Q: A $$0.5\ \mathrm{kg}$$ ball is dropped from a height of $$10\ \mathrm{m}. $$Ignoring air resistance, what is its speed just before it hits the ground?

$$\displaystyle v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = 14.0\ \mathrm{m/s}$$

Q: A $$2\ \mathrm{kg}$$ block is attached to a spring with a spring constant $$k = 100\ \mathrm{N/m}. If $$the block is pulled $$0.1\ \mathrm{m}$$ from equilibrium and released, what is the maximum potential energy stored in the spring?

$$\displaystyle U = \frac{1}{2}kx^2$ = \frac{1}{2} \times 100 \times (0.1)^2$ = 0.5\ \mathrm{J}$$

Q: A uniform beam of length $$6\ \mathrm{m}$$ and mass $$30\ \mathrm{kg} is $$supported at its ends. A $$60\ \mathrm{kg}$$ person stands $$2\ \mathrm{m}$$ from the left end. What is the force exerted by the right support?

$$\displaystyle F_{right} = \frac{(M_{beam} + M_{person})g \times d_{person}}{L} = \frac{(30+60)\times9.8\times2}{6} = 294\ \mathrm{N}$$

Question 1

A car accelerates uniformly from rest to a speed of $$20\ \mathrm{m/s} in$$ $$5\ \mathrm{s}. $$What is the magnitude of its acceleration?

Accepted Answer

$$2\ \mathrm{m/s^2$}$$

Question 2

Which of the following best describes Newton's Third Law of Motion?

Accepted Answer

For every action, there is an equal and opposite reaction.

Question 3

A $$10\ \mathrm{kg}$$ box is pulled across a horizontal surface with a force of $$50\ \mathrm{N}$$, and the coefficient of kinetic friction is $$0.2. $$What is the acceleration of the box? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$3.04\ \mathrm{m/s^2$}$$

Question 4

A projectile is launched at an angle of $$30^\circ$$ above the horizontal with an initial speed of $$40\ \mathrm{m/s}. $$What is the horizontal component of its velocity?

Accepted Answer

$$40\cos 30^\circ = 34.6\ \mathrm{m/s}$$

Question 5

Which of the following statements about the conservation of momentum is correct?

Accepted Answer

The total momentum of a closed system remains constant if no external forces act on it.

Question 6

A $$2\ \mathrm{kg}$$ mass attached to a string is whirled in a horizontal circle of radius $$1.5\ \mathrm{m} at a $$constant speed of $$4\ \mathrm{m/s}. $$What is the tension in the string?

Accepted Answer

$$\displaystyle T = m\frac{v^2$}{r} = 2\frac{16}{1.5} = 21.3\ \mathrm{N}$$

Question 7

A $$0.5\ \mathrm{kg}$$ ball is dropped from a height of $$10\ \mathrm{m}. $$Ignoring air resistance, what is its speed just before it hits the ground?

Accepted Answer

$$\displaystyle v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} = 14.0\ \mathrm{m/s}$$

Question 8

A $$5\ \mathrm{kg}$$ object moving at $$6\ \mathrm{m/s}$$ collides elastically with a stationary $$3\ \mathrm{kg}$$ object. What is the velocity of the $$5\ \mathrm{kg}$$ object after the collision?

Accepted Answer

$$\displaystyle v' = \frac{m_1$ - m_2$}{m_1$ + m_2$}v_1$ = \frac{5-3}{5+3} 	imes 6 = 1.5\ \mathrm{m/s}$$

Question 9

A $$2\ \mathrm{kg}$$ block is attached to a spring with a spring constant $$k = 100\ \mathrm{N/m}. If $$the block is pulled $$0.1\ \mathrm{m}$$ from equilibrium and released, what is the maximum potential energy stored in the spring?

Accepted Answer

$$\displaystyle U = \frac{1}{2}kx^2$ = \frac{1}{2} 	imes 100 	imes (0.1)^2$ = 0.5\ \mathrm{J}$$

Question 10

A solid disk of mass $$4\ \mathrm{kg}$$ and radius $$0.5\ \mathrm{m}$$ rotates about its center at $$10\ \mathrm{rad/s}. $$What is its rotational kinetic energy?

