Two identical carts sitting on an airtrack, are pushed towards each other. The c

Question

Two identical carts sitting on an airtrack, are pushed towards each other. The carts approach each other, then bounce off elastically. The figure below shows the carts approaching each other with equal speed. In the movie of the collision, the frame shown below is the one in which the carts are the closest to each other during the collision. At this instant of time, identify all the forces acting on the left cart. Are any of these forces of the same size, so that they will cancel? After bouncing off each other, the carts move apart once again. What are the respective velocities of the left and right carts? After the collision, cart 1 has reversed direction and moves to the left. a. Click on and drag next to cart 1 one of the arrows shown below which best represents the velocity of cart 1 after the collision. Repeat for cart 2 A B C D E F b. Is the magnitude of the change in momentum for cart 1 greater than, less than, or equal to the magnitude of the change in momentum for cart 2? Explain or show your calculations. Discuss what is incorrect in the following statement: "Cart 2 will move to the right after the collision, but it would move faster if cart 1 were to come to a stop, giving cart 2 all its momentum."

Explanation / Answer

when the two carts collides with each other their linear momentum will remain conserved and they will apply normal force on each other as the forces are acting on different bodies they won't cancel each other.

applying conservation of linear momentum -

mv0 - mv0 = mv + mv'

mv + mv' = 0

v = - v'

hence direction will be reveresed but magnitude of the velocity will remain same.

2> applying conservation of linear momentum -

mv0 + m*0 = - mv + 4m*0

v = - v0

change in momentum of cart 2 = 0

change in momentum of cart 1 = - mv0 - mv0 = -2mv0

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