Book cover for University Physics with Modern Physics

University Physics with Modern Physics

Wolfgang Bauer, Gary D. Westfall

ISBN #9780072857368

1st Edition

3,117 Questions

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Summary
Learning Objectives
Key Concepts
Example Problems
Explanations
Common Mistakes

Summary

This section introduces potential energy as the energy stored in a system due to its configuration. Gravitational and elastic potential energies are defined and described, with their corresponding formulas. The concept of conservative forces is emphasized, highlighting that the work done by such forces is independent of the path taken, which leads to the conservation of mechanical energy in an isolated system. Additionally, the relationship F = – dU/dx reveals how forces are derived from potential energy functions. The section also differentiates between energy-conserving processes and those involving nonconservative forces like friction, which dissipate energy into internal forms.

Learning Objectives

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Key Concepts

CONCEPT

DEFINITION

Definition: The study of the structure and behavior of atoms, from the early Bohr model to the complete quantum mechanical treatment of the hydrogen atom and multi?electron systems.

The study of the structure and behavior of atoms, from the early Bohr model to the complete quantum mechanical treatment of the hydrogen atom and multi?electron systems. •

Example Problems

Example 1

A block of mass $5.0 \mathrm{~kg}$ slides without friction at a speed of $8.0 \mathrm{~m} / \mathrm{s}$ on a horizontal table surface until it strikes and sticks to a mass of $4.0 \mathrm{~kg}$ attached to a horizontal spring (with spring constant of $k=2000.0 \mathrm{~N} / \mathrm{m}$ ), which in turn is attached to a wall. How far is the spring compressed before the masses come to rest? a) $0.40 \mathrm{~m}$ b) $0.54 \mathrm{~m}$ c) $0.30 \mathrm{~m}$ d) $0.020 \mathrm{~m}$ e) $0.67 \mathrm{~m}$

Example 2

A pendulum swings in a vertical plane. At the bottom of the swing, the kinetic energy is $8 \mathrm{~J}$ and the gravitational potential energy is 4 J. At the highest position of its swing, the kinetic and gravitational potential energies are a) kinetic energy $=0 \mathrm{~J}$ and gravitational potential energy $=4 \mathrm{~J}$ b) kinetic energy $=12 \mathrm{~J}$ and gravitational potential energy $=0 \mathrm{~J}$ c) kinetic energy $=0 \mathrm{~J}$ and gravitational potential energy $=12 \mathrm{~J}$ d) kinetic energy $=4$ J and gravitational potential energy $=8 \mathrm{~J}$ e) kinetic energy $=8 \mathrm{~J}$ and gravitational potential energy $=4$ J.

Example 3

A ball of mass $0.5 \mathrm{~kg}$ isreleased from rest at point $A$, which is $5 \mathrm{~m}$ above the bottom of a tank of oil, as shown in the figure. At $B$, which is $2 \mathrm{~m}$ above the bottom of the tank, the ball has a speed of $6 \mathrm{~m} / \mathrm{s}$. The work done on the ball by the force of fluid friction is a) +15 J. b) $+9 \mathrm{~J}$ c) $-15 \mathrm{~J}$. d) $-9 J$. e) $-5.7 \mathrm{~J}$

Example 4

A child throws three identical marbles from the same height above the ground so that they land on the flat roof of a building. The marbles are launched with the same initial speed. The first marble, marble $\mathrm{A}$, is thrown at an angle of $75^{\circ}$ above horizontal, while marbles $\mathrm{B}$ and $\mathrm{C}$ are thrown with launch angles of $60^{\circ}$ and $45^{\circ}$, respectively. Neglecting air resistance, rank the marbles according to the speeds with which they hit the roof. a) $A<B<C$ b) $C<B<A$ c) $\mathrm{A}$ and $\mathrm{C}$ have the same speed; B has a lower speed. d) $\mathrm{B}$ has the highest speed; $\mathrm{A}$ and $C$ have the same speed. e) $\mathrm{A}, \mathrm{B},$ and $\mathrm{C}$ all hit the roof with the same speed.

Example 5

Which of the following is not a valid potential energy function for the spring force $F=-k x ?$ a) $\left(\frac{1}{2}\right) k x^{2}$ b) $\left(\frac{1}{2}\right) k x^{2}+10 \mathrm{~J}$ c) $\left(\frac{1}{2}\right) k x^{2}-10 \mathrm{~J}$ d) $-\left(\frac{1}{2}\right) k x^{2}$ e) None of the above is valid.
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Step-by-Step Explanations

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Common Mistakes

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