Amy (mass 60kg) and Bob (mass 90kg) have gone fishing together. They find a good

Question

Amy (mass 60kg) and Bob (mass 90kg) have gone fishing together. They find a good spot and they sit in the center of the boat, right next to a stationary lilypad (we shall use the lilypad as a reference point where x=0). their boat is 4m long and has a mass of 70kg. Everything begins at rest.

A. How much total momentum does the system begin with?

B. Where is the center of mass of the system currently located? (The boat is uniform so by itself its CM is at its geometric center. Remember that amy and bob are currently sitting at x=0)

At some point, Amy gets up and walks to the left end of the boat, in the negative x direction, at a leisurely speed of .5 m/s. bob remains seated. Assume that the water is so still and the boat so buoyant that there is no resistive force from the water.

C. The boat and bob will move. which direction will they move and how fast will they go?

D. What force is actually responsible for causing the boat to accelerate up to the speed?

E. Amy sits down at the left end of the boat and stops moving. does the boat contunue moving or does it stop as well?

Now bob gets up and walks in the posotive x direction to the right end of the boat. Amy and bob have now each walked 2m away from each other toward the opposite ends of the boat, but because the boat shifted while they walked, they are not necessarily located at x=-2m and x=+2m

F. Because there were no external forces from the water, the center of mass of the system must sitll be located at its original position. therefore, is the center of the boat now located to the left or the right of the lilypad? (Hint: you can also thing of it this way: is the lilypad at x=0 now closer to amy or to bob?)

Explanation / Answer

Part A)

Initial momentum is zero since momentum = mv and everything is at rest.

Part B)

The lilly pad reference point is zero, so we base the center of mass from that.

We are told that the boat is uniform and since Bob and Amy sit in the center at x = 0, the net center of mass is at zero. All of the mass is currently concentrated at the center at the lilly pad reference point of zero.

Part C)

Since Amy moves to the left, Bob and the boat will move to the right. The total momentum must stay at zero, so

(60)(.5) = (90 + 70)(v)

v = .1875 m/s

Part D)

As Amy walks, her shoes make contact with the bottom of the boat and there is a frictional force that allows Amy's shoes to stick to the boat as she walks forward (thats how we all walk - friction between what is on the bottom of out feet (shoes or skin) and the surface. Thus the reaction force to that friction causes the boat and Bob to move backwards

Part E)

When Amy stops moving, so does the boat and Bob. Momentum must be conserved so the velocity must go back to zero overall

Part F)

Since Bob is heavier, the center of mass is closer to him. He is closer to the lilly pad. The way it would work by a formula of Force times distance = Force times distance. The weight is the force, so since Bob has more weight, he would have to have less distance.

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