---
title: "A \\( 4.0 \\) \\( \\text{kg} \\) block is held in place against a spring with spring constant \\( 1100 \\) \\( \\text{N/m} \\). The spring is compressed \\( 25 \\) \\( \\text{cm} \\) from its equilibrium position. After release, the block slides without friction along a track that first contains a vertical circular loop of radius \\( 20 \\) \\( \\text{cm} \\) and then continues up a straight incline that makes an angle of \\( 20^{\\circ} \\) with the horizontal, as shown in Figure \\( 1 \\). Assume friction between the block and the track is negligible throughout the motion."
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url: "https://nerd-notes.com/ubq/108969/"
date_modified: "2026-08-18T02:38:08+00:00"
---

# A \( 4.0 \) \( \text{kg} \) block is held in place against a spring with spring constant \( 1100 \) \( \text{N/m} \). The spring is compressed \( 25 \) \( \text{cm} \) from its equilibrium position. After release, the block slides without friction along a track that first contains a vertical circular loop of radius \( 20 \) \( \text{cm} \) and then continues up a straight incline that makes an angle of \( 20^{\circ} \) with the horizontal, as shown in Figure \( 1 \). Assume friction between the block and the track is negligible throughout the motion.

A \( 4.0 \) \( \text{kg} \) block is held in place against a spring with spring constant \( 1100 \) \( \text{N/m} \). The spring is compressed \( 25 \) \( \text{cm} \) from its equilibrium position. After release, the block slides without friction along a track that first contains a vertical circular loop of radius \( 20 \) \( \text{cm} \) and then continues up a straight incline that makes an angle of \( 20^{\circ} \) with the horizontal, as shown in Figure \( 1 \). Assume friction between the block and the track is negligible throughout the motion.

Figure 1. Spring launches block through loop then up a \( 20^{\circ} \) incline.

![Figure 1. Spring launches block through loop then up a \( 20^{\circ} \) incline.](https://nerd-notes.com/wp-content/uploads/ubq-diagrams/nerd-notes-physical-setup-108969-1773218278.png)

**Part a)** Calculate the speed of the block at the top of the loop. *(3 points)*

**Part b)** Calculate the normal force exerted on the block by the track when the block is at the top of the loop. *(3 points)*

**Part c)** Calculate the distance, \( D \), that the block slides up the incline before coming to rest. *(3 points)*


*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/108969/*