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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29,070 Students Helped

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This module covers the physics of uniform circular motion, emphasizing that while an object may maintain a constant speed along a circular path, its velocity continuously changes direction, giving rise to centripetal acceleration and force. Key formulas, such as v = 2?r/T, ac = v²/r, and Fc = m·v²/r, allow for the analysis of various scenarios including banked curves, satellite orbits, and vertical circular motion. Understanding these principles is fundamental for analyzing real-world systems like car motion on curved roads, the motion of satellites, and even artificial gravity in space habitats.

Learning Objectives

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Key Concepts

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Example Problems

Example 1

A car travels at a constant speed around a circular track whose radius is 2.6 km. The car goes once around the track in 360 s. What is the magnitude of the centripetal acceleration of the car?

Example 2

The following table lists data for the speed and radius of three examples of uniform circular motion. Find the magnitude of the centripetal acceleration for each example.

Example 3

Review Conceptual Example 2 as background for this problem. One kind of slingshot consists of a pocket that holds a pebble and is whirled on a circle of radius $r .$ The pebble is released from the circle at the angle $\theta$, so that it will hit the target. The distance to the target from the center of the circle is $d$. (See the drawing, which is not to scale.) The circular path is parallel to the ground, and the target lies in the plane of the circle. The distance $d$ is ten times the radius $r .$ Ignore the effect of gravity in pulling the stone downward after it is released and find the angle $\theta$

Example 4

Speedboat A negotiates a curve whose radius is $120 \mathrm{m} .$ Speedboat $\mathrm{B}$ negotiates a curve whose radius is $240 \mathrm{m}$. Each boat experiences the same centripetal acceleration. What is the ratio $v_{\Lambda} / v_{\mathrm{B}}$ of the speeds of the boats?

Example 5

How long does it take a plane, traveling at a constant speed of $110 \mathrm{m} / \mathrm{s},$ to fly once around a circle whose radius is $2850 \mathrm{m} ?$
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Step-by-Step Explanations

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Common Mistakes

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