Q: A ball of mass 0.5 kg is dropped from a height of 10 m. Neglecting air resistance, what is its speed just before it hits the ground? (Use $$ g = 9.8\ \mathrm{m/s^2$} )$$

$$ v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 10} = \sqrt{196} = 14\ \mathrm{m/s} $$

Q: A spring with a force constant $$ k = 200\ \mathrm{N/m} is $$compressed by 0.1 m. What is the elastic potential energy stored in the spring?

$$ U = \frac{1}{2} k x^2$ = \frac{1}{2} \times 200 \times (0.1)^2$ = 1\ \mathrm{J} $$

Q: A 0.2 kg ball moving at $$ 5\ \mathrm{m/s} is $$brought to rest by a constant force in 0.1 s. What is the magnitude of the force?

$$ F = \frac{\Delta p}{\Delta t} = \frac{0.2 \times 5}{0.1} = 10\ \mathrm{N} $$

Q: A disk of mass 2 kg and radius 0.5 m rotates about its center with angular velocity $$ 4\ \mathrm{rad/s} . $$What is its rotational kinetic energy?

$$ K = \frac{1}{2} I \$$omega^2$$ = \frac{1}{2} \times \frac{1}{2} m r^2$ \times (4)^2$ = \frac{1}{2} \times 0.25 \times 2 \times 16 = 4\ \mathrm{J} $$

Question 1

A 2 kg block is pushed by a constant horizontal force of 10 N across a frictionless surface for a distance of 5 m. What is the work done by the force on the block?

Accepted Answer

$$ W = Fd = (10\ \mathrm{N})(5\ \mathrm{m}) = 50\ \mathrm{J} $$

Question 2

Which of the following statements best describes a conservative force?

Accepted Answer

A force for which the work done depends only on the initial and final positions, not on the path taken.

Question 3

A ball of mass 0.5 kg is dropped from a height of 10 m. Neglecting air resistance, what is its speed just before it hits the ground? (Use $$ g = 9.8\ \mathrm{m/s^2$} )$$

Accepted Answer

$$ v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 10} = \sqrt{196} = 14\ \mathrm{m/s} $$

Question 4

A spring with a force constant $$ k = 200\ \mathrm{N/m}  is $$compressed by 0.1 m. What is the elastic potential energy stored in the spring?

Accepted Answer

$$ U = \frac{1}{2} k x^2$ = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1\ \mathrm{J} $$

Question 5

A 3 kg object moving at $$ 4\ \mathrm{m/s} $$ collides elastically with a stationary 2 kg object. What is the velocity of the 3 kg object after the collision?

Accepted Answer

$$ v_1$' = \frac{m_1$ - m_2$}{m_1$ + m_2$} v_1$ = \frac{3 - 2}{3 + 2} 	imes 4 = \frac{1}{5} 	imes 4 = 0.8\ \mathrm{m/s} $$

Question 6

Which of the following best describes the impulse-momentum theorem?

Accepted Answer

$$ \vec{J} = \Delta \vec{p} = \int \vec{F} dt $$

Question 7

A 0.2 kg ball moving at $$ 5\ \mathrm{m/s}  is $$brought to rest by a constant force in 0.1 s. What is the magnitude of the force?

Accepted Answer

$$ F = \frac{\Delta p}{\Delta t} = \frac{0.2 	imes 5}{0.1} = 10\ \mathrm{N} $$

Question 8

A disk of mass 2 kg and radius 0.5 m rotates about its center with angular velocity $$ 4\ \mathrm{rad/s} . $$What is its rotational kinetic energy?

Accepted Answer

$$ K = \frac{1}{2} I \$$omega^2$$ = \frac{1}{2} 	imes \frac{1}{2} m r^2$ 	imes (4)^2$ = \frac{1}{2} 	imes 0.25 	imes 2 	imes 16 = 4\ \mathrm{J} $$

Question 9

A solid sphere and a solid cylinder, both of mass $$ m $$ and radius $$ r $$, are released from rest at the top of an incline. Which reaches the bottom first and why?

Accepted Answer

The solid sphere, because it has a smaller moment of inertia relative to its mass and radius.

Question 10

A 1 kg object is attached to a spring ($$ k = 100\ \mathrm{N/m} ) $$and oscillates on a frictionless surface. If the maximum compression is 0.2 m, what is the maximum speed of the object?

Accepted Answer

$$ v_{max} = \sqrt{\frac{k}{m}} x_{max} = \sqrt{\frac{100}{1}} 	imes 0.2 = 2\ \mathrm{m/s} $$

Question 11

Which of the following is the correct relationship between angular and linear quantities for an object rotating in a circle of radius $$ r $$?

Accepted Answer

$$ v_{tan} = r \omega $$

Question 12

A 4 kg object moving at $$ 3\ \mathrm{m/s} $$ collides inelastically with a 2 kg object at rest. What is their final velocity after sticking together?

Accepted Answer

$$ v_f = \frac{m_1$ v_1$ + m_2$ v_2$}{m_1$ + m_2$} = \frac{4 	imes 3 + 2 	imes 0}{4 + 2} = 2\ \mathrm{m/s} $$

Question 13

A force $$ F $$ acts at an angle $$ 	heta  to $$the direction of displacement $$ d . $$Which equation gives the work done by the force?

Accepted Answer

$$ W = F d \cos 	heta $$

Question 14

A 5 kg object is moving in a circle of radius 2 m at a constant speed of $$ 3\ \mathrm{m/s} . $$What is its centripetal acceleration?

Accepted Answer

$$ a_{rad} = \frac{v^2$}{r} = \frac{9}{2} = 4.5\ \mathrm{m/s^2$} $$

Question 15

Which of the following is true about the center of mass of a system?

Accepted Answer

It is the point where the total mass of the system can be considered to be concentrated for translational motion.

Question 16

A wheel starts from rest and accelerates at $$ 2\ \mathrm{$$rad/s^2$$} $$ for 5 seconds. What is its angular displacement?

Accepted Answer

$$ 	heta = \$$omega_0$$ t + \frac{1}{2} \alpha t^2$ = 0 + 0.5 	imes 2 	imes 25 = 25\ \mathrm{rad} $$

Question 17

A 0.5 kg ball is thrown vertically upward with a speed of $$ 8\ \mathrm{m/s} . $$What is the maximum height it reaches? (Neglect air resistance, $$ g = 9.8\ \mathrm{m/s^2$} )$$

Accepted Answer

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

Question 18

A 2 kg hoop and a 2 kg disk, both of radius 0.5 m, roll without slipping down an incline of height 2 m. Which has the greater speed at the bottom?

Accepted Answer

The disk, because it has a smaller moment of inertia and thus more translational kinetic energy.

Physics 220 Exam 3 Review: Work, Energy, Momentum, and Rotational Motion

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