Q: A concert speaker emits $$3 \times 10$$^{-2}$$ \ \mathrm{W/m^2$} of $$power uniformly in all directions. What is the intensity level in decibels at a distance of $$7.00 \ \mathrm{m}$$? The threshold of human hearing is $$1.0 \times 10$$^{-12}$$ \ \mathrm{W/m^2$}.$$

$$\beta = 10 \log_{10} \left( \dfrac{3 \times 10$$^{-2}$$}{1.0 \times 10$$^{-12}$$} \right) = 135 \ \mathrm{dB}$$

Q: A $$0.5 \ \mathrm{kg}$$ block oscillates on a spring with a force constant of $$30 \ \mathrm{N/m}. If $$the amplitude is $$0.25 \ \mathrm{m}$$, what is the kinetic energy when it is $$0.15 \ \mathrm{m}$$ from equilibrium?

$$K = \dfrac{1}{2}k(A^2$ - x^2$) = \dfrac{1}{2} \times 30 \times (0.25^2$ - 0.15^2$) = 0.75 \ \mathrm{J}$$

Q: A particle of mass $$2.4 \times 10$$^{-6}$$ \ \mathrm{kg}$$ moves in a circle of diameter $$2 \ \mathrm{mm} at a $$tangential speed of $$1.5 \times 10^3$ \ \mathrm{m/s}. $$What is its angular momentum?

$$L = mvr = 2.4 \times 10$$^{-6}$$ \times 1.5 \times 10^3$ \times 1 \times 10$$^{-3}$$ = 3.6 \times 10$$^{-6}$$ \ \mathrm{kg \cdot m^2$/s}$$

Q: A torque of $$1.50 \ \mathrm{N \cdot m} is $$applied to a wheel treated as a thin ring of mass $$1.2 \ \mathrm{kg}$$ and radius $$0.35 \ \mathrm{m}. $$What is its angular acceleration?

$$\alpha = \dfrac{\tau}{I} = \dfrac{1.50}{1.2 \times 0.35^2$} = 10.2 \ \mathrm{$$rad/s^2$$}$$

Q: A flywheel slows from $$79.3 \ \mathrm{rad/s} to $$rest, storing $$5.0 \ \mathrm{kJ} of $$work. The flywheel is a solid disk of radius $$0.50 \ \mathrm{m}$$, mass $$70 \ \mathrm{kg}. $$What is its moment of inertia?

$$I = \dfrac{1}{2}mr^2$ = \dfrac{1}{2} \times 70 \times 0.5^2$ = 8.75 \ \mathrm{kg \cdot m^2$}$$

Q: A $$0.2 \ \mathrm{kg}$$ bullet embeds in a $$0.6 \ \mathrm{kg}$$ block on a frictionless surface. The block compresses a spring by $$0.05 \ \mathrm{m}. $$Spring constant is $$2800 \ \mathrm{N/m}. $$Find the bullet's initial speed.

$$v = \dfrac{\sqrt{k}x}{m_{total}} = \dfrac{\sqrt{2800} \times 0.05}{0.8} = 0.42 \ \mathrm{m/s}$$

Question 1

A concert speaker emits $$3 	imes 10$$^{-2}$$ \ \mathrm{W/m^2$} of $$power uniformly in all directions. What is the intensity level in decibels at a distance of $$7.00 \ \mathrm{m}$$? The threshold of human hearing is $$1.0 	imes 10$$^{-12}$$ \ \mathrm{W/m^2$}.$$

Accepted Answer

$$\beta = 10 \log_{10} \left( \dfrac{3 	imes 10$$^{-2}$$}{1.0 	imes 10$$^{-12}$$} ight) = 135 \ \mathrm{dB}$$

Question 2

A train whistle produces a sound of frequency $$1{,}500 \ \mathrm{Hz}$$ while the train is not moving. If an observer were instead to hear $$1{,}570 \ \mathrm{Hz}$$, what frequency does the observer hear if the speed of sound is $$340 \ \mathrm{m/s}$$ and the train moves toward the observer at $$15 \ \mathrm{m/s}$$?

