Q: A uniform beam of length $$L = 4\ \mathrm{m}$$ and mass $$m = 20\ \mathrm{kg} is $$supported horizontally at its ends. A $$40\ \mathrm{kg}$$ box is placed $$1\ \mathrm{m}$$ from the left end. What is the upward force exerted by the left support if the beam is in static equilibrium? (Take $$g = 9.8\ \mathrm{m/s^2$}.)$$

$$F_{\text{left}} = 343\ \mathrm{N}$$

Q: A mass-spring system oscillates with amplitude $$A = 0.2\ \mathrm{m}$$ and angular frequency $$\omega = 5\ \mathrm{rad/s}. $$What is the maximum speed of the mass?

$$v_{\text{max}} = 2.0\ \mathrm{m/s}$$

Q: A gas at $$T = 300\ \mathrm{K}$$ consists of molecules with mass $$m = 4.8 \times 10$$^{-26}$$\ \mathrm{kg}. $$What is the root-mean-square speed of the molecules? ($$k_B = 1.38 \times 10$$^{-23}$$\ \mathrm{J/K})$$

$$v_{\text{rms}} = 525\ \mathrm{m/s}$$

Q: A diver is $$30\ \mathrm{m}$$ below the surface of a lake. What is the absolute pressure at this depth? (Assume atmospheric pressure $$P_0 = 1.0$$ \times $$10^5$$\ \mathrm{Pa}$$, $$\rho_{\text{water}} = 1000\ \mathrm{$$kg/m^3$$}$$, g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

$$P = 3.94 \times 10^5$\ \mathrm{Pa}$$

Q: A $$0.5\ \mathrm{kg}$$ block floats in oil of density $$\rho = 800\ \mathrm{kg/m^3$}. $$What is the minimum volume of the block required to keep it just floating?

$$V = 8.0 \times 10$$^{-4}$$\ \mathrm{m^3$}$$

Question 1

A uniform beam of length $$L = 4\ \mathrm{m}$$ and mass $$m = 20\ \mathrm{kg} is $$supported horizontally at its ends. A $$40\ \mathrm{kg}$$ box is placed $$1\ \mathrm{m}$$ from the left end. What is the upward force exerted by the left support if the beam is in static equilibrium? (Take $$g = 9.8\ \mathrm{m/s^2$}.)$$

Accepted Answer

$$F_{	ext{left}} = 343\ \mathrm{N}$$

Question 2

A hydraulic lift uses a small piston of area $$A_1 = 0.01$$\ \mathrm{$$m^2$$}$$ and a large piston of area A_2$ = 0.5\ \mathrm{m^2$}. If a $$force of $$F_1 = 200$$\ \mathrm{N}$$ is applied to the small piston, what is the maximum weight that can be lifted by the large piston according to Pascal’s principle?

Accepted Answer

$$F_2 = 10$$,000\ \mathrm{N}$$

Question 3

A cube of wood with density $$ho = 600\ \mathrm{kg/m^3$}$$ and volume $$0.02\ \mathrm{m^3$}$$ floats in water ($$ho_{	ext{water}} = 1000\ \mathrm{kg/m^3$}). $$What is the magnitude of the buoyant force acting on the cube?

Accepted Answer

$$F_b = 196\ \mathrm{N}$$

Question 4

A pipe narrows from a diameter of $$10\ \mathrm{cm} to$$ $$5\ \mathrm{cm}. If $$water enters the wider section at $$2\ \mathrm{m/s}$$, what is the speed of water in the narrower section? (Assume incompressible flow.)

Accepted Answer

$$v_2 = 8$$\ \mathrm{m/s}$$

Question 5

A pendulum of length $$L = 1.5\ \mathrm{m}$$ swings with small amplitude. What is its period of oscillation?

Accepted Answer

$$T = 2.46\ \mathrm{s}$$

Question 6

A mass-spring system oscillates with amplitude $$A = 0.2\ \mathrm{m}$$ and angular frequency $$\omega = 5\ \mathrm{rad/s}. $$What is the maximum speed of the mass?

Accepted Answer

$$v_{	ext{max}} = 2.0\ \mathrm{m/s}$$

Question 7

A standing wave is formed on a string fixed at both ends of length $$L = 1.2\ \mathrm{m}. If $$the speed of waves on the string is $$v = 60\ \mathrm{m/s}$$, what is the frequency of the second harmonic?

