---
title: "Cart A of mass \\(M\\) is moving with initial speed \\(v_0\\) to the right on a horizontal, frictionless track. It approaches Cart B of mass \\(3M\\), which is initially at rest. The carts can be equipped with different bumpers to change the type of collision that occurs when they meet."
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url: "https://nerd-notes.com/ubq/110101/"
date_modified: "2026-03-26T22:33:44+00:00"
---

# Cart A of mass \(M\) is moving with initial speed \(v_0\) to the right on a horizontal, frictionless track. It approaches Cart B of mass \(3M\), which is initially at rest. The carts can be equipped with different bumpers to change the type of collision that occurs when they meet.

Cart A of mass \(M\) is moving with initial speed \(v_0\) to the right on a horizontal, frictionless track. It approaches Cart B of mass \(3M\), which is initially at rest. The carts can be equipped with different bumpers to change the type of collision that occurs when they meet.

![A horizontal line representing a track. On the track, there are two rectangular carts. The left cart is labeled 'Cart A' and has 'M' written inside it. It has a right-pointing vector arrow above it labeled 'v_0'. The right cart is labeled 'Cart B' and has '3M' written inside it. It has no velocity arrow. The surface below the carts is labeled 'Frictionless track'.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1774564423-8oL0za.jpg)

**Part a)** In Trial 1, the carts are equipped with Velcro bumpers so that they stick together after they collide. **Derive** an expression for the final speed of the two-cart system after the collision. Express your answer in terms of \(M\), \(v_0\), and fundamental constants. *(2 points)*

**Part b)** In Trial 2, the carts are equipped with magnetic bumpers. They collide and bounce off each other. After the collision, Cart A moves to the left with speed \(v_A\). **Derive** an expression for the final speed \(v_B\) of Cart B after the collision. Express your answer in terms of \(M\), \(v_0\), \(v_A\), and fundamental constants. *(2 points)*

**Part c)** In Trial 2, the students measure the speed of Cart A after the collision and find it is \(v_A = \dfrac{1}{2} v_0\). **Calculate** the speed of Cart B after the collision. Express your answer in terms of \(v_0\). *(1 points)*

**Part d)** **Determine** whether the collision in Trial 2 is elastic or inelastic. **Justify** your answer by calculating the change in kinetic energy of the two-cart system. *(3 points)*

**Part e)** **Compare** the velocity of the center of mass of the two-cart system after the collision in Trial 1 to the velocity of the center of mass of the system after the collision in Trial 2. - [ ] Greater in Trial 1 - [ ] Greater in Trial 2 - [ ] The same in both trials **Justify** your answer using physical principles. *(2 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/110101/*