Q: A 0.5 kg block is held against a vertical wall by a horizontal force of 20 N. The coefficient of static friction between the block and the wall is 0.6. What is the maximum mass that can be held without slipping?

$$m_{max} = \frac{\mu_s F_N}{g} = \frac{0.6 \times 20}{9.8} \approx 1.22\ \mathrm{kg}$$

Q: A 2.0 kg block is pulled across a horizontal surface with a constant velocity by a force of 10 N applied at $$30^\circ$$ above the horizontal. The coefficient of kinetic friction is 0.2. What is the normal force on the block?

$$N = mg - F \sin \theta = 2.0 \times 9.8 - 10 \times \sin 30^\circ = 19.6 - 5 = 14.6\ \mathrm{N}$$

Q: A crate of mass 95 kg begins to slide down a truck bed when the tilt angle reaches $$25^\circ. $$What is the coefficient of static friction between the crate and the truck?

$$\mu_s = \tan 25^\circ \approx 0.47$$

Q: A car travels around a curve of radius 45 m. If the coefficient of static friction between the tires and the road is 0.82, what is the maximum speed the car can have without skidding?

$$v_{max} = \sqrt{\mu_s g r} = \sqrt{0.82 \times 9.8 \times 45}$$

Q: A block of mass $$m is $$pulled across a rough surface by a force $$F at an $$angle $$\theta$$ above the horizontal. The coefficient of kinetic friction is $$\mu_k. $$Which equation gives the frictional force?

$$f_k = \mu_k (mg - F \sin \theta)$$

Q: A 3.0 kg mass is suspended by a rope and held stationary. What is the tension in the rope?

$$T = mg = 3.0 \times 9.8 = 29.4\ \mathrm{N}$$

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

$$F = 39.2\ \mathrm{N}$$

Question 2

A skier of mass 65 kg slides down a hill inclined at $$22^\circ to $$the horizontal. The coefficient of kinetic friction is $$\mu_k = 0.10. $$What is the acceleration of the skier?

Accepted Answer

$$a = g(\sin 22^\circ - 0.10 \cos 22^\circ)$$

Question 3

A 0.5 kg block is held against a vertical wall by a horizontal force of 20 N. The coefficient of static friction between the block and the wall is 0.6. What is the maximum mass that can be held without slipping?

Accepted Answer

$$m_{max} = \frac{\mu_s F_N}{g} = \frac{0.6 	imes 20}{9.8} \approx 1.22\ \mathrm{kg}$$

Question 4

A 2.0 kg block is pulled across a horizontal surface with a constant velocity by a force of 10 N applied at $$30^\circ$$ above the horizontal. The coefficient of kinetic friction is 0.2. What is the normal force on the block?

Accepted Answer

$$N = mg - F \sin 	heta = 2.0 	imes 9.8 - 10 	imes \sin 30^\circ = 19.6 - 5 = 14.6\ \mathrm{N}$$

Question 5

A crate of mass 95 kg begins to slide down a truck bed when the tilt angle reaches $$25^\circ. $$What is the coefficient of static friction between the crate and the truck?

Accepted Answer

$$\mu_s = 	an 25^\circ \approx 0.47$$

Question 6

A 5.0 kg pot of flowers hangs from two wires, each making a $$40^\circ$$ angle with the horizontal. What is the tension in each wire?

Accepted Answer

$$T = \frac{mg}{2 \sin 40^\circ}$$

Question 7

A 1.0 kg mass is suspended from a rope and is lifted with an acceleration of $$0.1g. $$What is the tension in the rope during the lift?

Accepted Answer

$$T = m(g + 0.1g) = 1.1mg$$

Question 8

A 20 kg and a 10 kg block are connected by a string and pulled across a frictionless surface by a 30 N force. What is the acceleration of the system?

Accepted Answer

$$a = \frac{F}{m_1$ + m_2$} = \frac{30}{20 + 10} = 1.0\ \mathrm{m/s^2$}$$

Question 9

A car travels around a curve of radius 45 m. If the coefficient of static friction between the tires and the road is 0.82, what is the maximum speed the car can have without skidding?

Accepted Answer

$$v_{max} = \sqrt{\mu_s g r} = \sqrt{0.82 	imes 9.8 	imes 45}$$

Question 10

If you push a wooden crate across the floor at constant speed, then turn the crate on end, reducing by half the surface area in contact with the floor, what happens to the force required to push the crate at the same speed?

Accepted Answer

It remains equally great.

Question 11

An object is held in place by friction on an inclined surface. The angle of inclination is increased until the object starts moving. If the surface is kept at this angle, the object:

Accepted Answer

Speeds up.

Question 12

A block of mass $$m is $$pulled across a rough surface by a force $$F at an $$angle $$	heta$$ above the horizontal. The coefficient of kinetic friction is $$\mu_k. $$Which equation gives the frictional force?

Accepted Answer

$$f_k = \mu_k (mg - F \sin 	heta)$$

Question 13

A spring with spring constant $$k = 120\ \mathrm{N/m} is $$compressed to hold a 0.27 kg block on a hill with $$\mu_s = 0.46. $$How much must the spring be compressed to prevent the block from sliding?

Accepted Answer

$$x = \frac{\mu_s mg}{k}$$

Question 14

A 3.0 kg mass is suspended by a rope and held stationary. What is the tension in the rope?

Accepted Answer

$$T = mg = 3.0 	imes 9.8 = 29.4\ \mathrm{N}$$

Question 15

A 2.0 kg block slides down a frictionless incline of $$30^\circ. $$What is the normal force acting on the block?

Accepted Answer

$$N = mg \cos 30^\circ$$

Question 16

A 1.5 kg block is attached to a spring and oscillates horizontally. If the maximum static friction force is 3.0 N, what is the minimum spring constant $$k$$ required to move the block if the maximum compression is 0.05 m?

Accepted Answer

$$k = \frac{f_{s,max}}{x_{max}} = \frac{3.0}{0.05} = 60\ \mathrm{N/m}$$

Applications of Newton's Laws of Motion: Frictional and Normal Forces

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