Question

Two carts, one of mass 2m and one of mass m, approach each other with the same speed, v. When the carts collide, they hook together. Assume that positive momentum is to the right.

A diagram of two rolling carts on a flat horizontal surface rolling toward each other at a velocity v. The cart on the left is labeled m and the cart on the right is labeled 2 m.
Which graph best represents the momentum of both carts over time, before and after the collision?

A graph with momentum on the y axis measured in kilogram meters per second and time on the x axis measured in seconds. There are no values on the axes. There are two curves on the graph. The first starts above the x axis and is horizontal before curving downward to the x axis labeled 2 m cart. The second curve starts below the axis, the same distance below as the first one was above, and is horizontal before curving upward toward the x axis at the same time and labeled m cart. Where they meet is labeled Collision. Both curves meet at the x axis at the same time and are both on the x axis for a time period labeled Combined carts.
A graph with momentum on the y axis measured in kilogram meters per second and time on the x axis measured in seconds. There are no values on the axes. There are two curves on the graph. The first starts above the x axis and is horizontal before curving downward to the x axis labeled 2 m cart. The second curve starts below the axis, the same distance below as the first one was above, and is horizontal before curving upward toward the x axis at the same time and labeled m cart. Where they meet is labeled Collision. Both curves meet at the x axis at the same time and are both on the x axis for a time period labeled Combined carts.
A graph with momentum on the y axis measured in kilogram meters per second and time on the x axis measured in seconds. There are no values on the axes. There are two curves on the graph the first starts above the x axis and is horizontal before curving downward toward the x axis labeled 2 m cart. The second curve starts below the axis, a smaller distance below as the first one was above, and is horizontal before curving upward toward and crosses the x axis and is labeled m cart. Where they meet is labeled Collision. Both curves meet above the axis at the same time and both go horizontal above the x axis for a time period labeled Combined carts.
A graph with momentum on the y axis measured in kilogram meters per second and time on the x axis measured in seconds. There are no values on the axes. There are two curves on the graph the first starts above the x axis and is horizontal before curving downward toward the x axis labeled 2 m cart. The second curve starts below the axis, a smaller distance below as the first one was above, and is horizontal before curving upward toward and crosses the x axis and is labeled m cart. Where they meet is labeled Collision. Both curves meet above the axis at the same time and both go horizontal above the x axis for a time period labeled Combined carts.
Mark this and return

Answer 1

The third graph.

Reason: Initially p_m = +mv (small positive) and p_2m = -2mv (larger negative). During the collision the momenta change by internal impulses but total momentum is conserved (P = mv - 2mv = -mv). After they hook together both carts move left with v_f = -v/3, so their individual momenta are p_m' = -m v/3 and p_2m' = -2m v/3 — both negative (same direction) and unequal in magnitude. The third graph is the one that shows the light cart's momentum crossing the axis and, after the collision, both momenta on the same side of the axis (i.e., moving left).