Q: A 32-kg traffic light is suspended by two cables at angles of $$30^\\circ$$ and $$60^\\circ to $$the horizontal. What is the tension in cable 1 (the cable at $$30^\\circ$$)?

$$T_1$$ = \\frac{mg \\sin 60^\\circ}{\\sin 30^\\circ}$$

Q: A box of mass $$m is at $$rest on a slope with angle $$\\theta. $$The coefficient of static friction is $$\\mu_s. $$What is the minimum angle $$\\$$theta_0$$ at which the box just starts to slide?

$$\\$$theta_0$$ = \\arctan(\\mu_s)$$

Q: A box slides down a slope at angle $$\\theta$$ with coefficient of kinetic friction $$\\mu_k. $$What is the acceleration of the box?

$$a = g(\\sin \\theta - \\mu_k \\cos \\theta)$$

Q: Three boxes, $$m_1 = 10$ kg, m_2$ = 18 kg$$, $$m_3 = 12$ kg, are connected by strings over a frictionless, massless pulley. If m_1$ moves up, what is the magnitude of the system's acceleration?

$$a = \\frac{(m_1$ - m_3$)g}{m_1$ + m_2$ + m_3$}$$

Q: A block of mass $$m_1$$ rests on top of block $$m_2 on a $$horizontal surface. The coefficient of static friction between the blocks is $$\\mu_s. $$What is the maximum force $$F$$ that can be applied to $$m_2 so $$that $$m_1$$ does not slip?

$$F_{max} = \\mu_s m_1$ g \\frac{m_1$ + m_2$}{m_1$}$$

Q: A box of mass $$m is $$being pulled up an incline at constant velocity. The incline makes an angle $$\\theta$$ with the horizontal, and the coefficient of kinetic friction is $$\\mu_k. $$What is the magnitude of the pulling force required?

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

Q: A car of mass $$m is $$moving at velocity $$v_i$$ and comes to a stop after traveling a distance $$d$$ due to kinetic friction. What is the coefficient of kinetic friction $$\\mu_k$$?

$$\\mu_k = \\frac{v_i^2$}{2gd}$$

Q: A box of mass $$m is $$pulled horizontally with force $$F on a $$surface with coefficient of kinetic friction $$\\mu_k. $$What is the acceleration of the box?

$$a = \\frac{F - \\mu_k mg}{m}$$

Q: A block of mass $$m is $$pulled up a rough incline at angle $$\\theta$$ with acceleration $$a. $$The coefficient of kinetic friction is $$\\mu_k. $$What is the net force required?

$$F = m(a + g \\sin \\theta + \\mu_k g \\cos \\theta)$$

Question 1

A 32-kg traffic light is suspended by two cables at angles of $$30^\circ$$ and $$60^\circ to $$the horizontal. What is the tension in cable 1 (the cable at $$30^\circ$$)?

Accepted Answer

$$T_1$$ = \frac{mg \sin 60^\circ}{\sin 30^\circ}$$

Question 2

A box of mass $$m is in an $$elevator accelerating upward at $$a. $$What is the magnitude of the force the box exerts on the floor of the elevator?

Accepted Answer

$$F = m(g + a)$$

Question 3

A box of mass $$m is at $$rest on a slope with angle $$\theta. $$The coefficient of static friction is $$\mu_s. $$What is the minimum angle $$\$$theta_0$$ at which the box just starts to slide?

Accepted Answer

$$\$$theta_0$$ = \arctan(\mu_s)$$

Question 4

A box slides down a slope at angle $$\theta$$ with coefficient of kinetic friction $$\mu_k. $$What is the acceleration of the box?

Accepted Answer

$$a = g(\sin \theta - \mu_k \cos \theta)$$

Question 5

Three boxes, $$m_1 = 10$ kg, m_2$ = 18 kg$$, $$m_3 = 12$ kg, are connected by strings over a frictionless, massless pulley. If m_1$ moves up, what is the magnitude of the system's acceleration?

Accepted Answer

$$a = \frac{(m_1$ - m_3$)g}{m_1$ + m_2$ + m_3$}$$

Question 6

A block of mass $$m_1$$ rests on top of block $$m_2 on a $$horizontal surface. The coefficient of static friction between the blocks is $$\mu_s. $$What is the maximum force $$F$$ that can be applied to $$m_2 so $$that $$m_1$$ does not slip?

Accepted Answer

$$F_{max} = \mu_s m_1$ g \frac{m_1$ + m_2$}{m_1$}$$

Question 7

A box of mass $$m is $$being pulled up an incline at constant velocity. The incline makes an angle $$\theta$$ with the horizontal, and the coefficient of kinetic friction is $$\mu_k. $$What is the magnitude of the pulling force required?

Accepted Answer

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

Question 8

A car of mass $$m is $$moving at velocity $$v_i$$ and comes to a stop after traveling a distance $$d$$ due to kinetic friction. What is the coefficient of kinetic friction $$\mu_k$$?

Accepted Answer

$$\mu_k = \frac{v_i^2$}{2gd}$$

Question 9

A block of mass $$m is $$dropped from rest and falls a distance $$h. $$What is its final velocity just before hitting the ground?

Accepted Answer

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

Question 10

A box of mass $$m is $$pulled horizontally with force $$F on a $$surface with coefficient of kinetic friction $$\mu_k. $$What is the acceleration of the box?

Accepted Answer

$$a = \frac{F - \mu_k mg}{m}$$

Question 11

A block slides down a frictionless incline of height $$h$$ and base length $$d. $$What is its speed at the bottom?

Accepted Answer

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

Question 12

A box of mass $$m is at $$rest on a horizontal surface. What is the normal force acting on the box?

Accepted Answer

$$N = mg$$

Question 13

A block of mass $$m is $$pulled up a rough incline at angle $$\theta$$ with acceleration $$a. $$The coefficient of kinetic friction is $$\mu_k. $$What is the net force required?

Accepted Answer

$$F = m(a + g \sin \theta + \mu_k g \cos \theta)$$

Question 14

A block of mass $$m is $$being pulled horizontally at constant velocity on a surface with coefficient of kinetic friction $$\mu_k. $$What is the magnitude of the pulling force?

Accepted Answer

$$F = \mu_k mg$$

Question 15

A block of mass $$m is on a $$horizontal surface. What is the maximum static friction force that can act on the block?

Accepted Answer

$$F_{f,max} = \mu_s mg$$

Question 16

A car accelerates from rest with constant acceleration $$a$$ for time $$t. $$What is its final velocity?

Accepted Answer

$$v_f = a t$$

Question 17

A block of mass $$m is $$dropped from height $$h. $$How long does it take to reach the ground?

Accepted Answer

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

Question 18

A block of mass $$m is $$pulled up an incline at angle $$\theta$$ with constant velocity. What is the normal force acting on the block?

Accepted Answer

$$N = mg \cos \theta$$

Question 19

A block of mass $$m is $$pulled horizontally with force $$F$$ and accelerates at $$a. $$What is the net force acting on the block?

Accepted Answer

$$F_{net} = ma$$

Fundamental Concepts in Newtonian Mechanics: Formula Sheet and Problem Applications

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