Book cover for Fundamentals of Physics

Fundamentals of Physics

David Halliday, Robert Resnick

ISBN #9781119460138

11th Edition

4,175 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This module covers the fundamental concepts of energy in physics, including kinetic energy, work, and potential energy, as well as the relationships that govern energy transfer. Essential formulas such as K = ½mv² for kinetic energy, W = Fd cos? for work, and U = mgy or U = ½kx² for gravitational and elastic potential energy are highlighted. Additionally, the distinction between conservative and nonconservative forces is discussed, emphasizing that for conservative forces the work done is path-independent. Understanding these principles is vital for analyzing and solving a wide range of physical problems.

Learning Objectives

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Key Concepts

CONCEPT

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Example Problems

Example 1

A proton (mass $m=1.67 \times 10^{-27} \mathrm{~kg}$ ) is being accelerated along a straight line at $3.6 \times 10^{15} \mathrm{~m} / \mathrm{s}^{2}$ in a machine. If the proton has an initial speed of $2.4 \times 10^{7} \mathrm{~m} / \mathrm{s}$ and travels $3.5 \mathrm{~cm},$ what then is (a) its speed and (b) the increase in its kinetic energy?

Example 2

If a Saturn $\mathrm{V}$ rocket with an Apollo spacecraft attached had a combined mass of $2.9 \times 10^{5} \mathrm{~kg}$ and reached a speed of $11.2 \mathrm{~km} / \mathrm{s}$, how much kinetic energy would it then have?

Example 3

On August $10,1972,$ a large meteorite skipped across the atmosphere above the western United States and western Canada, much like a stone skipped across water. The accompanying fireball was so bright that it could be seen in the daytime sky and was brighter than the usual meteorite trail. The meteorite's mass was about $4 \times 10^{6} \mathrm{~kg}$ : its speed was about $15 \mathrm{~km} / \mathrm{s}$. Had it entered the atmosphere vertically, it would have hit Earth's surface with about the same speed. (a) Calculate the meteorite's loss of kinetic energy (in joules) that would have been associated with the vertical impact. (b) Express the energy as a multiple of the explosive energy of 1 megaton of $\mathrm{TNT}$, which is $4.2 \times 10^{15} \mathrm{~J}$. (c) The energy associated with the atomic bomb explosion over Hiroshima was equivalent to 13 kilotons of TNT. To how many Hiroshima bombs would the meteorite impact have been equivalent?

Example 4

An explosion at ground level leaves a crater with a diameter that is proportional to the energy of the explosion raised to the $\frac{1}{3}$ power; an explosion of 1 megaton of TNT leaves a crater with a $1 \mathrm{~km}$ diameter. Below Lake Huron in Michigan there appears to be an ancient impact crater with a $50 \mathrm{~km}$ diameter. What was the kinetic energy associated with that impact, in terms of (a) megatons of TNT (1 megaton yields $4.2 \times 10^{15} \mathrm{~J}$ ) and (b) Hiroshima bomb equivalents (13 kilotons of TNT each)? (Ancient meteorite or comet impacts may have significantly altered the climate, killing off the dinosaurs and other life-forms.)

Example 5

A father racing his son has half the kinetic energy of the son, who has half the mass of the father. The father speeds up by $1.0 \mathrm{~m} / \mathrm{s}$ and then has the same kinetic energy as the son. What are the original speeds of (a) the father and (b) the son?

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