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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