---
title: "A block of mass \\(m\\) is dropped from rest from a height \\(h\\) above a vertical, non-ideal spring mounted on the ground. During compression, internal material damping within the spring exerts a resistive force that opposes the motion and depends on the speed of compression. When the block momentarily comes to rest at maximum compression \\(x_{\\max}\\), the elastic potential energy stored in the spring is measured to be strictly less than the gravitational potential energy lost by the block-Earth system. Which of the following explanations correctly accounts for this discrepancy?"
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url: "https://nerd-notes.com/ubq/120651/"
date_modified: "2026-08-23T04:42:30+00:00"
---

# A block of mass \(m\) is dropped from rest from a height \(h\) above a vertical, non-ideal spring mounted on the ground. During compression, internal material damping within the spring exerts a resistive force that opposes the motion and depends on the speed of compression. When the block momentarily comes to rest at maximum compression \(x_{\max}\), the elastic potential energy stored in the spring is measured to be strictly less than the gravitational potential energy lost by the block-Earth system. Which of the following explanations correctly accounts for this discrepancy?

A block of mass \(m\) is dropped from rest from a height \(h\) above a vertical, non-ideal spring mounted on the ground. During compression, internal material damping within the spring exerts a resistive force that opposes the motion and depends on the speed of compression. When the block momentarily comes to rest at maximum compression \(x_{\max}\), the elastic potential energy stored in the spring is measured to be strictly less than the gravitational potential energy lost by the block-Earth system. Which of the following explanations correctly accounts for this discrepancy?

![A vertical schematic drawing shows a horizontal ground line with a vertical helical spring attached firmly to the ground, extending upward with an uncompressed top end. Directly above the top of the spring, a solid rectangular block labeled m is positioned in midair. A vertical dimension line with arrowheads at both ends spans between the bottom face of the block and the top of the uncompressed spring, labeled h. A downward dashed vertical line indicates the path of motion toward the spring. No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1787460149-DsWAfN.jpg)

- **A.** At the point of maximum compression, the block maintains a nonzero net upward acceleration, which prevents the full transformation of initial gravitational potential energy into potential energy stored in the spring.
- **B.** The velocity-dependent resistive force does negative nonconservative work as the spring compresses, dissipating a portion of the system's initial mechanical energy into internal thermal energy.
- **C.** The contact force between the falling block and the top of the spring performs negative work on the block, which removes mechanical energy from the defined block-spring-Earth system.
- **D.** The downward gravitational force and the upward elastic restoring force act in opposition throughout the descent, causing destructive work that decreases the total mechanical energy stored by the spring.

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/120651/*