A plank is floating motionless on a lake. A rabbit now hops from the right end o

Question

A plank is floating motionless on a lake. A rabbit now hops from the right end of the plank to the left end. The length of the plank is L. The plank is initially at rest. The mass of the rabbit is mR. The mass of the plank is mp. The plank moves only along its length, in the x-direction. As the rabbit moves on the plank, describe in a sentence or two the corresponding motion of the center of mass. (In this problem, we are concerned only with motion in the x-direction.) Describe in words, the difference in the initial and final position of the center of mass in the case that (i) the rabbit hops the full length of the plank, versus (ii) the rabbit takes two hops to get to the left end of the plank. For the case that the rabbit hops only half the distance to the end of the plank, determine the distance that the plank moves. Now, determine the distance that the plank moves when the rabbit finishes his excursion and hops from the center of the plank to the left end. What is the total motion of the plank for the two hops together? For the case that the rabbit hops the full length of the plank in one hop, determine the distance that the plank moves. Compare the two-hop versus one-hop answers. After the rabbit has landed at the left-end of the plank, say, after one minute, how far has the plank moved further than when he had just landed?

Explanation / Answer

a) COM does not move as no external force..

b) both will be same....as final position of rabbit same..

c) mp x = mr (l/2-x) [let plank move x distance, com is at rest] => x = mr/(mr+mp) *l/2

d) same as c

e) total distance = mr/(mr+mp) *l

f) same as e

g) they are same

h) it wont move furthur as COM remains at rest..

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