3) Two carts on an air track are pushed towards each other. Initially, cart 1 mo

Question

3) Two carts on an air track are pushed towards each other. Initially, cart 1 moves in the positive x direction and cart 2 moves in the negative x direction. They bounce off each other elastically. The graphs below describe some of the variables associated with the motion as a function of time. For the experiment described and for each item in the list below, identify which graph is a possible display of that variable as a function of time. If none apply, write N (for none).

(a) the momentum of cart 1
(b) the force on cart 1
(c) the position of cart 2
(d) the force on cart 2
(e) the position of cart 1.

Explanation / Answer

A) Momentum = mv: Velocity is positive for cart 1, as is mass. velocity changes after impact, reversing suddenly, but is quickly stable. Therefore Graph D is correct. B)Force on cart 1 will be 0 until impact, briefly negative (to reverse velocity) and then 0 again: Graph C C)Position of cart 2 will be positive (since it's above the point of impact), decreasing towards 0 (the point of impact) and then increasing after impact: B is the only position graph, but it's for Cart 1 since it starts below the point of impact, approaches it, and then backs away while being negative the whole time, so there is no graph for this: N d) Force on cart 2 will be the opposite of cart 1 for the same reason (0 to briefly positive to reverse velocity to 0): Graph C e) we've already discussed this (see point C) therefore graph B is correct

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