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)

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