Accepted Answer

$$\displaystyle KE_{rot} = \frac{1}{2}I\$$omega^2$$ = \frac{1}{2} 	imes \frac{1}{2}mr^2$ 	imes \$$omega^2$$ = \frac{1}{4} 	imes 4 	imes 0.25 	imes 100 = 25\ \mathrm{J}$$

Question 11

A uniform beam of length $$6\ \mathrm{m}$$ and mass $$30\ \mathrm{kg} is $$supported at its ends. A $$60\ \mathrm{kg}$$ person stands $$2\ \mathrm{m}$$ from the left end. What is the force exerted by the right support?

Accepted Answer

$$\displaystyle F_{right} = \frac{(M_{beam} + M_{person})g 	imes d_{person}}{L} = \frac{(30+60)	imes9.8	imes2}{6} = 294\ \mathrm{N}$$

Question 12

Which of the following best describes the efficiency of a real-world energy transformation?

Accepted Answer

Efficiency is always less than 100% due to energy lost as heat or other forms.

Question 13

A $$1.5\ \mathrm{kg}$$ object is moving in a circle of radius $$0.75\ \mathrm{m} at a $$constant speed of $$3\ \mathrm{m/s}. $$What is the magnitude of the centripetal force acting on the object?

Accepted Answer

$$\displaystyle F_c = m\frac{v^2$}{r} = 1.5\frac{9}{0.75} = 18\ \mathrm{N}$$

Question 14

A $$0.2\ \mathrm{kg}$$ ice cube at $$0^\circ\mathrm{C} is $$placed in $$0.5\ \mathrm{kg} of $$water at $$20^\circ\mathrm{C}. $$What is the final temperature after the ice melts? (Assume no heat loss to the environment, $$L_f = 334,000\ \mathrm{J/kg}$$, $$c_{water} = 4,186\ \mathrm{J/(kg\cdot K)})$$

Accepted Answer

The final temperature is less than $$20^\circ\mathrm{C}$$ but above $$0^\circ\mathrm{C}$$ because the ice absorbs heat to melt, cooling the water.

Question 15

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 $$200\ \mathrm{N} is $$applied to the small piston, what is the maximum weight that can be lifted by the large piston (neglecting friction)?

Accepted Answer

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

Question 16

Which of the following is the correct expression for the gravitational force between two masses $$m_1$$ and $$m_2$$ separated by a distance $$r$$?

Accepted Answer

$$\displaystyle F = G\frac{m_1$ m_2$}{r^2$}$$

Question 17

A $$3\ \mathrm{kg}$$ object is moving with a velocity of $$4\ \mathrm{m/s}$$ east. It collides inelastically with a $$2\ \mathrm{kg}$$ object moving at $$6\ \mathrm{m/s}$$ west. What is the velocity of the combined mass after the collision?

Accepted Answer

$$\displaystyle v = \frac{3	imes4 + 2	imes(-6)}{3+2} = 0\ \mathrm{m/s}$$

Question 18

A $$1\ \mathrm{kg}$$ object is attached to a string and swung in a vertical circle of radius $$2\ \mathrm{m}. $$What is the minimum speed at the top of the circle so the string remains taut? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\displaystyle v_{min} = \sqrt{gr} = \sqrt{9.8 	imes 2} = 4.43\ \mathrm{m/s}$$

Question 19

A $$0.5\ \mathrm{kg}$$ ball moving at $$10\ \mathrm{m/s}$$ strikes a wall and rebounds in the opposite direction at $$8\ \mathrm{m/s}. $$What is the magnitude of the impulse delivered to the ball?

Accepted Answer

$$\displaystyle |\Delta p| = m|v_f - v_i| = 0.5 	imes |(-8) - 10| = 9\ \mathrm{kg\cdot m/s}$$

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