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? (Use $g = 9.8\ \mathrm{m/s^2}$)

$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = 14\ \mathrm{m/s}$

Q: A block slides down a frictionless ramp inclined at $30^\circ$ to the horizontal. What is the acceleration of the block?

$a = g \sin\theta = 9.8 \times \sin 30^\circ = 4.9\ \mathrm{m/s^2}$

Q: A $2.0\ \mathrm{kg}$ object moves at $3.0\ \mathrm{m/s}$ east. What is its momentum?

$p = mv = 2.0 \times 3.0 = 6.0\ \mathrm{kg\cdot m/s}$\ east

Q: A $5.0\ \mathrm{kg}$ box is pulled across a horizontal surface with a force of $20\ \mathrm{N}$ at an angle of $30^\circ$ above the horizontal. What is the horizontal component of the force?

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

Q: A $10\ \mathrm{kg}$ mass is attached to a $2\ \mathrm{m}$ long rope and swung in a horizontal circle at $4\ \mathrm{m/s}$. What is the tension in the rope?

$T = \frac{mv^2}{r} = \frac{10 \times 16}{2} = 80\ \mathrm{N}$

Q: A $1.0\ \mathrm{kg}$ object is dropped from rest. How much gravitational potential energy does it lose after falling $5.0\ \mathrm{m}$? (Use $g = 9.8\ \mathrm{m/s^2}$)

$\Delta U = mgh = 1.0 \times 9.8 \times 5.0 = 49\ \mathrm{J}$

Q: A $2.0\ \mathrm{kg}$ block slides $3.0\ \mathrm{m}$ across a horizontal surface with a kinetic friction coefficient $\mu_k = 0.2$. What is the work done by friction?

$W = -\mu_k m g d = -0.2 \times 2.0 \times 9.8 \times 3.0 = -11.76\ \mathrm{J}$

Question 1

A car accelerates from rest at a constant rate of $2.0\ \mathrm{m/s^2}$ for $5.0\ \mathrm{s}$. What is its final velocity?

Accepted Answer

$v_f = 10\ \mathrm{m/s}$

Question 2

Which of the following statements about Newton's Third Law is correct?

Accepted Answer

For every force, there is an equal and opposite force acting on a different object.

Question 3

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? (Use $g = 9.8\ \mathrm{m/s^2}$)

Accepted Answer

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

Question 4

A block slides down a frictionless ramp inclined at $30^\circ$ to the horizontal. What is the acceleration of the block?

Accepted Answer

$a = g \sin	heta = 9.8 	imes \sin 30^\circ = 4.9\ \mathrm{m/s^2}$

Question 5

Which of the following is a scalar quantity?

Accepted Answer

Speed

Question 6

A $2.0\ \mathrm{kg}$ object moves at $3.0\ \mathrm{m/s}$ east. What is its momentum?

Accepted Answer

$p = mv = 2.0 	imes 3.0 = 6.0\ \mathrm{kg\cdot m/s}$\ east

Question 7

A $5.0\ \mathrm{kg}$ box is pulled across a horizontal surface with a force of $20\ \mathrm{N}$ at an angle of $30^\circ$ above the horizontal. What is the horizontal component of the force?

Accepted Answer

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

Question 8

A $0.2\ \mathrm{kg}$ ball moving at $5\ \mathrm{m/s}$ collides elastically with a stationary $0.3\ \mathrm{kg}$ ball. What is the velocity of the $0.2\ \mathrm{kg}$ ball after the collision?

Accepted Answer

$v_1' = \frac{m_1 - m_2}{m_1 + m_2} v_1 = \frac{0.2 - 0.3}{0.2 + 0.3} 	imes 5 = -1\ \mathrm{m/s}$

Question 9

A $10\ \mathrm{kg}$ mass is attached to a $2\ \mathrm{m}$ long rope and swung in a horizontal circle at $4\ \mathrm{m/s}$. What is the tension in the rope?

Accepted Answer

$T = \frac{mv^2}{r} = \frac{10 	imes 16}{2} = 80\ \mathrm{N}$

Question 10

Which equation correctly expresses the work done by a constant force $\vec{F}$ over a displacement $\vec{d}$?

Accepted Answer

$W = \vec{F} \cdot \vec{d}$

Question 11

A $1.0\ \mathrm{kg}$ object is dropped from rest. How much gravitational potential energy does it lose after falling $5.0\ \mathrm{m}$? (Use $g = 9.8\ \mathrm{m/s^2}$)

Accepted Answer

$\Delta U = mgh = 1.0 	imes 9.8 	imes 5.0 = 49\ \mathrm{J}$

Question 12

A $0.5\ \mathrm{kg}$ ball is thrown vertically upward with an initial speed of $8\ \mathrm{m/s}$. What is its maximum height? (Use $g = 9.8\ \mathrm{m/s^2}$)

Accepted Answer

$h = \frac{v^2}{2g} = \frac{64}{19.6} = 3.27\ \mathrm{m}$

Question 13

A $2.0\ \mathrm{kg}$ block slides $3.0\ \mathrm{m}$ across a horizontal surface with a kinetic friction coefficient $\mu_k = 0.2$. What is the work done by friction?

Accepted Answer

$W = -\mu_k m g d = -0.2 	imes 2.0 	imes 9.8 	imes 3.0 = -11.76\ \mathrm{J}$

Question 14

A $0.5\ \mathrm{kg}$ ball moving at $2\ \mathrm{m/s}$ collides inelastically with a $0.5\ \mathrm{kg}$ stationary ball. What is their final velocity after sticking together?

Accepted Answer

$v_f = \frac{m_1 v_1 + m_2 v_2}{m_1 + m_2} = \frac{0.5 	imes 2 + 0.5 	imes 0}{1.0} = 1\ \mathrm{m/s}$

Question 15

A $3.0\ \mathrm{kg}$ object moves in a circle of radius $2.0\ \mathrm{m}$ at $6.0\ \mathrm{m/s}$. What is its centripetal acceleration?

Accepted Answer

$a_c = \frac{v^2}{r} = \frac{36}{2} = 18\ \mathrm{m/s^2}$

Question 16

A $2.0\ \mathrm{kg}$ mass is attached to a $0.5\ \mathrm{m}$ long string and rotates in a horizontal circle. If the tension in the string is $32\ \mathrm{N}$, what is the speed of the mass?

Accepted Answer

$v = \sqrt{\frac{T r}{m}} = \sqrt{\frac{32 	imes 0.5}{2.0}} = 2.83\ \mathrm{m/s}$

Question 17

What is the gravitational force between two $5.0\ \mathrm{kg}$ masses separated by $2.0\ \mathrm{m}$? ($G = 6.67 	imes 10^{-11}\ \mathrm{N\cdot m^2/kg^2}$)

Accepted Answer

$F = G \frac{m_1 m_2}{r^2} = 6.67 	imes 10^{-11} \frac{25}{4} = 4.17 	imes 10^{-10}\ \mathrm{N}$

Question 18

A $0.2\ \mathrm{kg}$ ball is attached to a $0.5\ \mathrm{m}$ string and swung in a vertical circle. At the bottom, its speed is $4\ \mathrm{m/s}$. What is the tension in the string at the bottom?

Accepted Answer

$T = mg + \frac{mv^2}{r} = 0.2 	imes 9.8 + 0.2 	imes \frac{16}{0.5} = 1.96 + 6.4 = 8.36\ \mathrm{N}$

Fundamental Concepts in College Physics: Kinematics, Dynamics, Work, Energy, Momentum, Rotation, and Gravitation

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