Q: A car accelerates uniformly from rest and covers a distance of 100 m in 5 seconds. What is its acceleration?

$$a = \frac{2 \times 100}{5^2$} = 8\ \text{m/s}^2$$

Q: A projectile is launched at an angle $$\theta$$ with initial speed $$v_0. $$Which equation gives the maximum height reached?

$$H = \frac{v_0$^2 \sin^2$ \theta}{2g}$$

Q: A 2 kg block is pulled horizontally with a force of 10 N. If the coefficient of kinetic friction is 0.2, what is the acceleration?

$$a = \frac{10 - (0.2 \times 2 \times 9.8)}{2} = 3.04\ \text{m/s}^2$$

Q: A 5 kg object moving at 4 m/s collides and sticks to a 3 kg object at rest. What is their final velocity?

$$v_f = \frac{5 \times 4 + 3 \times 0}{5 + 3} = 2.5\ \text{m/s}$$

Q: A 0.5 kg mass attached to a spring oscillates with a frequency of 2 Hz. What is the spring constant $$k$$?

$$k = (2\pi f)^2$ m = (2\pi \times 2)^2$ \times 0.5 = 79\ \text{N/m}$$

Q: A sound wave travels through air at 340 m/s. If its wavelength is 0.85 m, what is its frequency?

$$f = \frac{v}{\lambda} = \frac{340}{0.85} = 400\ \text{Hz}$$

Q: A metal rod is heated from 20°C to 120°C. If its initial length is 1 m and the coefficient of linear expansion is $$2 \times 10$$^{-5}$$\ \text{K}^{-1}$$, what is its final length?

$$L = L_0$ (1 + \alpha \Delta T) = 1 \times (1 + 2 \times 10$$^{-5}$$ \times 100) = 1.002\ \text{m}$$

Q: A resistor of 10 $$\Omega is $$connected to a 12 V battery. What is the power dissipated?

$$P = \frac{V^2$}{R} = \frac{12^2$}{10} = 14.4\ \text{W}$$

Q: A wire carries a current of 5 A perpendicular to a magnetic field of 0.2 T. If the wire is 0.4 m long, what is the force on the wire?

$$F = I \ell B = 5 \times 0.4 \times 0.2 = 0.4\ \text{N}$$

Question 1

A car accelerates uniformly from rest and covers a distance of 100 m in 5 seconds. What is its acceleration?

Accepted Answer

$$a = \frac{2 	imes 100}{5^2$} = 8\ 	ext{m/s}^2$$

Question 2

A projectile is launched at an angle $$	heta$$ with initial speed $$v_0. $$Which equation gives the maximum height reached?

Accepted Answer

$$H = \frac{v_0$^2 \sin^2$ 	heta}{2g}$$

Question 3

A 2 kg block is pulled horizontally with a force of 10 N. If the coefficient of kinetic friction is 0.2, what is the acceleration?

Accepted Answer

$$a = \frac{10 - (0.2 	imes 2 	imes 9.8)}{2} = 3.04\ 	ext{m/s}^2$$

Question 4

A 5 kg object moving at 4 m/s collides and sticks to a 3 kg object at rest. What is their final velocity?

Accepted Answer

$$v_f = \frac{5 	imes 4 + 3 	imes 0}{5 + 3} = 2.5\ 	ext{m/s}$$

Question 5

A satellite orbits Earth at a height where the acceleration due to gravity is $$6\ 	ext{m/s}^2. If $$Earth's radius is $$6.4 	imes 10^6$\ 	ext{m}$$, what is the satellite's orbital radius?

Accepted Answer

$$r = \frac{GM}{g}$$; but since $$g = \frac{GM}{r^2$}$$, $$r = \sqrt{\frac{GM}{g}}$$; $$r = \sqrt{\frac{6.67 	imes 10$$^{-11}$$ 	imes 5.98 	imes 10$$^{24}$$}{6}} \approx 1.0 	imes 10^7$\ 	ext{m}$$

Question 6

A 0.5 kg mass attached to a spring oscillates with a frequency of 2 Hz. What is the spring constant $$k$$?

