Q: A block of mass $$m$$ slides down a rough incline of angle $$\theta$$ with coefficient of kinetic friction $$\mu_k. $$What is the acceleration of the block?

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

Question 1

A block of mass $$m is at $$rest on a frictionless inclined plane that makes an angle $$	heta$$ with the horizontal. What is the magnitude of the normal force acting on the block?

Accepted Answer

$$mg \cos 	heta$$

Question 2

A crate of mass $$m is $$being pulled across a rough horizontal floor by a force $$F at an $$angle $$\phi$$ above the horizontal. The coefficient of kinetic friction is $$\mu_k. $$Which equation correctly gives the magnitude of the frictional force?

Accepted Answer

$$\mu_k (m g - F \sin \phi)$$

Question 3

A person of mass $$m$$ stands on a scale in an elevator that is accelerating upward with acceleration $$a. $$What does the scale read?

Accepted Answer

$$m(g+a)$$

Question 4

A block slides down a frictionless incline of angle $$	heta. $$What is its acceleration?

Accepted Answer

$$g \sin 	heta$$

Question 5

A block of mass $$m is $$pulled by a force $$F on a $$rough surface with coefficient of kinetic friction $$\mu_k. If $$the block moves with constant velocity, what is the value of $$F$$?

Accepted Answer

$$\mu_k m g$$

Question 6

A mass $$m is $$suspended from a rope of mass $$M. $$What is the tension at the top of the rope?

Accepted Answer

$$(m + M)g$$

Question 7

A car of mass $$m$$ moves in a circle of radius $$R at $$constant speed $$v. $$What is the magnitude of the centripetal force acting on the car?

Accepted Answer

$$m v^2$ / R$$

Question 8

A block of mass $$m is at $$rest on a horizontal surface. The maximum static friction force is $$f_{s,	ext{max}} = \mu_s N. If a $$horizontal force $$F is $$applied, what happens when $$F \u003e f_{s,	ext{max}}$$?

Accepted Answer

The block starts to move and kinetic friction acts.

Question 9

A skydiver of mass $$m$$ falls through air and eventually reaches terminal speed. Which force balances the weight at terminal speed?

Accepted Answer

Fluid resistance (drag)

Question 10

A block of mass $$m$$ slides down a rough incline of angle $$	heta$$ with coefficient of kinetic friction $$\mu_k. $$What is the acceleration of the block?

Accepted Answer

$$g (\sin 	heta - \mu_k \cos 	heta)$$

Question 11

A block of mass $$m is $$connected to another block of mass $$M by a $$light string over a frictionless pulley. If $$m \u003e M$$, what is the acceleration of the system?

Accepted Answer

$$\dfrac{m-M}{m+M}g$$

Question 12

A block of mass $$m is $$pushed up a frictionless incline of angle $$	heta$$ with a force $$F$$ parallel to the incline. What is the minimum value of $$F$$ required to move the block up at constant speed?

Accepted Answer

$$mg \sin 	heta$$

Question 13

A block of mass $$m is $$sliding on a horizontal surface with kinetic friction coefficient $$\mu_k. If a $$constant force $$F is $$applied and the block accelerates at $$a$$, what is the equation relating $$F$$, $$m$$, $$a$$, and $$\mu_k$$?

Accepted Answer

$$F = m a + \mu_k m g$$

Question 14

A block of mass $$m is $$attached to a rope and swung in a vertical circle of radius $$R. $$What is the tension in the rope at the bottom of the circle if the speed is $$v$$?

Accepted Answer

$$m g + m v^2$ / R$$

Question 15

A block of mass $$m is $$sliding down a rough incline of angle $$	heta$$ and coefficient of kinetic friction $$\mu_k. If $$the block moves at constant speed, what is the relationship between $$\mu_k$$ and $$	heta$$?

Accepted Answer

$$\mu_k = 	an 	heta$$

Question 16

A block of mass $$m is $$pulled by a force $$F at an $$angle $$	heta$$ above the horizontal on a rough surface. If the block moves at constant velocity, what is the vertical component of the normal force?

Accepted Answer

$$N = m g - F \sin 	heta$$

Question 17

A block of mass $$m is $$sliding on a horizontal surface with friction. If the applied force is less than the maximum static friction, what happens?

Accepted Answer

The block remains at rest.

Question 18

A block of mass $$m is $$dropped from rest into a fluid. It eventually reaches terminal speed $$v_t. $$Which equation correctly relates $$v_t to $$the drag coefficient $$k$$ and $$m$$?

Accepted Answer

$$v_t = \sqrt{\dfrac{m g}{k}}$$

Question 19

A block of mass $$m is $$attached to a rope and swung in a horizontal circle of radius $$R at $$constant speed $$v. $$What is the tension in the rope?

Accepted Answer

$$m v^2$ / R$$

Chapter 5: Applying Newton's Laws – Equilibrium, Friction, and Circular Motion

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