For the following questions: You are standing in canoe at rest, on a perfectly s

Question

For the following questions: You are standing in canoe at rest, on a perfectly smooth lake. There is no wind. Your mass is 60 kg, and the mass of the canoe is 90 kg. You start to walk East at 3 m/s.

1. You then stop walking in the canoe. What does the canoe do?

A. None of the given answers is correct.

B. The canoe starts moving east.

C. The canoe continues moving west with the same speed as before.

D. The canoe also stops.

2. The canoe is three meters long. As you walked from one end of the canoe to the other, how far did the center-of-mass of the person-and-canoe system move?

A. 2 m

B. zero

C. 0.9 m

D. none of the given answers is correct.

Explanation / Answer

(1.) Initially, you and the canoe were both at rest. That means total intial momentum was zero for this system. Then you started walking on the canoe. Since, there is still no external force on this system, linear momentum must be conserved and thus will be zero at all times no matter how you walk or dance on it. So, to componstate your momentum the canoe will move in the west as you move in the east in such a way so as to make whole momentum of the system zero. But, as soon as you stop, your canoe must also stop.

Thus, option (D) is the answer.

(2.) As explained in the previous part, since there is no external force on person-canoe system, it's centre of mass cannot be displaced. Thus, no matter how you walked over it, the boat will always move in a way so as to exactly cancel any net displacement of the centre of mass of the system.

Thus, option (B) will be the right answer.

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