Physics 105 - How Things Work - Fall, 2000

Problem Set #2 – Laws of Motion, Part 2

Your friends have dared you to try the “Test-Your-Strength” game at the county fair. Your task is to swing a huge mallet over your head and hit one end of a small lever with it. The lever will then propel a metal weight resting on its other end up a vertical track toward a bell high overhead. If you are strong enough and you hit the lever hard enough with the mallet, the weight will travel all the way to the top of the track and ring the bell. You’ll win a huge stuffed animal and everyone’s admiration. Being such a daredevil and showoff, you can’t resist. You pay the cashier and pick up the mallet.

1. The mallet is heavier than you had expected and you find that you can't swing it well. To make it easier to swing, you "choke up" -- that is, instead of gripping the end of the mallet's handle, you grip the handle about midway between its end and the head of the mallet. You find that you can then swing the mallet more easily. The mass of the mallet didn't change, so why is it easier to swing once you have choked up?

2. When the mallet hits the lever, it exerts an enormous downward force on the lever. This downward force is far greater than the mallet's weight, even with your hands attached to it. How is the mallet able to exert this enormous downward force?

3. When the mallet hits the lever, the lever begins to rotate and begins to push the weight upward. During this process, what torques are acting on the lever and why does the lever undergo angular acceleration in a clockwise manner (according to the figure) rather than counterclockwise?

4. The lever always pushes on the weight for a certain distance as the lever turns. After that distance, the weight loses contact with the lever and must coast up the track on its own, against the force of gravity. The main determinant of how high the weight will go is the angular acceleration of the lever: the faster the lever undergoes angular acceleration, the higher the weight will go. That's because more rapid angular acceleration leads to a larger transfer of energy to the weight, which in turn lets it travel farther up the track before all of its kinetic energy has become gravitational potential energy. In terms of forces, distances, and work, explain briefly (two good sentences should be enough) why a more rapid angular acceleration of the lever leads to a larger transfer of energy to the weight.

You have become bored with sedate sports like street luge, sky surfing, and competitive snowboarding, so you decide to take up something truly thrilling: lawn bowling. In this adrenaline junkie's delight, you and your opponents take turns rolling heavy balls along the grass, trying to see who can leave his/her balls closest to a smaller ball known as the jack. You are allowed to use your balls to knock opponents' balls away from the jack.

5. It's your turn to throw, so you pick up a ball and throw it underhanded across the lawn. The ball arcs briefly through the air before landing on the grass and continuing on toward the jack. At the moment the ball first touches the grass, the ball is not spinning. During the ball's first few moments of contact with the ground, what happens to its total energy, its momentum, and its angular momentum? (report all three)

6. After a few moments, the ball begins to roll smoothly along the grass without sliding at all. During this period of its travels, does the ball's total energy increase, decrease, or stay constant?

7. Exactly as planned, your ball slams head on into your opponent's ball and knocks it far away from the jack. Your ball comes abruptly to a stop following the collision. It has transferred most of its energy and momentum to your opponent's ball. In one sentence each, use words like force, time, and distance to show that (a) energy and (b) momentum were transferred to the opponent's ball.

8. Lawn bowling is normally done on a level lawn. If the lawn had some bowl-shaped depressions in it, then any ball that passed through one of these depressions would tend to accelerate toward the bottom of the depression (and would not go straight). Use the concept of potential energy to show why a ball passing through one of these depressions would accelerate directly toward the bottom of the depression.