Question

1b: what is cart 2s change in momentum? explain how you know. (clue: go back and read the stamp)

Explanation:

To determine cart 2's change in momentum, we use the principle of conservation of momentum (and likely the "stamp" refers to information about cart 1's momentum change, as in a collision, the change in momentum of cart 2 is equal in magnitude and opposite in direction to the change in momentum of cart 1, due to Newton's third law and conservation of momentum in a closed system).

Step 1: Recall the Law of Conservation of Momentum

In a system with no external net force (like two carts colliding), the total momentum is conserved. So, the change in momentum of cart 1 ($\Delta p_1$) and the change in momentum of cart 2 ($\Delta p_2$) satisfy:
$$\Delta p_1 + \Delta p_2 = 0$$
Which rearranges to:
$$\Delta p_2 = -\Delta p_1$$

Step 2: Use the "Stamp" (Cart 1’s Momentum Change)

The clue says to "read the stamp," which likely gives $\Delta p_1$. For example, if cart 1’s change in momentum is, say, $+X$ (where $X$ is a value from the stamp), then cart 2’s change in momentum is $-X$ (equal magnitude, opposite direction).

Example Application (If Stamp Gives $\Delta p_1 = +5\ \text{kg·m/s}$)

If $\Delta p_1 = +5\ \text{kg·m/s}$, then:
$$\Delta p_2 = -\Delta p_1 = -5\ \text{kg·m/s}$$

Key Reasoning

In collisions (or interactions), the impulse (change in momentum) on one object is equal and opposite to the impulse on the other (Newton’s third law: $F_{12} = -F_{21}$, and impulse $J = F\Delta t$). Thus, $\Delta p_2 = -\Delta p_1$.

Answer:

To find cart 2’s change in momentum, use the conservation of momentum (or Newton’s third law): $\boldsymbol{\Delta p_2 = -\Delta p_1}$, where $\Delta p_1$ is from the "stamp" (cart 1’s momentum change). For example, if $\Delta p_1 = +X$, then $\Delta p_2 = -X$ (same magnitude, opposite direction).