Q: A 10 kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.4. What is the minimum horizontal force required to start moving the box?

$$F = 10 \times 9.8 \times 0.4 = 39.2\ \mathrm{N}$$

Q: A spring with a spring constant $$k = 500\ \mathrm{N/m} is $$stretched by $$0.02\ \mathrm{m}. $$What is the force exerted by the spring?

$$F = -kx = -500 \times 0.02 = -10\ \mathrm{N}$$

Q: A 5 kg block is pulled across a horizontal surface with a force of $$30\ \mathrm{N}. $$The coefficient of kinetic friction is $$0.2. $$What is the acceleration of the block?

$$a = \frac{F - \mu_k mg}{m} = \frac{30 - 0.2 \times 5 \times 9.8}{5} = 3.04\ \mathrm{m/s^2$}$$

Q: A 1.5 kg object is attached to a vertical spring and stretches it by $$0.0123\ \mathrm{m}. $$What is the spring constant $$k$$?

$$k = \frac{mg}{x} = \frac{1.5 \times 9.8}{0.0123} = 1195\ \mathrm{N/m}$$

Q: A 70 kg person stands on a scale in an elevator accelerating upward at $$2\ \mathrm{m/s^2$}. $$What does the scale read?

$$N = m(g + a) = 70 \times (9.8 + 2) = 826\ \mathrm{N}$$

Q: A conical pendulum consists of a mass $$m$$ attached to a string of length $$L$$, moving in a horizontal circle of radius $$r at $$constant speed $$v. $$What is the tension $$T in $$the string?

$$T = \frac{mg}{\cos\theta}$$,\ where\ \theta = \arccos\left(\frac{r}{L}\right)$

Q: A 3 kg block is connected by a light string to a 2 kg block over a frictionless pulley (Atwood machine). What is the tension in the string?

$$T = \frac{2 \times 3}{2 + 3} \times 9.8 = 11.76\ \mathrm{N}$$

Q: A block is at rest on an inclined plane. The coefficient of static friction is $$\mu_s. $$What is the maximum angle $$\theta_{max}$$ before the block starts to slide?

$$\theta_{max} = \arctan\mu_s$$

Question 1

A 10 kg box rests on a horizontal surface. The coefficient of static friction between the box and the surface is 0.4. What is the minimum horizontal force required to start moving the box?

Accepted Answer

$$F = 10 	imes 9.8 	imes 0.4 = 39.2\ \mathrm{N}$$

Question 2

A car of mass $$m is at $$rest on a frictionless ramp inclined at an angle $$	heta to $$the horizontal. What is the normal force exerted by the ramp on the car?

Accepted Answer

$$N = mg\cos	heta$$

Question 3

A block slides down a rough incline at constant velocity. If the incline angle is $$	heta$$ and the coefficient of kinetic friction is $$\mu_k$$, what is the relationship between $$\mu_k$$ and $$	heta$$?

Accepted Answer

$$\mu_k = 	an	heta$$

Question 4

A 2 kg mass is suspended from a ceiling by two strings, each making an angle of $$45^\circ$$ with the ceiling. What is the tension in each string?

Accepted Answer

$$T = \frac{mg}{2\sin45^\circ} = 13.86\ \mathrm{N}$$

Question 5

A spring with a spring constant $$k = 500\ \mathrm{N/m} is $$stretched by $$0.02\ \mathrm{m}. $$What is the force exerted by the spring?

Accepted Answer

$$F = -kx = -500 	imes 0.02 = -10\ \mathrm{N}$$

Question 6

A 5 kg block is pulled across a horizontal surface with a force of $$30\ \mathrm{N}. $$The coefficient of kinetic friction is $$0.2. $$What is the acceleration of the block?

Accepted Answer

$$a = \frac{F - \mu_k mg}{m} = \frac{30 - 0.2 	imes 5 	imes 9.8}{5} = 3.04\ \mathrm{m/s^2$}$$

Question 7

A 1.5 kg object is attached to a vertical spring and stretches it by $$0.0123\ \mathrm{m}. $$What is the spring constant $$k$$?

Accepted Answer

$$k = \frac{mg}{x} = \frac{1.5 	imes 9.8}{0.0123} = 1195\ \mathrm{N/m}$$

Question 8

A car of mass $$m$$ moves at speed $$v$$ around a flat circular track of radius $$R. $$What is the maximum speed before it starts to skid, given the coefficient of static friction $$\mu_s$$?

Accepted Answer

$$v_{max} = \sqrt{\mu_s g R}$$

Question 9

In an Atwood machine, two masses $$m_1$$ and $$m_2$$ are connected by a massless string over a massless pulley. If $$m_1$$ \u003e $$m_2$$, what is the acceleration of the system?

Accepted Answer

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

Question 10

A 70 kg person stands on a scale in an elevator accelerating upward at $$2\ \mathrm{m/s^2$}. $$What does the scale read?

Accepted Answer

$$N = m(g + a) = 70 	imes (9.8 + 2) = 826\ \mathrm{N}$$

Question 11

A block of mass $$m is on a $$frictionless incline of angle $$	heta. $$What is its acceleration down the incline?

Accepted Answer

$$a = g\sin	heta$$

Question 12

A block is pulled at constant velocity across a horizontal surface by a force $$F$$ applied at an angle $$	heta$$ above the horizontal. The coefficient of kinetic friction is $$\mu_k. $$What is the expression for the normal force?

Accepted Answer

$$N = mg - F\sin	heta$$

Question 13

A conical pendulum consists of a mass $$m$$ attached to a string of length $$L$$, moving in a horizontal circle of radius $$r at $$constant speed $$v. $$What is the tension $$T in $$the string?

Accepted Answer

$$T = \frac{mg}{\cos	heta}$$,\ where\ 	heta = \arccos\left(\frac{r}{L}ight)$

Question 14

A 3 kg block is connected by a light string to a 2 kg block over a frictionless pulley (Atwood machine). What is the tension in the string?

Accepted Answer

$$T = \frac{2 	imes 3}{2 + 3} 	imes 9.8 = 11.76\ \mathrm{N}$$

Question 15

A block is at rest on an inclined plane. The coefficient of static friction is $$\mu_s. $$What is the maximum angle $$	heta_{max}$$ before the block starts to slide?

Accepted Answer

$$	heta_{max} = \arctan\mu_s$$

Question 16

A car travels around a banked curve of radius $$R at $$speed $$v. $$The banking angle is $$	heta. If $$there is no friction, what is the required speed for the car to make the turn?

Accepted Answer

$$v = \sqrt{gR	an	heta}$$

Question 17

A block of mass $$m is $$connected to another block of mass $$M by a $$massless string over a frictionless table and pulley. If $$m$$ hangs vertically and $$M is on $$the table, what is the acceleration of the system?

Accepted Answer

$$a = \frac{mg}{m + M}$$

Question 18

A skydiver of mass $$m$$ falls through the air and eventually reaches terminal velocity. At terminal velocity, which of the following is true?

Accepted Answer

$$\sum F = 0$$,\ so\ mg = F_{drag}$

Question 19

A block is pushed up a rough incline at constant speed. The incline angle is $$	heta$$, and the coefficient of kinetic friction is $$\mu_k. $$What is the total force required parallel to the incline?

Accepted Answer

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

Chapter 5: Applying Newton’s Laws – Statics, Dynamics, and Friction

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