Accepted Answer

$$k = (2\pi f)^2$ m = (2\pi 	imes 2)^2$ 	imes 0.5 = 79\ 	ext{N/m}$$

Question 7

A sound wave travels through air at 340 m/s. If its wavelength is 0.85 m, what is its frequency?

Accepted Answer

$$f = \frac{v}{\lambda} = \frac{340}{0.85} = 400\ 	ext{Hz}$$

Question 8

A metal rod is heated from 20°C to 120°C. If its initial length is 1 m and the coefficient of linear expansion is $$2 	imes 10$$^{-5}$$\ 	ext{K}^{-1}$$, what is its final length?

Accepted Answer

$$L = L_0$ (1 + \alpha \Delta T) = 1 	imes (1 + 2 	imes 10$$^{-5}$$ 	imes 100) = 1.002\ 	ext{m}$$

Question 9

A resistor of 10 $$\Omega is $$connected to a 12 V battery. What is the power dissipated?

Accepted Answer

$$P = \frac{V^2$}{R} = \frac{12^2$}{10} = 14.4\ 	ext{W}$$

Question 10

A wire carries a current of 5 A perpendicular to a magnetic field of 0.2 T. If the wire is 0.4 m long, what is the force on the wire?

Accepted Answer

$$F = I \ell B = 5 	imes 0.4 	imes 0.2 = 0.4\ 	ext{N}$$

Question 11

A light ray passes from air ($$n=1.0) $$into glass ($$n=1.5) at an $$angle of $$30^\circ to $$the normal. What is the angle of refraction?

Accepted Answer

$$n_1$$ \sin \$$theta_1$$ = $$n_2$$ \sin \$$theta_2$$; $$\sin \$$theta_2$$ = \frac{1.0 \sin 30^\circ}{1.5} = \frac{0.5}{1.5} = 0.333$$; $$\$$theta_2$$ = 19.5^\circ$$

Question 12

A capacitor of $$10\ \mu	ext{F} is $$charged to 5 V. What is the energy stored?

Accepted Answer

$$U = \frac{1}{2} C V^2$ = \frac{1}{2} 	imes 10 	imes 10$$^{-6}$$ 	imes 25 = 1.25 	imes 10$$^{-4}$$\ 	ext{J}$$

Question 13

A heat engine absorbs 500 J of heat and does 200 J of work. What is its efficiency?

Accepted Answer

$$\eta = \frac{W}{Q_h} = \frac{200}{500} = 0.4 = 40\%$$

Question 14

A 1 kg object is dropped from a height of 10 m. Ignoring air resistance, what is its speed just before hitting the ground?

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} = 14\ 	ext{m/s}$$

Question 15

A circuit contains a 2 $$\Omega$$ resistor and a 4 $$\Omega$$ resistor in series with a 12 V battery. What is the current?

Accepted Answer

$$I = \frac{V}{R_{	ext{total}}} = \frac{12}{2+4} = 2\ 	ext{A}$$

Question 16

A 0.2 kg ball is swung in a circle of radius 0.5 m at a speed of 3 m/s. What is the centripetal force?

Accepted Answer

$$F_c = \frac{mv^2$}{r} = \frac{0.2 	imes 3^2$}{0.5} = 3.6\ 	ext{N}$$

Question 17

A wave on a string is described by $$y(x,t) = 0.05 \sin(4\pi x - 20\pi t). $$What is the wave's speed?

Accepted Answer

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

Question 18

A lens has a focal length of 10 cm. An object is placed 30 cm from the lens. What is the image distance?

Accepted Answer

$$\frac{1}{f} = \frac{1}{d_o} + \frac{1}{d_i}$$; $$\frac{1}{10} = \frac{1}{30} + \frac{1}{d_i}$$; $$\frac{1}{d_i} = \frac{1}{10} - \frac{1}{30} = \frac{2}{30}$$; $$d_i = 15\ 	ext{cm}$$

PEN120 Physics with Calculus: Semester Study Guide and Topic Overview

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