Q: A ball is thrown straight up with an initial velocity of $$20\ \mathrm{m/s}. $$What is the maximum height it reaches? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

$$h = \frac{v_0$^2}{2g} = \frac{20^2$}{2 \times 9.8} = 20.4\ \mathrm{m}$$

Q: A projectile is launched at $$30^\circ$$ above the horizontal with a speed of $$50\ \mathrm{m/s}. $$What is the initial vertical component of its velocity?

$$v_{0y} = v_0$ \sin \theta = 50 \sin 30^\circ = 25\ \mathrm{m/s}$$

Q: A 10 kg object is at rest on a frictionless incline of $$30^\circ. $$What is the component of gravitational force parallel to the incline?

$$F_{\parallel} = mg \sin \theta = 10 \times 9.8 \times \sin 30^\circ = 49\ \mathrm{N}$$

Q: A solid disk ($$I = \frac{1}{2}MR^2$) of mass 2 kg and radius 0.5 m rotates at 10 rad/s. What is its rotational kinetic energy?

$$K = \frac{1}{2}I\$$omega^2$$ = \frac{1}{2} \times \frac{1}{2} \times 2 \times 0.5^2$ \times 10^2$ = 12.5\ \mathrm{J}$$

Q: A 3 kg object moves in a circle of radius 2 m at a constant speed of 4 m/s. What is the magnitude of the centripetal force?

$$F_c = m \frac{v^2$}{r} = 3 \times \frac{16}{2} = 24\ \mathrm{N}$$

Q: A hydraulic lift has a small piston of area $$0.01\ \mathrm{m^2$}$$ and a large piston of area $$0.5\ \mathrm{m^2$}. If a $$force of 200 N is applied to the small piston, what is the maximum weight that can be lifted (ignoring friction)?

$$F_{out} = F_{in} \frac{A_{out}}{A_{in}} = 200 \times \frac{0.5}{0.01} = 10,000\ \mathrm{N}$$

Question 1

A car travels 100 km north, then 60 km east. What is the magnitude of its displacement?

Accepted Answer

$$\sqrt{100^2$ + 60^2$} = 116 km$$

Question 2

A ball is thrown straight up with an initial velocity of $$20\ \mathrm{m/s}. $$What is the maximum height it reaches? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$h = \frac{v_0$^2}{2g} = \frac{20^2$}{2 	imes 9.8} = 20.4\ \mathrm{m}$$

Question 3

A projectile is launched at $$30^\circ$$ above the horizontal with a speed of $$50\ \mathrm{m/s}. $$What is the initial vertical component of its velocity?

Accepted Answer

$$v_{0y} = v_0$ \sin 	heta = 50 \sin 30^\circ = 25\ \mathrm{m/s}$$

Question 4

A 5 kg box is pulled across a horizontal surface with a force of 20 N at an angle of $$30^\circ$$ above the horizontal. What is the horizontal component of the force?

Accepted Answer

$$F_x = 20 \cos 30^\circ = 17.3\ \mathrm{N}$$

Question 5

A 10 kg object is at rest on a frictionless incline of $$30^\circ. $$What is the component of gravitational force parallel to the incline?

Accepted Answer

$$F_{\parallel} = mg \sin 	heta = 10 	imes 9.8 	imes \sin 30^\circ = 49\ \mathrm{N}$$

Question 6

A 2 kg mass is attached to a spring with $$k = 200\ \mathrm{N/m}. $$What is the period of oscillation?

Accepted Answer

$$T = 2\pi \sqrt{\frac{m}{k}} = 2\pi \sqrt{\frac{2}{200}} = 0.63\ \mathrm{s}$$

Question 7

A 0.5 kg ball moving at $$4\ \mathrm{m/s}$$ collides elastically with a stationary 0.5 kg ball. What is the velocity of the first ball after the collision?

Accepted Answer

$$0\ \mathrm{m/s}$$

Question 8

A solid disk ($$I = \frac{1}{2}MR^2$) of mass 2 kg and radius 0.5 m rotates at 10 rad/s. What is its rotational kinetic energy?

Accepted Answer

$$K = \frac{1}{2}I\$$omega^2$$ = \frac{1}{2} 	imes \frac{1}{2} 	imes 2 	imes 0.5^2$ 	imes 10^2$ = 12.5\ \mathrm{J}$$

Question 9

A 1.5 m long simple pendulum swings with a small amplitude. What is its period? ($$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$T = 2\pi \sqrt{\frac{L}{g}} = 2\pi \sqrt{\frac{1.5}{9.8}} = 2.46\ \mathrm{s}$$

Question 10

A 3 kg object moves in a circle of radius 2 m at a constant speed of 4 m/s. What is the magnitude of the centripetal force?

Accepted Answer

$$F_c = m \frac{v^2$}{r} = 3 	imes \frac{16}{2} = 24\ \mathrm{N}$$

Question 11

A hydraulic lift has a small piston of area $$0.01\ \mathrm{m^2$}$$ and a large piston of area $$0.5\ \mathrm{m^2$}. If a $$force of 200 N is applied to the small piston, what is the maximum weight that can be lifted (ignoring friction)?

Accepted Answer

$$F_{out} = F_{in} \frac{A_{out}}{A_{in}} = 200 	imes \frac{0.5}{0.01} = 10,000\ \mathrm{N}$$

Question 12

A 0.2 kg ice cube at $$0^\circC is $$placed in 0.5 kg of water at $$20^\circC. $$What is the final temperature after the ice melts? ($$c_{water} = 4186\ \mathrm{J/kg\cdot K}$$, $$L_f = 3.34 	imes 10^5$\ \mathrm{J/kg})$$

Accepted Answer

The final temperature is less than $$20^\circC $$but above $$0^\circC$$, since the heat from water is enough to melt the ice and warm the mixture.

Question 13

A gas in a cylinder expands isothermally at $$300\ \mathrm{K}$$, doing $$500\ \mathrm{J} of $$work. What is the change in internal energy?

Accepted Answer

$$\Delta U = 0 ($$for isothermal process in ideal gas)

Question 14

A 2 kg object floats in water. What is the buoyant force acting on it?

Accepted Answer

$$F_b = mg = 2 	imes 9.8 = 19.6\ \mathrm{N}$$

Question 15

A sound wave travels through air at $$340\ \mathrm{m/s}$$ with a frequency of $$1700\ \mathrm{Hz}. $$What is its wavelength?

Accepted Answer

$$\lambda = \frac{v}{f} = \frac{340}{1700} = 0.2\ \mathrm{m}$$

Question 16

A 0.1 mol sample of an ideal gas at $$300\ \mathrm{K}$$ occupies $$2.46\ \mathrm{L}. $$What is the pressure? ($$R = 8.314\ \mathrm{J/(mol\cdot K)})$$

Accepted Answer

$$P = \frac{nRT}{V} = \frac{0.1 	imes 8.314 	imes 300}{0.00246} = 101,400\ \mathrm{Pa}$$

Question 17

A force of $$10\ \mathrm{N} is $$applied tangentially to a wheel of radius $$0.2\ \mathrm{m}. $$What is the torque produced?

Accepted Answer

$$	au = rF = 0.2 	imes 10 = 2\ \mathrm{N\cdot m}$$

Question 18

A block slides down a frictionless incline of height $$h. $$What is its speed at the bottom?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 19

A 0.5 kg ball is attached to a string and swung in a horizontal circle of radius 1 m at 2 m/s. What is its angular momentum?

Accepted Answer

$$L = mvr = 0.5 	imes 2 	imes 1 = 1\ \mathrm{kg\cdot m^2$/s}$$

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