---
title: "Two identical spheres, Sphere 1 and Sphere 2, each of mass \\(m\\), slide horizontally across a frictionless floor toward a fixed vertical wall with the same initial speed \\(v_0\\). Sphere 1 collides elastically with the wall, rebounding in the opposite direction with speed \\(v_0\\) during a contact time interval of duration \\(2\\Delta t_0\\). Sphere 2 collides inelastically with the wall, coming completely to rest and sticking to the wall during a contact time interval of duration \\(\\Delta t_0\\). Which of the following correctly compares the magnitude of the average force \\(\\bar{F}_1\\) exerted by the wall on Sphere 1 to the magnitude of the average force \\(\\bar{F}_2\\) exerted by the wall on Sphere 2, and provides the correct physical justification?"
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url: "https://nerd-notes.com/ubq/121033/"
date_modified: "2026-08-23T04:47:49+00:00"
---

# Two identical spheres, Sphere 1 and Sphere 2, each of mass \(m\), slide horizontally across a frictionless floor toward a fixed vertical wall with the same initial speed \(v_0\). Sphere 1 collides elastically with the wall, rebounding in the opposite direction with speed \(v_0\) during a contact time interval of duration \(2\Delta t_0\). Sphere 2 collides inelastically with the wall, coming completely to rest and sticking to the wall during a contact time interval of duration \(\Delta t_0\). Which of the following correctly compares the magnitude of the average force \(\bar{F}_1\) exerted by the wall on Sphere 1 to the magnitude of the average force \(\bar{F}_2\) exerted by the wall on Sphere 2, and provides the correct physical justification?

Two identical spheres, Sphere 1 and Sphere 2, each of mass \(m\), slide horizontally across a frictionless floor toward a fixed vertical wall with the same initial speed \(v_0\). Sphere 1 collides elastically with the wall, rebounding in the opposite direction with speed \(v_0\) during a contact time interval of duration \(2\Delta t_0\). Sphere 2 collides inelastically with the wall, coming completely to rest and sticking to the wall during a contact time interval of duration \(\Delta t_0\). Which of the following correctly compares the magnitude of the average force \(\bar{F}_1\) exerted by the wall on Sphere 1 to the magnitude of the average force \(\bar{F}_2\) exerted by the wall on Sphere 2, and provides the correct physical justification?

- **A.** The magnitude \(\bar{F}_1\) is greater than \(\bar{F}_2\) because Sphere 1 conserves mechanical energy, requiring the wall to exert a larger peak force to reverse the sphere's momentum rather than absorb its motion.
- **B.** The magnitude \(\bar{F}_1\) is equal to \(\bar{F}_2\) because the magnitude of the impulse delivered to Sphere 1 is twice that delivered to Sphere 2, which is exactly offset by its contact time being twice as long.
- **C.** The magnitude \(\bar{F}_1\) is equal to \(\bar{F}_2\) because both spheres have an initial momentum of magnitude \(mv_0\) and transfer the same total energy to the rigid wall during the collision.
- **D.** The magnitude \(\bar{F}_1\) is less than \(\bar{F}_2\) because the longer contact time for Sphere 1 cushions the impact, resulting in a smaller rate of momentum transfer to the wall.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/121033/*