Q: A 2 kg block slides down a frictionless incline of angle $$30^\circ. $$What is the acceleration of the block?

$$a = g \sin 30^\circ = 9.8 \times 0.5 = 4.9 \, \mathrm{m/s^2$}$$

Q: A block of mass $$m$$ slides down a ramp of height $$h$$ and angle $$\theta$$ with friction coefficient $$\mu_k. $$Which equation gives the net force down the ramp?

$$F_{\text{net}} = mg \sin \theta - \mu_k mg \cos \theta$$

Q: A projectile is launched at an angle $$\theta$$ above the horizontal with initial speed $$v_0. $$What is the maximum height reached by the projectile?

$$h_{\text{max}} = \frac{v_0$^2 \sin^2$ \theta}{2g}$$

Q: A 10 kg box is pulled up a $$30^\circ$$ incline at constant speed by a rope parallel to the incline. The coefficient of kinetic friction is $$0.2. $$What is the tension in the rope? ($$g = 9.8 \, \mathrm{m/s^2$})$$

$$T = mg \sin 30^\circ + \mu_k mg \cos 30^\circ = 10 \times 9.8 \times 0.5 + 0.2 \times 10 \times 9.8 \times 0.866 = 49 + 16.98 = 65.98 \, \mathrm{N}$$

Q: In a two-block system on a frictionless surface, block A (2 kg) is pulled by a string connected to block B (3 kg). If a force of 10 N is applied to block B, what is the tension in the string between the blocks?

$$T = F \frac{m_A}{m_A + m_B} = 10 \times \frac{2}{5} = 4 \, \mathrm{N}$$

Question 1

A 5 kg block is at rest on a frictionless horizontal surface. A horizontal force of 20 N is applied to the block. What is the acceleration of the block?

Accepted Answer

$$a = \frac{20}{5} = 4 \, \mathrm{m/s^2$}$$

Question 2

A block of mass $$m is $$suspended by two ropes at angles $$\$$theta_1$$ and $$\$$theta_2$$ from the horizontal. Which equation correctly expresses the vertical equilibrium condition for the block?

Accepted Answer

$$T_1$$ \sin \$$theta_1$$ + $$T_2$$ \sin \$$theta_2 = mg$

Question 3

A 2 kg block slides down a frictionless incline of angle $$30^\circ. $$What is the acceleration of the block?

Accepted Answer

$$a = g \sin 30^\circ = 9.8 	imes 0.5 = 4.9 \, \mathrm{m/s^2$}$$

Question 4

Two blocks, $$m_1 = 3$ kg and m_2$ = 2 kg$$, are connected by a light string and pulled across a frictionless surface by a force $$F = 25 N. $$What is the acceleration of the system?

Accepted Answer

$$a = \frac{F}{m_1$ + m_2$} = \frac{25}{5} = 5 \, \mathrm{m/s^2$}$$

Question 5

A block of mass $$m is on a $$rough horizontal surface with coefficient of kinetic friction $$\mu_k. A $$force $$F is $$applied horizontally. What is the condition for the block to move at constant velocity?

Accepted Answer

$$F = \mu_k mg$$

Question 6

A 1 kg block is attached to a light string passing over a frictionless pulley and connected to a 2 kg block hanging vertically. If the system is released from rest, what is the acceleration of the blocks? (Neglect friction and assume $$g = 9.8 \, \mathrm{m/s^2$})$$

Accepted Answer

$$a = \frac{(2 - 1)g}{2 + 1} = \frac{9.8}{3} = 3.27 \, \mathrm{m/s^2$}$$

Question 7

A projectile is launched horizontally from a cliff of height $$h$$ with initial speed $$v_0. $$What is the time it takes to hit the ground?

Accepted Answer

$$t = \sqrt{\frac{2h}{g}}$$

Question 8

A block of mass $$m$$ slides down a ramp of height $$h$$ and angle $$	heta$$ with friction coefficient $$\mu_k. $$Which equation gives the net force down the ramp?

Accepted Answer

$$F_{	ext{net}} = mg \sin 	heta - \mu_k mg \cos 	heta$$

Question 9

A block is at rest on an inclined plane. Which of the following must be true for the block to remain at rest?

Accepted Answer

$$\mu_s \geq 	an 	heta$$

Question 10

A projectile is launched at an angle $$	heta$$ above the horizontal with initial speed $$v_0. $$What is the maximum height reached by the projectile?

Accepted Answer

$$h_{	ext{max}} = \frac{v_0$^2 \sin^2$ 	heta}{2g}$$

Question 11

A 10 kg box is pulled up a $$30^\circ$$ incline at constant speed by a rope parallel to the incline. The coefficient of kinetic friction is $$0.2. $$What is the tension in the rope? ($$g = 9.8 \, \mathrm{m/s^2$})$$

Accepted Answer

$$T = mg \sin 30^\circ + \mu_k mg \cos 30^\circ = 10 	imes 9.8 	imes 0.5 + 0.2 	imes 10 	imes 9.8 	imes 0.866 = 49 + 16.98 = 65.98 \, \mathrm{N}$$

Question 12

In a two-block system on a frictionless surface, block A (2 kg) is pulled by a string connected to block B (3 kg). If a force of 10 N is applied to block B, what is the tension in the string between the blocks?

Accepted Answer

$$T = F \frac{m_A}{m_A + m_B} = 10 	imes \frac{2}{5} = 4 \, \mathrm{N}$$

Question 13

A block of mass $$m is $$attached to a rope over a pulley and connected to a hanging mass $$M. If$$ $$M \u003e m$$, what is the acceleration of the system? (Neglect friction and mass of the pulley)

Accepted Answer

$$a = \frac{(M - m)g}{M + m}$$

Question 14

A projectile is launched from the ground at $$45^\circ$$ with speed $$v_0. $$What is the total time the projectile is in the air?

Accepted Answer

$$t = \frac{2 v_0$ \sin 45^\circ}{g}$$

Question 15

A block of mass $$m is $$sliding down a rough incline of angle $$	heta at $$constant velocity. What is the coefficient of kinetic friction?

Accepted Answer

$$\mu_k = 	an 	heta$$

Question 16

A block of mass $$m is $$pushed up a frictionless ramp of height $$h. $$What is the minimum initial speed required to reach the top?

Accepted Answer

$$v_0$$ = \sqrt{2gh}$$

Question 17

A block of mass $$m is at $$rest on a horizontal surface. A horizontal force $$F is $$applied, but the block does not move. What is the maximum value of $$F$$ before the block starts to move?

Accepted Answer

$$F_{	ext{max}} = \mu_s mg$$

Question 18

A block of mass $$m is $$attached to a rope over a frictionless pulley and connected to a hanging mass $$M. If$$ $$M = m$$, what is the acceleration of the system?

Accepted Answer

$$a = 0$$

Question 19

A projectile is launched horizontally from a height $$h$$ and lands a distance $$d$$ from the base of the cliff. What was its initial speed?

Accepted Answer

$$v_0$$ = \frac{d}{\sqrt{2h/g}}$$

Exam Guide and Core Problem Types in Introductory Physics

Study Guide - Practice Questions

Study Guide - Flashcards