Q: A car accelerates from rest at $$2\ \mathrm{m/s^2$}$$ for $$5\ \mathrm{s}. $$What is the distance traveled?

$$s = \frac{1}{2} a t^2$ = \frac{1}{2} \times 2 \times 5^2$ = 25\ \mathrm{m}$$

Q: A block of mass $$m$$ slides down a rough incline. If the coefficient of kinetic friction is $$\mu_k$$ and the angle of incline is $$\theta$$, what is the net force acting on the block?

$$F = m g (\sin \theta - \mu_k \cos \theta)$$

Q: A $$2\ \mathrm{kg}$$ object is lifted vertically by $$3\ \mathrm{m}. $$What is the work done against gravity?

$$W = m g h = 2 \times 9.8 \times 3 = 58.8\ \mathrm{J}$$

Q: A $$1\ \mathrm{kg}$$ ball is thrown vertically upward with an initial speed of $$10\ \mathrm{m/s}. $$How long does it take to return to the ground?

$$t = \frac{2 v_0$}{g} = \frac{2 \times 10}{9.8} \approx 2.04\ \mathrm{s}$$

Q: A spring with spring constant $$k = 200\ \mathrm{N/m} is $$compressed by $$0.1\ \mathrm{m}. $$What is the work done on the spring?

$$W = \frac{1}{2} k x^2$ = \frac{1}{2} \times 200 \times 0.1^2$ = 1\ \mathrm{J}$$

Q: A simple harmonic oscillator has amplitude $$A = 0.5\ \mathrm{m}$$ and angular frequency $$\omega = 2\ \mathrm{rad/s}. $$What is its maximum speed?

$$v_{\text{max}} = \omega A = 2 \times 0.5 = 1\ \mathrm{m/s}$$

Q: At a depth of $$1000\ \mathrm{m} in $$the ocean, what is the hydrostatic pressure due to the water alone? (Assume $$\rho = 1000\ \mathrm{kg/m^3$}$$, $$g = 9.8\ \mathrm{m/s^2$})$$

$$P = \rho g h = 1000 \times 9.8 \times 1000 = 9.8 \times 10^6$\ \mathrm{Pa}$$

Q: A light ray travels from water ($$n_1 = 1.33$) to air (n_2$ = 1.00). $$What is the minimum angle of incidence for total internal reflection?

$$\theta_c = \arcsin\left(\frac{n_2$}{n_1$}\right) = \arcsin\left(\frac{1.00}{1.33}\right) \approx 48.8^\circ$$

Q: A tennis ball is hit at an angle of $$30^\circ$$ with an initial speed of $$20\ \mathrm{m/s}. $$What is the horizontal component of its velocity?

$$v_x = v_0$ \cos \theta = 20 \cos 30^\circ = 20 \times 0.866 = 17.32\ \mathrm{m/s}$$

Question 1

A vector $$	extbf{A}$$ has components $$A_x = 3$$ and $$A_y = 4. $$What is the magnitude of $$	extbf{A}$$?

Accepted Answer

$$\sqrt{3^2$ + 4^2$} = 5$$

Question 2

A car accelerates from rest at $$2\ \mathrm{m/s^2$}$$ for $$5\ \mathrm{s}. $$What is the distance traveled?

Accepted Answer

$$s = \frac{1}{2} a t^2$ = \frac{1}{2} 	imes 2 	imes 5^2$ = 25\ \mathrm{m}$$

Question 3

A block of mass $$m$$ slides down a rough incline. If the coefficient of kinetic friction is $$\mu_k$$ and the angle of incline is $$	heta$$, what is the net force acting on the block?

Accepted Answer

$$F = m g (\sin 	heta - \mu_k \cos 	heta)$$

Question 4

A $$2\ \mathrm{kg}$$ object is lifted vertically by $$3\ \mathrm{m}. $$What is the work done against gravity?

Accepted Answer

$$W = m g h = 2 	imes 9.8 	imes 3 = 58.8\ \mathrm{J}$$

Question 5

A $$1\ \mathrm{kg}$$ ball is thrown vertically upward with an initial speed of $$10\ \mathrm{m/s}. $$How long does it take to return to the ground?

Accepted Answer

$$t = \frac{2 v_0$}{g} = \frac{2 	imes 10}{9.8} \approx 2.04\ \mathrm{s}$$

Question 6

A spring with spring constant $$k = 200\ \mathrm{N/m} is $$compressed by $$0.1\ \mathrm{m}. $$What is the work done on the spring?

