Q: A metal rod of length $2.0\ \mathrm{m}$ at $20^\circ\mathrm{C}$ is heated to $120^\circ\mathrm{C}$. If the coefficient of linear expansion is $1.2 \times 10^{-5}\ ^\circ\mathrm{C}^{-1}$, what is the change in length?

$\Delta \ell = 2.4 \times 10^{-3}\ \mathrm{m}$

Question 1

A hydraulic lift is used to raise a car weighing 12,000 N. If the area of the input piston is $0.01\ \mathrm{m}^2$ and the area of the output piston is $0.5\ \mathrm{m}^2$, what minimum force must be applied to the input piston to lift the car, neglecting friction?

Accepted Answer

$F_{in} = 240\ \mathrm{N}$

Question 2

A block of wood with a density of $600\ \mathrm{kg/m}^3$ floats in water. What fraction of the block's volume is submerged?

Accepted Answer

$0.60$

Question 3

A 2.0 kg mass is attached to a spring with a force constant $k = 200\ \mathrm{N/m}$. What is the period of oscillation for this mass-spring system?

Accepted Answer

$T = 0.63\ \mathrm{s}$

Question 4

A simple pendulum has a length of $0.50\ \mathrm{m}$. What is its period of oscillation near the surface of the Earth ($g = 9.8\ \mathrm{m/s}^2$)?

Accepted Answer

$T = 0.99\ \mathrm{s}$

Question 5

A sound wave in air at $20^\circ\mathrm{C}$ has a frequency of $686\ \mathrm{Hz}$. What is its wavelength?

Accepted Answer

$\lambda = 0.50\ \mathrm{m}$

Question 6

A string fixed at both ends has a length of $1.2\ \mathrm{m}$ and supports a standing wave at its fundamental frequency. What is the wavelength of this fundamental mode?

Accepted Answer

$\lambda_1 = 2.4\ \mathrm{m}$

Question 7

A wave on a string has a speed of $120\ \mathrm{m/s}$ and a frequency of $40\ \mathrm{Hz}$. What is its wavelength?

Accepted Answer

$\lambda = 3.0\ \mathrm{m}$

Question 8

A sound intensity of $1.0 	imes 10^{-6}\ \mathrm{W/m}^2$ is measured. What is the corresponding sound level in decibels?

Accepted Answer

$\beta = 60\ \mathrm{dB}$

Question 9

A gas is contained in a rigid vessel at a pressure of $2.0\ \mathrm{atm}$ and a temperature of $300\ \mathrm{K}$. If the temperature is increased to $600\ \mathrm{K}$, what is the new pressure, assuming the volume and amount of gas remain constant?

Accepted Answer

$4.0\ \mathrm{atm}$

Question 10

A metal rod of length $2.0\ \mathrm{m}$ at $20^\circ\mathrm{C}$ is heated to $120^\circ\mathrm{C}$. If the coefficient of linear expansion is $1.2 	imes 10^{-5}\ ^\circ\mathrm{C}^{-1}$, what is the change in length?

Accepted Answer

$\Delta \ell = 2.4 	imes 10^{-3}\ \mathrm{m}$

Question 11

A sample of an ideal gas occupies $5.0\ \mathrm{L}$ at $1.0\ \mathrm{atm}$ and $300\ \mathrm{K}$. How many moles of gas are present? (Use $R = 0.0821\ \mathrm{L \cdot atm/(mol \cdot K)}$)

Accepted Answer

$n = 0.20$

Question 12

A 0.5 kg object oscillates in simple harmonic motion with an amplitude of $0.10\ \mathrm{m}$ and a spring constant $k = 50\ \mathrm{N/m}$. What is the total mechanical energy of the system?

Accepted Answer

$E = 0.50\ \mathrm{J}$

Question 13

A wave traveling outward from a point source has an intensity of $I_0$ at a distance $r_0$. What is the intensity at a distance $2r_0$ from the source, assuming no damping?

Accepted Answer

$I = I_0/4$

Question 14

A 1.0 L container holds $2.0 	imes 10^{23}$ molecules of an ideal gas at $300\ \mathrm{K}$. What is the pressure in the container? (Use $k = 1.38 	imes 10^{-23}\ \mathrm{J/K}$)

Accepted Answer

$P = 8.28\ \mathrm{kPa}$

Question 15

A cube of ice (density $= 917\ \mathrm{kg/m}^3$) floats in seawater (density $= 1030\ \mathrm{kg/m}^3$). What percentage of the ice cube's volume is above the water surface?

Accepted Answer

$11\%$

Question 16

A 0.75 m long guitar string is fixed at both ends. What is the frequency of its fundamental mode if the wave speed on the string is $300\ \mathrm{m/s}$?

Accepted Answer

$f_1 = 200\ \mathrm{Hz}$

Question 17

A steel bridge is $500\ \mathrm{m}$ long at $20^\circ\mathrm{C}$. If the temperature increases to $40^\circ\mathrm{C}$, by how much does the bridge expand? (Coefficient of linear expansion for steel $= 1.2 	imes 10^{-5}\ ^\circ\mathrm{C}^{-1}$)

Accepted Answer

$\Delta \ell = 0.12\ \mathrm{m}$

Question 18

Which of the following statements about resonance is correct?

Accepted Answer

Resonance occurs when the frequency of an applied force matches the natural frequency of a system, resulting in large amplitude oscillations.

Question 19

A gas sample at $27^\circ\mathrm{C}$ is heated to $127^\circ\mathrm{C}$ at constant pressure. By what factor does its volume increase?

Accepted Answer

$V_{final}/V_{initial} = 1.33$

Question 20

Which of the following best explains why water's volume decreases as it is heated from $0^\circ\mathrm{C}$ to $4^\circ\mathrm{C}$?

Accepted Answer

Hydrogen bonding causes water molecules to pack more closely as temperature increases in this range.

Study Guide: Fluids, Vibrations & Waves, Sound, and Kinetic Theory (Chapters 10–13)

Study Guide - Practice Questions

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