Friday, August 10, 2018

newtonian mechanics - Will the box move?


Here is a man in a box with wheels on a frictionless surface.


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Case 1 - The person constantly pushes the box while standing near its wall. Why doesn’t it move? (I know it is because of the 3rd law, but I am not able to understand the “why” here, please explain.)


Case 2 - If he runs inside the box will it move backwards? (Due to the force of his feet?)


Case 3 - If he runs from the right side to the left one, and just before colliding with the left side of the box, he jumps and while he is in the air, he collides with the box. Will it move?



Answer



Case 1 - The box will not move. Although the man is pushing on the wall, the floor is pushing on the man though his feet. These cancel each other out, meaning there's no net force on the whole system.


Case 2 - The box will move as the man walks. As he steps forward, the box moves backwards. How much will depend on the relative masses of the box and the man. If they weigh the same, the box will move as much as the man.



Case 3 - The box will come to rest. As the man starts running, both he and the box start to move, with their momentum equal and opposite. When the man runs into the side, the momentum cancels out again. It doesn't matter if he jumps or is still on the floor.


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