Accepted Answer

$$W = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 200 	imes 0.1^2$ = 1\ \mathrm{J}$$

Question 7

A simple harmonic oscillator has amplitude $$A = 0.5\ \mathrm{m}$$ and angular frequency $$\omega = 2\ \mathrm{rad/s}. $$What is its maximum speed?

Accepted Answer

$$v_{	ext{max}} = \omega A = 2 	imes 0.5 = 1\ \mathrm{m/s}$$

Question 8

At a depth of $$1000\ \mathrm{m} in $$the ocean, what is the hydrostatic pressure due to the water alone? (Assume $$\rho = 1000\ \mathrm{kg/m^3$}$$, $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$P = ho g h = 1000 	imes 9.8 	imes 1000 = 9.8 	imes 10^6$\ \mathrm{Pa}$$

Question 9

A light ray travels from water ($$n_1 = 1.33$) to air (n_2$ = 1.00). $$What is the minimum angle of incidence for total internal reflection?

Accepted Answer

$$	heta_c = \arcsin\left(\frac{n_2$}{n_1$}ight) = \arcsin\left(\frac{1.00}{1.33}ight) \approx 48.8^\circ$$

Question 10

Express $$0.00056 in $$scientific notation.

Accepted Answer

$$5.6 	imes 10$$^{-4}$$

Question 11

A tennis ball is hit at an angle of $$30^\circ$$ with an initial speed of $$20\ \mathrm{m/s}. $$What is the horizontal component of its velocity?

Accepted Answer

$$v_x = v_0$ \cos 	heta = 20 \cos 30^\circ = 20 	imes 0.866 = 17.32\ \mathrm{m/s}$$

Question 12

A train approaches a stationary observer at $$30\ \mathrm{m/s}. $$The train emits a whistle at $$500\ \mathrm{Hz}. $$What frequency does the observer hear? (Speed of sound $$v = 340\ \mathrm{m/s})$$

Accepted Answer

$$f' = f \frac{v}{v - v_s} = 500 \frac{340}{340 - 30} = 500 \frac{340}{310} \approx 548\ \mathrm{Hz}$$

Question 13

A wall clock's second hand completes one revolution in $$60\ \mathrm{s}. $$What is its angular frequency?

Accepted Answer

$$\omega = \frac{2\pi}{T} = \frac{2\pi}{60} \approx 0.105\ \mathrm{rad/s}$$

Question 14

A transverse wave on a string is described by $$y(x,t) = 0.05 \sin(4\pi x - 20\pi t)$$, where $$x$$ and $$y$$ are in meters and $$t in $$seconds. What is the speed of the wave?

Accepted Answer

$$v = \frac{\omega}{k} = \frac{20\pi}{4\pi} = 5\ \mathrm{m/s}$$

Question 15

Blood flows through an artery with cross-sectional area $$A_1 = 2$$\ \mathrm{$$cm^2$$}$$ at v_1$ = 0.5\ \mathrm{m/s}. If $$plaque reduces the area to $$A_2 = 1$$\ \mathrm{$$cm^2$$}$$, what is the new velocity v_2$?

Accepted Answer

$$v_2$$ = \frac{$$A_1$$ $$v_1$$}{$$A_2$$} = \frac{2 	imes 0.5}{1} = 1\ \mathrm{m/s}$$

Question 16

A $$5\ \mathrm{kg}$$ block is pulled across a horizontal surface with a force of $$20\ \mathrm{N} at $$constant speed. What is the coefficient of kinetic friction?

Accepted Answer

$$\mu_k = \frac{F}{m g} = \frac{20}{5 	imes 9.8} \approx 0.41$$

Question 17

According to Pascal's Law, what happens to the pressure in a fluid when force is applied to a closed system?

Accepted Answer

The pressure increases equally at all points in the fluid.

Question 18

A projectile is launched at $$45^\circ$$ with an initial speed of $$10\ \mathrm{m/s}. $$What is its maximum height?

Accepted Answer

$$h_{	ext{max}} = \frac{v_0$^2 \sin^2$ 	heta}{2g} = \frac{10^2$ 	imes (\sin 45^\$$circ)^2$$}{2 	imes 9.8} = \frac{100 	imes 0.5}{19.6} \approx 2.55\ \mathrm{m}$$

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