry's well-being requires that the tension be 500 N. Since this is above the breaking point of the rope, it breaks. The net force on Harry is then only his weight, giving him a downward acceleration of g. The sudden return to zero acceleration changes his vacation plans.

17. The scale will read 100 N, the same it would read if one of the ends were tied to a wall instead of tied to the 100-N hanging weight. Although the net force on the system is zero, the tension in the rope within the system is 100 N, as shown on the scale reading.

19. High-speed meteorites grazing the earth's atmosphere burn up because of friction against the air.

20. When held at rest the upward support force equals the weight of the apple and the net force is zero. When released, the upward support force is no longer there and the net force is the weight of the apple, 1 N. (If the apple falls fast enough for air resistance, then the net force will be less than 1 N, and eventually reach zero if the apple falls fast enough for the air resistance to build up to l N.)

22. If the dog wags its tail (action), the tail will in turn wag the dog (reaction). How noticeable this is depends on the relative masses of the dog and the tail being wagged!

25. In accord with Newton's 3rd law, if the earth exerts a force of 1000 N on the satellite, the satellite will exert an oppositely directed 1000 N of force on the earth. Or better, the earth and the satellite pull on each other with 1000 N of force.

27. The strongman can exert only equal forces on both cars, just as your push against a wall equals the push of the wall on you. Like-wise for two walls, or two freight cars. Since their masses are equal, they will undergo equal accelerations and move equally.

28. Like the preceding exercise, the force on each cart will be the same. But since the masses are different, the accelerations will differ. The twice-as-massive cart will undergo only half the acceleration of the less massive cart. The less massive cart will spring apart with twice the speed of the more massive cart.

30. In accord with Newton's 3rd law, the force on each will be of the same magnitude. But the effect of the force (acceleration) will be different for each because of the different mass. The more massive truck undergoes less change in motion than the yolks.

31. The forces on each are the same in magnitude, and their masses are the same, so their accelerations will be the same. They will slide equal distances of 6 meters to the midpoint.

32. The twice-as-massive person will undergo half the acceleration and slide half as far as the less massive person&emdash;that is, 4 m for the more massive person, and 8 m for the less massive person [so their combined sliding distance equals the 12 m].

35. Explain to your friend the difference between velocity and acceleration. Further explain that to say acceleration decreases is to say the rate of increase in velocity decreases&emdash;the rate decreases, not the velocity. As an example, if the rate remained the same, then the diver would pick up the same amount of velocity each second. But the rate in fact decreases because of the buildup of air resistance, so the amount of pick up each second is less and less. When the rate of increase reaches zero, terminal velocity has been reached and stays at the same maximum value all the way down.

36. The terminal velocity attained by the dropped tennis ball is the same whether dropped from 50 stories or 20 stories. Once terminal velocity is reached, falling extra distance does not affect the speed with which it hits the ground.

Problems

1. a. Fnet = 30 N + 20 N = 50 N, in the direction of the forces.

b. Fnet = 30 N - 20 N = 10 N, in the direction of the 30-N force.

3.a. Fnet = ma = 0, because a = (change in velocity)/time = 0 (no change in speed), so Fnet = 0.

b. Since the box requires a force of 100 N to be moved from a position at rest, the frictional force = - 100 N. Negative to illustrate it is in the opposite direction to the force that would be applied to push it.