Book cover for Physics

Physics

John D. Cutnell, Kenneth W. Johnson, David Young, Shane Stadler

ISBN #9781118486894

10th Edition

2,562 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This section covers the behavior of ideal springs and their role in simple harmonic motion, illustrating how Hooke’s law (F = -kx) governs the restoring force. It explains key parameters of SHM—amplitude, period, frequency, and angular frequency—and shows how energy oscillates between kinetic and elastic potential forms. The material further discusses real-world adjustments through damping and external driving forces (resonance) in oscillatory systems. Finally, the concepts of stress, strain, and elastic moduli are introduced to explain how materials deform under various forces, highlighting the universality of Hooke’s law in both mechanical oscillation and solid mechanics.

Learning Objectives

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Key Concepts

CONCEPT

DEFINITION

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Example Problems

Example 1

Ssm A hand exerciser utilizes a coiled spring. A force of $89.0 \mathrm{N}$ is required to compress the spring by $0.0191 \mathrm{m} .$ Determine the force needed to compress the spring by $0.0508 \mathrm{m}$.

Example 2

The drawing shows three identical springs hanging from the ceiling. Nothing is attached to the first spring, whereas a 4.50-N block hangs from the second spring. A block of unknown weight hangs from the third spring. From the drawing, determine (a) the spring constant (in $\mathrm{N} / \mathrm{m}$ ) and (b) the weight of the block hanging from the third spring.

Example 3

In a room that is 2.44 m high, a spring (unstrained length $=0.30 \mathrm{m}$ ) hangs from the ceiling. A board whose length is $1.98 \mathrm{m}$ is attached to the free end of the spring. The board hangs straight down, so that its $1.98-\mathrm{m}$ length is perpendicular to the floor. The weight of the board $(104 \mathrm{N})$ stretches the spring so that the lower end of the board just extends to, but does not touch, the floor. What is the spring constant of the spring?

Example 4

ao $A$ spring lies on a horizontal table, and the left end of the spring is attached to a wall. The other end is connected to a box. The box is pulled to the right, stretching the spring. Static friction exists between the box and the table, so when the spring is stretched only by a small amount and the box is released, the box does not move. The mass of the box is $0.80 \mathrm{kg},$ and the spring has a spring constant of $59 \mathrm{N} / \mathrm{m} .$ The coefficient of static friction between the box and the table on which it rests is $\mu_{\mathrm{s}}=0.74$ How far can the spring be stretched from its unstrained position without the box moving when it is released?

Example 5

55m A person who weighs $670 \mathrm{N}$ steps onto a spring scale in the bathroom, and the spring compresses by $0.79 \mathrm{cm} .$ (a) What is the spring constant? (b) What is the weight of another person who compresses the spring by $0.34 \mathrm{cm} ?$
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