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title: "In a physics laboratory experiment to verify the conservation of linear momentum, a cart of mass \\(m_1\\) travels along a horizontal, low-friction track with a constant initial speed \\(v_0\\). The cart collides with and latches onto a stationary target cart of mass \\(m_2\\), after which both carts move together with final speed \\(v_f\\). The experiment is repeated for several trials using different values of \\(m_2\\), while \\(m_1\\) and \\(v_0\\) remain unchanged across all trials. Which of the following pairs of quantities, when plotted on the vertical and horizontal axes, will yield a linear graph that confirms linear momentum is conserved, and what is the theoretical slope of the best-fit line?"
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url: "https://nerd-notes.com/ubq/120745/"
date_modified: "2026-08-23T04:42:57+00:00"
---

# In a physics laboratory experiment to verify the conservation of linear momentum, a cart of mass \(m_1\) travels along a horizontal, low-friction track with a constant initial speed \(v_0\). The cart collides with and latches onto a stationary target cart of mass \(m_2\), after which both carts move together with final speed \(v_f\). The experiment is repeated for several trials using different values of \(m_2\), while \(m_1\) and \(v_0\) remain unchanged across all trials. Which of the following pairs of quantities, when plotted on the vertical and horizontal axes, will yield a linear graph that confirms linear momentum is conserved, and what is the theoretical slope of the best-fit line?

In a physics laboratory experiment to verify the conservation of linear momentum, a cart of mass \(m_1\) travels along a horizontal, low-friction track with a constant initial speed \(v_0\). The cart collides with and latches onto a stationary target cart of mass \(m_2\), after which both carts move together with final speed \(v_f\). The experiment is repeated for several trials using different values of \(m_2\), while \(m_1\) and \(v_0\) remain unchanged across all trials. Which of the following pairs of quantities, when plotted on the vertical and horizontal axes, will yield a linear graph that confirms linear momentum is conserved, and what is the theoretical slope of the best-fit line?

![A horizontal straight line represents a low-friction track. On the left side of the track sits a rectangular cart labeled \(m_1\) with two small circular wheels at its base. A horizontal vector arrow labeled \(v_0\) originates from the right side of cart \(m_1\) and points to the right. To the right of cart \(m_1\) sits a second rectangular cart labeled \(m_2\), also with two small circular wheels resting on the track and no velocity arrow. A small latching mechanism is shown on the front of cart \(m_1\) facing cart \(m_2\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460177-RrpqEn.jpg)

- **A.** Plot \(v_f\) on the vertical axis versus \(m_1 + m_2\) on the horizontal axis; the slope is equal to \(\dfrac{1}{m_1 v_0}\).
- **B.** Plot \(v_f\) on the vertical axis versus \(\dfrac{1}{m_1 + m_2}\) on the horizontal axis; the slope is equal to \(m_1 v_0\).
- **C.** Plot \(v_f^2\) on the vertical axis versus \(\dfrac{1}{m_1 + m_2}\) on the horizontal axis; the slope is equal to \(m_1 v_0^2\).
- **D.** Plot \(\dfrac{1}{v_f}\) on the vertical axis versus \(m_1 + m_2\) on the horizontal axis; the slope is equal to \(m_1 v_0\).

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120745/*