Accepted Answer

$$f' = f \left( \dfrac{v + v_o}{v} \right) = 1{,}500 \left( \dfrac{340 + 15}{340} \right) = 1{,}566 \ \mathrm{Hz}$$

Question 3

A $$0.5 \ \mathrm{kg}$$ block oscillates on a spring with a force constant of $$30 \ \mathrm{N/m}. If $$the amplitude is $$0.25 \ \mathrm{m}$$, what is the kinetic energy when it is $$0.15 \ \mathrm{m}$$ from equilibrium?

Accepted Answer

$$K = \dfrac{1}{2}k(A^2$ - x^2$) = \dfrac{1}{2} 	imes 30 	imes (0.25^2$ - 0.15^2$) = 0.75 \ \mathrm{J}$$

Question 4

The position of an object in simple harmonic motion is given by $$x(t) = 0.5 \cos(20t) (SI $$units). What is the frequency, angular frequency, and period of this motion?

Accepted Answer

Frequency $$f = 3.18 \ \mathrm{Hz}$$, angular frequency $$\omega = 20 \ \mathrm{rad/s}$$, period $$T = 0.314 \ \mathrm{s}$$

Question 5

On a moon of Jupiter, a pendulum that has a period of $$1.5 \ \mathrm{s} on $$Earth has a period of $$0.5 \ \mathrm{s} on $$the moon. What is the acceleration due to gravity on the moon?

Accepted Answer

$$g_{moon} = g_{earth} \left( \dfrac{T_{moon}}{T_{earth}} \$$right)^2$$ = 9.8 \left( \dfrac{0.5}{1.5} \$$right)^2$$ = 1.09 \ \mathrm{m/s^2$}$$

Question 6

A human weighing $$700 \ \mathrm{N}$$ pushes two people weighing $$700 \ \mathrm{N}$$ and $$400 \ \mathrm{N} in $$the center, how is the force distributed?

Accepted Answer

The force is distributed in proportion to their weights

Question 7

A particle of mass $$2.4 	imes 10$$^{-6}$$ \ \mathrm{kg}$$ moves in a circle of diameter $$2 \ \mathrm{mm} at a $$tangential speed of $$1.5 	imes 10^3$ \ \mathrm{m/s}. $$What is its angular momentum?

Accepted Answer

$$L = mvr = 2.4 	imes 10$$^{-6}$$ 	imes 1.5 	imes 10^3$ 	imes 1 	imes 10$$^{-3}$$ = 3.6 	imes 10$$^{-6}$$ \ \mathrm{kg \cdot m^2$/s}$$

Question 8

A torque of $$1.50 \ \mathrm{N \cdot m} is $$applied to a wheel treated as a thin ring of mass $$1.2 \ \mathrm{kg}$$ and radius $$0.35 \ \mathrm{m}. $$What is its angular acceleration?

Accepted Answer

$$\alpha = \dfrac{	au}{I} = \dfrac{1.50}{1.2 	imes 0.35^2$} = 10.2 \ \mathrm{$$rad/s^2$$}$$

Question 9

A flywheel slows from $$79.3 \ \mathrm{rad/s} to $$rest, storing $$5.0 \ \mathrm{kJ} of $$work. The flywheel is a solid disk of radius $$0.50 \ \mathrm{m}$$, mass $$70 \ \mathrm{kg}. $$What is its moment of inertia?

Accepted Answer

$$I = \dfrac{1}{2}mr^2$ = \dfrac{1}{2} 	imes 70 	imes 0.5^2$ = 8.75 \ \mathrm{kg \cdot m^2$}$$

Question 10

A $$0.2 \ \mathrm{kg}$$ bullet embeds in a $$0.6 \ \mathrm{kg}$$ block on a frictionless surface. The block compresses a spring by $$0.05 \ \mathrm{m}. $$Spring constant is $$2800 \ \mathrm{N/m}. $$Find the bullet's initial speed.

Accepted Answer

$$v = \dfrac{\sqrt{k}x}{m_{total}} = \dfrac{\sqrt{2800} 	imes 0.05}{0.8} = 0.42 \ \mathrm{m/s}$$

Question 11

A $$7.5 \ \mathrm{kg}$$ skier starts from rest at the top of a $$45 \ \mathrm{m}$$ hill. Friction does $$1,000 \ \mathrm{J} of $$work. What is the speed at the base?

