Q: A block of mass $$m is $$pushed against a wall at an angle $$\theta$$ above the horizontal. The coefficient of friction between the block and the wall is $$\mu. $$What is the minimum force $$F$$ required to keep the block from sliding down?

$$F = \frac{mg}{\mu \cos \theta + \sin \theta}$$

Q: A block of mass $$m is $$pulled up a rough incline of angle $$\theta$$ with friction coefficient $$\mu. $$What is the minimum force $$F$$ required to move the block up at constant velocity?

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

Question 1

A block of mass $$m is $$suspended by a rope over a frictionless pulley and is connected to another block of mass $$M$$ resting on a frictionless table. If $$m is $$released from rest, what is the acceleration $$a of $$the system?

Accepted Answer

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

Question 2

A 5.0 kg block is pulled horizontally on a frictionless surface by a rope with a tension of 20 N. What is the acceleration of the block?

Accepted Answer

$$a = 4.0\ \mathrm{m/s^2$}$$

Question 3

A block is pressed against the vertical side of a seat with friction coefficient $$\mu. $$What is the minimum normal force $$F_N$$ required to keep the block from sliding down?

Accepted Answer

$$F_N = \frac{mg}{\mu}$$

Question 4

A roller coaster car of mass $$m$$ moves over the top of a circular loop of radius $$r at $$the minimum speed required to stay on the track. What is the normal force $$N$$ exerted by the track on the car at the top?

Accepted Answer

$$N = 0$$

Question 5

A block of mass $$m is $$pushed against a wall at an angle $$	heta$$ above the horizontal. The coefficient of friction between the block and the wall is $$\mu. $$What is the minimum force $$F$$ required to keep the block from sliding down?

Accepted Answer

$$F = \frac{mg}{\mu \cos 	heta + \sin 	heta}$$

Question 6

A block is placed against the vertical front of a seat as shown. As the seat accelerates to the right, what is the direction of the frictional force acting on the block?

Accepted Answer

Upward

Question 7

Three sleds of masses 20 kg, 20 kg, and 10 kg are being pulled horizontally by a rope with a force of 50 N. What is the tension in the rope between the first and second sleds?

Accepted Answer

$$T = 30\ \mathrm{N}$$

Question 8

A box of mass $$m is at $$rest on a horizontal surface. A constant horizontal force $$F is $$applied, and the coefficient of friction is $$\mu. $$What is the acceleration $$a of $$the box?

Accepted Answer

$$a = \frac{F}{m} - \mu g$$

Question 9

Which of the following statements is always TRUE for an object moving at constant velocity?

Accepted Answer

The net force on the object is zero.

Question 10

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

Accepted Answer

$$a = g \sin 	heta$$

Question 11

A block of mass $$m is $$pulled by a force $$F at an $$angle $$	heta$$ above the horizontal on a rough surface with friction coefficient $$\mu. $$What is the normal force on the block?

Accepted Answer

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

Question 12

A block of mass $$m is $$attached to a rope and pulled horizontally with tension $$T on a $$frictionless surface. If the block starts from rest and is pulled for time $$t$$, what is its final velocity?

Accepted Answer

$$v = \frac{T}{m} t$$

Question 13

A block of mass $$m is $$sliding on a horizontal surface with initial velocity $$v_0. $$The coefficient of kinetic friction is $$\mu_k. $$What is the distance $$d$$ the block travels before coming to rest?

Accepted Answer

$$d = \frac{v_0$^2}{2 \mu_k g}$$

Question 14

A block of mass $$m is $$pressed against a wall with a horizontal force $$F. $$The coefficient of static friction is $$\mu_s. $$What is the maximum mass $$m$$ that can be supported without sliding down?

Accepted Answer

$$m = \frac{\mu_s F}{g}$$

Question 15

A block of mass $$m is $$pulled up a rough incline of angle $$	heta$$ with friction coefficient $$\mu. $$What is the minimum force $$F$$ required to move the block up at constant velocity?

Accepted Answer

$$F = mg (\sin 	heta + \mu \cos 	heta)$$

Question 16

A block of mass $$m is $$attached to a rope and pulled horizontally with tension $$T on a $$surface with friction coefficient $$\mu. $$What is the acceleration of the block?

Accepted Answer

$$a = \frac{T}{m} - \mu g$$

Question 17

A roller coaster car of mass $$m$$ moves over the top of a circular loop of radius $$r at $$speed $$v. $$What is the net force acting on the car at the top of the loop?

Accepted Answer

$$F_{net} = mg + \frac{mv^2$}{r}$$

Question 18

A block of mass $$m is $$sliding down a frictionless incline of angle $$	heta. If $$the block starts from rest and travels a distance $$d$$, what is its final velocity?

Accepted Answer

$$v = \sqrt{2gd \sin 	heta}$$

Dynamics: Force, Motion, and Friction – Study Notes and Worked Examples

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