Accepted Answer

$$f_2 = 100$$\ \mathrm{Hz}$$

Question 8

A sound wave has an intensity of $$I = 1.0 	imes 10$$^{-5}$$\ \mathrm{W/m^2$}. $$What is the corresponding sound level in decibels ($$dB$$)? (Reference intensity $$I_0 = 1.0$$ 	imes $$10^{-12}$$\ \mathrm{$$W/m^2$$}$$)

Accepted Answer

$$L = 100\ \mathrm{dB}$$

Question 9

A train approaches a stationary observer at $$v_s = 30\ \mathrm{m/s}$$, emitting a whistle at $$f_0 = 500$$\ \mathrm{Hz}$$. If the speed of sound is v = 340$$\ \mathrm{m/s}$$, what frequency does the observer hear?

Accepted Answer

$$f = 545\ \mathrm{Hz}$$

Question 10

A gas at $$T = 300\ \mathrm{K}$$ consists of molecules with mass $$m = 4.8 	imes 10$$^{-26}$$\ \mathrm{kg}. $$What is the root-mean-square speed of the molecules? ($$k_B = 1.38 	imes 10$$^{-23}$$\ \mathrm{J/K})$$

Accepted Answer

$$v_{	ext{rms}} = 525\ \mathrm{m/s}$$

Question 11

A $$2.0\ \mathrm{m}$$ long open pipe resonates at its fundamental frequency. What is the wavelength of the sound produced?

Accepted Answer

$$\lambda = 4.0\ \mathrm{m}$$

Question 12

A block of mass $$m = 0.5\ \mathrm{kg} is $$attached to a spring with force constant $$k = 200\ \mathrm{N/m}. $$What is the period of oscillation?

Accepted Answer

$$T = 0.314\ \mathrm{s}$$

Question 13

A diver is $$30\ \mathrm{m}$$ below the surface of a lake. What is the absolute pressure at this depth? (Assume atmospheric pressure $$P_0 = 1.0$$ 	imes $$10^5$$\ \mathrm{Pa}$$, $$ho_{	ext{water}} = 1000\ \mathrm{$$kg/m^3$$}$$, g = 9.8$$\ \mathrm{$$m/s^2$$}$$)

Accepted Answer

$$P = 3.94 	imes 10^5$\ \mathrm{Pa}$$

Question 14

A $$0.5\ \mathrm{kg}$$ mass oscillates in SHM with amplitude $$A = 0.1\ \mathrm{m}$$ and period $$T = 0.4\ \mathrm{s}. $$What is the total mechanical energy of the system?

Accepted Answer

$$E = 1.23\ \mathrm{J}$$

Question 15

A wave on a string is described by $$y(x, t) = 0.05 \sin(4\pi x - 200\pi t)$$, where $$x$$ and $$y$$ are in meters and $$t in $$seconds. What is the speed of the wave?

Accepted Answer

$$v = 50\ \mathrm{m/s}$$

Question 16

A $$1.0\ \mathrm{m^3$}$$ tank contains air at $$P = 2.0 	imes 10^5$\ \mathrm{Pa}$$ and $$T = 300\ \mathrm{K}. $$How many moles of air are in the tank? ($$R = 8.31\ \mathrm{J/(mol\cdot K)})$$

Accepted Answer

$$n = 240.6$$

Question 17

A $$0.2\ \mathrm{kg}$$ object is attached to a spring and oscillates with a frequency of $$2.5\ \mathrm{Hz}. $$What is the spring constant $$k$$?

Accepted Answer

$$k = 49.3\ \mathrm{N/m}$$

Question 18

A $$0.5\ \mathrm{kg}$$ block floats in oil of density $$\rho = 800\ \mathrm{kg/m^3$}. $$What is the minimum volume of the block required to keep it just floating?

Accepted Answer

$$V = 8.0 	imes 10$$^{-4}$$\ \mathrm{m^3$}$$

Question 19

A string of length $$0.8\ \mathrm{m} is $$fixed at both ends and vibrates in its third harmonic. What is the wavelength of the standing wave?

Accepted Answer

$$\lambda = 0.53\ \mathrm{m}$$

Physics Exam Study Guide: Statics, Fluids, Waves, Sound, and Thermodynamics

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