Q: A projectile is launched at an angle $$\theta$$ above the horizontal with initial speed $$v_0. $$Which of the following correctly gives the time of flight until it returns to the same vertical level?

$$t = \dfrac{2 v_0$ \sin \theta}{g}$$

Q: A $$5\ \mathrm{kg}$$ box is pulled up a rough incline at constant speed by a force parallel to the incline. The incline makes an angle of $$30^\circ$$ with the horizontal, and the coefficient of kinetic friction is $$0.2. $$What is the magnitude of the pulling force?

$$F = mg \sin \theta + \mu_k mg \cos \theta$$

Q: Two ice skaters, one with mass $$50\ \mathrm{kg}$$ and the other $$70\ \mathrm{kg}$$, push off from each other on frictionless ice. If the $$50\ \mathrm{kg}$$ skater moves away at $$3\ \mathrm{m/s}$$, what is the velocity of the $$70\ \mathrm{kg}$$ skater?

$$v = -\dfrac{50}{70} \times 3 = -2.14\ \mathrm{m/s}$$

Question 1

A car accelerates uniformly from rest to a speed of $$30\ \mathrm{m/s} in$$ $$10\ \mathrm{s}. $$What is the car's acceleration?

Accepted Answer

$$3.0\ \mathrm{m/s^2$}$$

Question 2

A projectile is launched at an angle $$	heta$$ above the horizontal with initial speed $$v_0. $$Which of the following correctly gives the time of flight until it returns to the same vertical level?

Accepted Answer

$$t = \dfrac{2 v_0$ \sin 	heta}{g}$$

Question 3

A $$5\ \mathrm{kg}$$ box is pulled up a rough incline at constant speed by a force parallel to the incline. The incline makes an angle of $$30^\circ$$ with the horizontal, and the coefficient of kinetic friction is $$0.2. $$What is the magnitude of the pulling force?

Accepted Answer

$$F = mg \sin 	heta + \mu_k mg \cos 	heta$$

Question 4

A $$2\ \mathrm{kg}$$ object moves in a circle of radius $$4\ \mathrm{m} at a $$constant speed of $$6\ \mathrm{m/s}. $$What is the magnitude of the net force acting on the object?

Accepted Answer

$$F = m \dfrac{v^2$}{r}$$

Question 5

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

Accepted Answer

$$v = \sqrt{2 g h}$$

Question 6

A $$3\ \mathrm{kg}$$ block slides $$5\ \mathrm{m}$$ down a rough incline, losing $$20\ \mathrm{J} of $$energy to friction. If it started from rest, what is its speed at the bottom? (Assume $$g = 10\ \mathrm{m/s^2$}$$ and the incline is $$4\ \mathrm{m}$$ high.)

Accepted Answer

$$v = \sqrt{2 (mgh - 20)/m}$$

Question 7

Two ice skaters, one with mass $$50\ \mathrm{kg}$$ and the other $$70\ \mathrm{kg}$$, push off from each other on frictionless ice. If the $$50\ \mathrm{kg}$$ skater moves away at $$3\ \mathrm{m/s}$$, what is the velocity of the $$70\ \mathrm{kg}$$ skater?

Accepted Answer

$$v = -\dfrac{50}{70} 	imes 3 = -2.14\ \mathrm{m/s}$$

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' = \dfrac{m_1$ - m_2$}{m_1$ + m_2$} v_1$

Question 9

A solid disk of mass $$2\ \mathrm{kg}$$ and radius $$0.5\ \mathrm{m}$$ rotates at $$10\ \mathrm{rad/s}. $$What is its rotational kinetic energy?

Accepted Answer

$$K = \dfrac{1}{2} I \$$omega^2$$ = \dfrac{1}{2} \left(\dfrac{1}{2} m r^2$\right) \$$omega^2$$

Question 10

A figure skater pulls in her arms to spin faster. Which principle explains this change in angular velocity?

Accepted Answer

Conservation of angular momentum: $$L = I \omega$$

Question 11

A hydraulic lift uses 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 $$100\ \mathrm{N} is $$applied to the small piston, what is the maximum weight that can be lifted by the large piston (neglecting friction)?

Accepted Answer

$$F_{out} = F_{in} \dfrac{A_{out}}{A_{in}}$$

Question 12

A mass on a spring oscillates with amplitude $$A$$ and period $$T. $$What is the maximum speed of the mass?

Accepted Answer

$$v_{max} = \dfrac{2 \pi A}{T}$$

Question 13

A sound wave travels through air at $$340\ \mathrm{m/s}. If $$its frequency is $$1700\ \mathrm{Hz}$$, what is its wavelength?

Accepted Answer

$$\lambda = \dfrac{v}{f}$$

Question 14

A $$1\ \mathrm{kg}$$ block at $$20^\circ\mathrm{C}$$ absorbs $$4200\ \mathrm{J} of $$heat. If the specific heat of the material is $$420\ \mathrm{J/(kg \cdot ^\circ C)}$$, what is the final temperature?

Accepted Answer

$$T_f = T_i + \dfrac{Q}{m c}$$

Question 15

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

Accepted Answer

$$\Delta U = 0$$

Question 16

A $$2\ \mathrm{kg}$$ object is thrown horizontally from a $$45\ \mathrm{m}$$ high cliff with a speed of $$10\ \mathrm{m/s}. $$How far from the base of the cliff does it land? (Neglect air resistance, $$g = 10\ \mathrm{m/s^2$})$$

Accepted Answer

$$x = v_{0x} t$$,\ t = \sqrt{\dfrac{2h}{g}}$

Question 17

A $$0.5\ \mathrm{kg}$$ ball is attached to a string and swung in a horizontal circle of radius $$2\ \mathrm{m} at$$ $$4\ \mathrm{m/s}. $$What is the tension in the string?

Accepted Answer

$$T = m \dfrac{v^2$}{r}$$

Question 18

A $$1\ \mathrm{kg}$$ block slides at $$5\ \mathrm{m/s} on a $$horizontal surface and comes to rest after $$10\ \mathrm{m}. $$What is the coefficient of kinetic friction?

Accepted Answer

$$\mu_k = \dfrac{v^2$}{2 g d}$$

Question 19

A $$0.3\ \mathrm{kg}$$ mass attached to a spring oscillates with a period of $$0.5\ \mathrm{s}. $$What is the spring constant $$k$$?

Accepted Answer

$$k = \dfrac{4 \pi^2$ m}{T^2$}$$

Core Concepts in General Physics I: Kinematics, Dynamics, Energy, and More

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