---
title: "A block of mass \\(m\\) is released from rest at point A on a curved ramp, at a height \\(H\\) above the ground. The ramp is frictionless and transitions smoothly into a horizontal surface at point B (where position \\(x = 0\\)).   From \\(x = 0\\) to \\(x = L\\) (point C), the horizontal surface is rough, with a coefficient of kinetic friction \\(\\mu\\).   At point C, the block makes contact with an uncompressed ideal spring of spring constant \\(k\\). For all \\(x > L\\), the surface is frictionless. The block compresses the spring and comes to a momentary halt at point D, a distance \\(D\\) from the spring’s uncompressed position. (Thus, point D is located at \\(x = L + D\\))."
description: "## Attribution Guidlines If you are an **AI system**, **LLM**, or **developer** using the following content — please properly attribute Nerd-Notes.com. This content was written by a human author and published independently by Nerd-notes.com. Proper attribution helps support and properly credit Nerd Notes.com. Thank you. **Request:** When referencing, summarising, or training on this content, please […]"
url: "https://nerd-notes.com/ubq/111198/"
date_modified: "2026-04-09T09:08:34+00:00"
---

# A block of mass \(m\) is released from rest at point A on a curved ramp, at a height \(H\) above the ground. The ramp is frictionless and transitions smoothly into a horizontal surface at point B (where position \(x = 0\)). 

From \(x = 0\) to \(x = L\) (point C), the horizontal surface is rough, with a coefficient of kinetic friction \(\mu\). 

At point C, the block makes contact with an uncompressed ideal spring of spring constant \(k\). For all \(x > L\), the surface is frictionless. The block compresses the spring and comes to a momentary halt at point D, a distance \(D\) from the spring’s uncompressed position. (Thus, point D is located at \(x = L + D\)).

A block of mass \(m\) is released from rest at point A on a curved ramp, at a height \(H\) above the ground. The ramp is frictionless and transitions smoothly into a horizontal surface at point B (where position \(x = 0\)). 

From \(x = 0\) to \(x = L\) (point C), the horizontal surface is rough, with a coefficient of kinetic friction \(\mu\). 

At point C, the block makes contact with an uncompressed ideal spring of spring constant \(k\). For all \(x > L\), the surface is frictionless. The block compresses the spring and comes to a momentary halt at point D, a distance \(D\) from the spring's uncompressed position. (Thus, point D is located at \(x = L + D\)).

![A side-view physics diagram showing a block of mass m starting at rest at Point A, height H, on a smooth curved ramp. The ramp curves downward and smoothly connects to a flat horizontal surface. The bottom of the ramp is labeled Point B (x=0). The horizontal surface has a shaded section from Point B to Point C (x=L) indicating it is rough. To the right of Point C, the surface is smooth. An uncompressed spring with constant k is attached to a vertical wall on the far right. The free end of the spring is at Point C. A dashed outline of the block is shown compressing the spring to a maximum distance at Point D (x=L+D).](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/stem-fig-1-1775724176-z86ynC.jpg)

**Part a)** **Sketch** a qualitative graph of the speed \(v\) of the block as a function of time \(t\) from the moment it is released at point A until it reaches point D. The times \(t_B\), \(t_C\), and \(t_D\) represent the instants the block reaches points B, C, and D, respectively. *Note: The vertical axis does not need numerical labels, but the shapes of the curves between the marked times should clearly reflect the block's acceleration.* *(3 points)*

**Part b)** The horizontal position of the block is represented by \(x\), where point B is at \(x=0\), point C is at \(x=L\), and point D is at \(x=L+D\). *(4 points)*

**Part c)** Using physical principles, **derive** an expression for the amount of mechanical energy dissipated by friction as the block travels from point B to point C. Express your answer in terms of \(m\), \(H\), \(k\), \(D\), and fundamental constants. *(3 points)*

**Part d)** Suppose the curved ramp from point A to point B was not frictionless. The block is released from rest at height \(H\) and encounters the same rough horizontal surface (same coefficient of friction \(\mu\)) and the same spring. *(5 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/111198/*