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title: "A block of mass \\(m_1\\) slides along a rough horizontal table with kinetic friction coefficient \\(\\mu_k\\) and collides with an initially stationary block of mass \\(m_2\\). High-speed sensors measure the total linear momentum of the two-block system immediately before contact, \\(p_i\\), and immediately after contact ceases, \\(p_f\\), over a finite contact duration \\(\\Delta t\\). The measurements show that the final total linear momentum is measurably less than the initial total linear momentum, such that \\(p_f – p_i < 0\\). Which of the following provides the correct physical explanation for this observation?"
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url: "https://nerd-notes.com/ubq/124252/"
date_modified: "2026-09-28T14:04:31+00:00"
---

# A block of mass \(m_1\) slides along a rough horizontal table with kinetic friction coefficient \(\mu_k\) and collides with an initially stationary block of mass \(m_2\). High-speed sensors measure the total linear momentum of the two-block system immediately before contact, \(p_i\), and immediately after contact ceases, \(p_f\), over a finite contact duration \(\Delta t\). The measurements show that the final total linear momentum is measurably less than the initial total linear momentum, such that \(p_f – p_i < 0\). Which of the following provides the correct physical explanation for this observation?

A block of mass \(m_1\) slides along a rough horizontal table with kinetic friction coefficient \(\mu_k\) and collides with an initially stationary block of mass \(m_2\). High-speed sensors measure the total linear momentum of the two-block system immediately before contact, \(p_i\), and immediately after contact ceases, \(p_f\), over a finite contact duration \(\Delta t\). The measurements show that the final total linear momentum is measurably less than the initial total linear momentum, such that \(p_f - p_i < 0\). Which of the following provides the correct physical explanation for this observation?

![A single continuous horizontal line represents the flat surface of a rough table. Below this line, evenly spaced short diagonal hatching lines indicate a rough contact interface. Resting on the horizontal line is a rectangular block labeled \(m_1\) on the left, with a single horizontal arrow pointing rightward originating from its right edge, labeled \(v_0\). Directly to the right along the same horizontal surface rests a second rectangular block labeled \(m_2\), shown at rest. A horizontal dashed line segment between the two blocks denotes the path of motion before collision. No other labels, vectors, forces, coordinate axes, or background elements appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1790604270-5lwRVe.jpg)

- **A.** A net external frictional force acts on the blocks throughout the finite collision duration \(\Delta t\), delivering a non-zero external impulse \(\int_{t_i}^{t_f} \vec{F}_{\text{ext}} \, dt\) that causes the measured decrease in total system momentum.
- **B.** A portion of the system's translational kinetic energy is converted into internal thermal energy and vibrational deformation during the impact, which intrinsically reduces the total linear momentum of the two-block system.
- **C.** The rapid rate of deformation during impact induces a time lag in the propagation of elastic stress, preventing the internal contact forces from balancing instantaneously and leaving an uncancelled net internal impulse.
- **D.** The contact friction at the track interface exerts an unbalanced torque about the center of mass of each block, transferring translational linear momentum into unmeasured rotational angular momentum of the system.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/124252/*