A man with a mass of 65 kg stands up in a 64-kg canoe of length 4.0 m floating on water. He walks from a point 0.75 m from the back of the canoe to a point 0.75 m from the front of the canoe. Assume negligible friction between the canoe and the water. How far does the canoe move? (Assume the canoe has a uniform density such that its center of mass location is at the center of the canoe.)
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an canoe is 5.67 in m how long in cent?
To find out how far the canoe moves when the man walks, we need to consider the conservation of momentum. When the man walks towards the front of the canoe, he exerts a backward force on it due to his mass. According to Newton's third law of motion, the canoe exerts an equal and opposite force on the man.
1. First, let's calculate the total initial momentum of the system (man + canoe). The initial momentum is given by the product of mass and velocity. Since the man and the canoe are initially at rest, their initial momentum is zero.
2. As the man walks towards the front of the canoe, he exerts a backward force due to his mass. This force causes the canoe to move forward.
3. To counterbalance the backward force, the canoe moves forward, and in doing so, it acquires some momentum in the forward direction.
4. We can calculate the change in momentum of the canoe using the principle of conservation of momentum. The final momentum of the canoe is equal and opposite to the initial momentum of the man.
5. The momentum of an object is given by its mass multiplied by its velocity. Since the man is at rest initially, his momentum is zero. Therefore, the change in momentum of the canoe is also zero.
6. Since the canoe experiences no change in momentum, it does not move during the man's walk from the back to the front.
Therefore, the canoe does not move when the man walks from a point 0.75 m from the back to a point 0.75 m from the front of the canoe.