1. You are standing on the dock, looking at the batteau. As the batteau rests motionless on the river, a few feet from the dock, (A) what two forces is it experiencing and (B) what is the net force on it? (Identify each force or net force and give its amount and direction. You can identify the force by name or by describing it.)

Answer: (A) The batteau is experiencing its weight downward and a force equal in amount (or magnitude) to its weight upward from the water. (B) The net force on the batteau is zero.

Why: The batteau is motionless, so it is not accelerating. Therefore, the net force on it must be zero. However, we know that it experiences its weight, a downward gravitational force, so the water must be supporting it with an equal force in the upward direction.

2. Using the pole, you push the river bottom southward with a force of 250 newtons (56 pounds). What force does the river bottom exert on you (A) when the batteau is motionless? (B) when the batteau is already moving northward at 3 meters-per-second (6.7 miles-per-hour)? (Give the amount and direction for each force.)

Answer: In both (A) and (B), the river bottom pushes you northward with a force of 250 newtons.

Why: As recognized by Newton's third law, forces always occur in equal but oppositely directed pairs. When your pole pushes the river bottom southward with 250 newtons of force, the river bottom pushes the pole northward with 250 newtons of force. The velocities of the objects simply don’t matter here.

3. Your batteau is by far the lightest one moored at the dock. It's now late on a moonless Saturday evening and you're trying to find your batteau in total darkness. You reach out and touch one batteau after the next, but they all feel identical. You could try lifting each batteau, to see which one is lightest, but there is another way to identify your batteau without moving it up or down. Using only your hand and the laws of physics, how can you tell which boat is yours?

Answer: You could shake each batteau horizontally. The one that responded (accelerated) most easily is your batteau.

Why: The lightest batteau is also the one with the least mass. As such, it accelerates most rapidly in response to a given horizontal force. By shaking the various bateaux, you'll quickly find the one that's easiest to shake and that will be yours.

4. You are heading northward with a load of passengers. As you approach the dock, it's time to slow down. (A) Which way should you push on the river bottom in order to slow the batteau down? (B) As you slow down, in which direction is your velocity? (C) As you slow down, in which direction is your acceleration?

Answer: (A) You should push the river bottom northward to slow down. As you slow, (B) your velocity is northward and (C) your acceleration is southward.

Why: Your inertia alone will carry you to the dock with a constant northward velocity, so you have to act to slow yourself down. By push the river bottom northward, you cause it to push you southward. This southward force makes you and the batteau accelerate southward. Although your velocity was and continues to be northward until the moment you stop altogether, your acceleration during the slowing period is southward.

5. You start far from the ramp and begin to pole furiously toward it. By the time you reach the ramp, you are traveling fast enough to go all the way up and over the ramp. You stop poling once you reach the ramp and let the batteau coast. As the batteau coasts up the flat surface of the ramp, (A) what 3 forces act on it? (B) In which direction does each of those forces act? (For simplicity, consider yourself part of the batteau so that there is only a single object sliding up the ramp.)

Answer: (A) The three forces are the batteau's weight, the support force from the ramp, and sliding friction. (B) The weight acts straight down, the support force acts at right angles to the ramp's surface, and sliding friction acts directly downhill (toward the start of the ramp).

Why: As the batteau moves along the ramp's surface, it still has a weight (which always points directly downward). It is prevented from entering the surface of the ramp by the ramp's support force (which always points directly away from the ramp's surface). And as the batteau moves up the ramp, the ramp exerts a sliding friction force in the direction opposite the batteau's velocity, so directly downhill.

6. You and the batteau coast off the top of the ramp and travel through the air. You are so startled to have made the jump successfully, that you let go of the pole while the batteau is in the air. Amazingly, the pole appears to hang motionless in front of you even though you are not touching it. Only when the batteau lands in the water does the pole suddenly begin to shift toward the floor. Explain why the pole didn't move relative to you as the batteau was falling.

Answer: Both the batteau and the pole fall freely and, since all freely falling objects fall at the same rate (accelerate downward at the same rate), they fall together.

Why: Objects that begin to fall with identical velocities travel parallel paths as they fall. That's because they coast and fall together. Coasting keeps them moving at their starting velocities, while falling causes those starting velocities to change in the downward direction at 9.8 m/s².

7. You are so excited to have completed the jump that you grab your pole at its middle and try to spin it in your hand like a baton twirler. But the pole is heavy and long and you have a difficult time starting it spinning. What physical quantity or characteristic of the pole is making it so hard to start the pole spinning?

Answer: The pole has an enormous moment-of-inertia (or rotational mass).

Why: When you twist something, you exert a torque on it and it may undergo angular acceleration. That angular acceleration is inversely proportional to the object's moment-of-inertia (or rotational mass), the measure if its rotational inertia. Since the pole has a huge moment-of-inertia, you don't get much angular acceleration from it, despite subjecting it to large torques.

8. It's the end of the batteau season and you have to pull your batteau up a ramp and onto the shore. (A) Use the relationship between force, distance, and work to prove that you are transferring energy to the batteau as you pull it up the ramp at a steady speed. (B) What becomes of the energy you transfer to the batteau?

Answer: (A) Since the ramp force on the batteau is downhill, you must be pulling the batteau uphill to keep it moving steadily up the ramp. Because the batteau moves in the direction of the force you exert on it, you are doing work on the batteau. Since work is the mechanical means of transfering energy, you are therefore transfering energy to the bateaux. (B) The batteau's altitude increases, so its gravitational potential energy is increasing.

Why: Whenever you push or pull the batteau in the direction that it moves, you do work on it. In this case, you are pulling the batteau uphill as it moves uphill, so you are doing work on it. Work is a transfer of energy, so you are transferring energy to the batteau. That energy is stored in the gravitational force between the batteau and the earth, so the batteau's gravitational potential energy increases.