Physics 101: How Things Work

These are the answers to the even-numbered exercises and problems, and all of the cases assigned in Chapter 2. The answers to the others appear in the back of the textbook.

Exercises

2. The propellers have rotational inertia (as measured by their moments of inertia). The propellers must undergo angular acceleration and only gradually speed up to their full rotational speeds.

4. A boomerang or horseshoe's center of mass is in the air between the two arms of the object.

8. When you arm is pointing straight out in front of you, any weight force exerted on your hand is at right angles to the lever arm between your shoulder and hand and produces a large torque about your shoulder. On the other hand, when you arm is at your side, any weight force exerted on your hand is directed away from your shoulder and produces no torque about your shoulder.

18. The farther out the limb that your weight is exerted on the branch, the larger the torque you produce on the limb and the more likely it is to begin rotating.

30. While you are traveling straight at constant speed, you are coasting and experience zero net force. It's only when you try to accelerate horizontally that you need a frictional force from the pavement and find yourself sliding on ice instead.

36. Because of your rotational inertia (as measured by your moment of inertia), you need an external torque in order to begin spinning. While you aren't touching anything in the swivel chair, you can't obtain any external torque and can't start spinning.

40. When the bowling ball is rotating, it has rotational kinetic energy. That energy must come from somewhere and since the only type of energy the ball has as it first begins to slide down the lane is translational kinetic energy, the rotational energy must come from the translational kinetic energy. As a result, the translational kinetic energy must decrease, so the ball must slow down.

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Problems

6. The jaw will exert a force of 100 N on the nut.

8. The fly's momentum is 0.0001 kg m/s.

10. It will take 12 seconds to push the car up to 3 m/s.

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Cases

1a. The person wearing skates moves forward. 1b. Because the bus cannot exert a force on the person. 1c. The friction between the shoes and the bus makes the person accelerate with the us. 1d. The net force is zero. 1e. The frictional force between the shoes and the bus is not enough to make the person decelerate as fast as the bus.

3a. The net force is zero. 2b. 3.0 x 10⁶ kg m/s 2c. - 3.0 x 10⁶ kg m/s 2d. The time to stop the train is the change in momentum divided by the force: 6.0 x 10^{3 = 1 hour and 40 minutes.}

5a. The average force you exert on the pedals equals your weight. 5b. Your foot does positive work on the pedal, and the pedal does negative work on your foot. 5c. The pedal does positive work on your foot, and your foot does negative work on the pedal. 5d. Since you exert a greater force on the machine on the downward part of the cycle than the machine exerts on you during the upward cycle, you are doing positive net work on the machine. 5e. The final form of the energy is mostly heat.

6a. The fact that the bottles have much more mass than the ball means that the ball must hit at a high speed to topple the bottle. (And you must hit two of them at once with a high speed to topple all three. 6b. The glass plate provides little friction, so the coin just slides across it. Even if the plate contains a depression, energy conservation will prevent the coin from stopping if the friction is insignificant. 6c. To be swung past the pin, the ball must have angular momentum about a vertical axis through the pin. To hit the pin, the ball must have zero angular momentum about a vertical axis through the pin when it strikes. Conservation of angular momentum prevents the ball from losing its initial angular momentum and striking the pin (until it has orbited many times and eventually lost it through air resistance). 6d. Unless the ball is thrown so that the apex of its trajectory is precisely at the basket, it will arrive with excess kinetic energy which cannot be lost (through friction) in time to avoid bouncing out of the basket.