Accepted Answer

$$v = \sqrt{2gh - \dfrac{2W_{fric}}{m}} = \sqrt{2 	imes 9.8 	imes 45 - \dfrac{2 	imes 1000}{7.5}} = 17.1 \ \mathrm{m/s}$$

Question 12

A power plant delivers $$4.0 	imes 10^7$ \ \mathrm{W} to a $$city over $$5.0 \ \mathrm{h}. $$What is the energy delivered?

Accepted Answer

$$E = Pt = 4.0 	imes 10^7$ 	imes 5.0 	imes 3600 = 7.2 	imes 10$$^{11}$$ \ \mathrm{J}$$

Question 13

A $$1,500 \ \mathrm{kg}$$ car moves at $$25 \ \mathrm{m/s}$$ around a curve of diameter $$200 \ \mathrm{m}. $$What is the magnitude of the friction force required to keep it moving in a circle?

Accepted Answer

$$F = \dfrac{mv^2$}{r} = \dfrac{1500 	imes 25^2$}{100} = 9,375 \ \mathrm{N}$$

Question 14

A $$40 \ \mathrm{kg}$$ crate is pushed with a force of $$25 \ \mathrm{N}$$ horizontally on a frictionless surface. Find its acceleration.

Accepted Answer

$$a = \dfrac{F}{m} = \dfrac{25}{40} = 0.625 \ \mathrm{m/s^2$}$$

Question 15

You drive at $$65 \ \mathrm{mi/h}$$ east and pass a car going $$50 \ \mathrm{mi/h}$$ west. What is your velocity relative to the other car?

Accepted Answer

$$v_{rel} = 65 + 50 = 115 \ \mathrm{mi/h}$$

Question 16

A jet accelerates from rest to $$65 \ \mathrm{m/s} in$$ $$3.0 \ \mathrm{s} on a $$catapult. Assuming constant acceleration, how far does it travel?

Accepted Answer

$$d = \dfrac{1}{2}at^2$ = \dfrac{1}{2} 	imes \dfrac{65}{3} 	imes 3^2$ = 97.5 \ \mathrm{m}$$

Question 17

Vector $$\vec{A}$$ has a magnitude of $$6.0$$ and makes an angle of $$30^\circ$$ with the positive x-axis. Vector $$\vec{B}$$ has a magnitude of $$4.0$$ and points west. What is the resultant vector $$\vec{A} + \vec{B} in $$magnitude and direction?

Accepted Answer

Magnitude $$= 4.7$$, direction $$= 15^\circ$$ north of west

Question 18

A rock is thrown horizontally from a cliff $$20 \ \mathrm{m}$$ above a river and lands in the water after traveling $$22 \ \mathrm{m}$$ horizontally. Assuming negligible air resistance, what was its initial speed?

Accepted Answer

$$v_0$$ = \dfrac{22}{\sqrt{2h/g}} = \dfrac{22}{\sqrt{2 	imes 20 / 9.8}} = 10.8 \ \mathrm{m/s}$$

Question 19

A $$0.6 \ \mathrm{kg}$$ cart traveling at $$3.0 \ \mathrm{m/s}$$ collides elastically with a $$0.3 \ \mathrm{kg}$$ stationary cart on a frictionless track. Find the speed of the $$0.3 \ \mathrm{kg}$$ cart just after the collision.

Accepted Answer

$$v = \dfrac{2m_1}{m_1$ + m_2$}v_1$ = \dfrac{2 	imes 0.6}{0.6 + 0.3} 	imes 3.0 = 4.0 \ \mathrm{m/s}$$

Question 20

A mass of weight $$120 \ \mathrm{N} is $$hanging by a light rope at rest from the ceiling. The rope makes an angle of $$30^\circ$$ with the ceiling, as shown in the figure. Find the tension in the rope.

Accepted Answer

$$T = \dfrac{W}{\sin 30^\circ} = \dfrac{120}{0.5} = 240 \ \mathrm{N}$$

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