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

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

Q: A block of mass $$m_1 is $$stacked on top of a block of mass $$m_2 on an $$inclined plane. If you push on the larger block and give it an acceleration $$a$$, for what value of $$a is $$there no relative motion between the masses?

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

Question 1

A 1 kg block is pulled by several forces across a frictionless floor. If the net force acting on the block is $$2 \mathrm{N} in $$the x-direction and $$0 \mathrm{N} in $$the y-direction, what is the magnitude of the block's acceleration?

Accepted Answer

$$2 \mathrm{m}/\mathrm{s}^2$$

Question 2

Which of the following best describes the direction of the acceleration vector for an object moving in uniform circular motion?

Accepted Answer

It always points toward the center of the circle.

Question 3

A block of mass $$m is at $$rest on a plane inclined at angle $$	heta. $$The forces acting on the block are gravity, normal force $$N$$, and static friction $$F_s. $$Which of the following is always true?

Accepted Answer

$$mg \sin 	heta \leq F_s$$

Question 4

A bead of mass $$m$$ moves with constant speed around a loop of radius $$R in a $$vertical plane. Where is the magnitude of the net force on the bead largest?

Accepted Answer

At the bottom of the loop

Question 5

A hockey puck of mass $$m is $$pushed with a constant force $$F$$ along the x-axis for a time $$\Delta t. If $$the puck starts from rest, what is its speed after time $$\Delta t$$?

Accepted Answer

$$v = \frac{F}{m} \Delta t$$

Question 6

A sphere of mass $$m$$ and radius $$r$$ falls through the air with a terminal speed $$v_t. $$The drag force is given by $$F_D = \frac{1}{2} C_D \rho A v_t^2$. What is the correct expression for the mass of the sphere in terms of v_t$?

Accepted Answer

$$m = \frac{1}{g} \left( \frac{1}{2} C_D \rho A v_t^2$ \right)$$

Question 7

A block of mass $$m is $$pushed along a floor by a constant applied force $$F$$ and experiences a kinetic friction force $$F_k. If $$the block moves at constant velocity, what is the coefficient of kinetic friction $$\mu_k$$?

Accepted Answer

$$\mu_k = \frac{F_k}{mg}$$

Question 8

Two people pull on opposite ends of a rope, each with a force $$F. $$What is the tension in the rope?

Accepted Answer

$$F$$

Question 9

A block of mass $$m$$ slides in a circle of radius $$r on a $$frictionless table while attached to a hanging cylinder of mass $$M by $$means of a cord that passes through a hole in the table. What must be the magnitude of the cord's tension $$F_T to $$keep the cylinder at rest?

Accepted Answer

$$F_T = \frac{m v^2$}{r}$$

Question 10

A block of mass $$m$$ sits on a frictionless plane inclined at angle $$	heta. If $$the block is accelerated up the incline with proper acceleration $$a$$, what is the normal force between the block and the plane?

Accepted Answer

$$N = m g \cos 	heta$$

Question 11

Which of the following is the correct formula for the acceleration of an object moving in uniform circular motion with speed $$v$$ and radius $$R$$?

Accepted Answer

$$a_c = \frac{v^2$}{R}$$

Question 12

A block of mass $$m is $$pushed along a floor by a force $$F at an $$angle $$	heta$$ above the horizontal. If the block moves at constant velocity, what is the magnitude of the normal force?

Accepted Answer

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

Question 13

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

Accepted Answer

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

Question 14

A block of mass $$m_1 is $$stacked on top of a block of mass $$m_2 on an $$inclined plane. If you push on the larger block and give it an acceleration $$a$$, for what value of $$a is $$there no relative motion between the masses?

Accepted Answer

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

Question 15

Which of the following statements about static friction is correct?

Accepted Answer

Static friction opposes potential movement and can vary up to a maximum value.

Question 16

A block of mass $$m is $$pushed along a floor by a force $$F$$ and experiences a kinetic friction force $$F_k. If $$the block accelerates, what is the net force acting on the block?

Accepted Answer

$$F_{net} = F - F_k$$

Question 17

Which of the following is the correct expression for the force of kinetic friction?

Accepted Answer

$$F_k = \mu_k N$$

Question 18

A block of mass $$m is $$pushed along a floor by a force $$F$$ and moves with constant velocity. What is the relationship between $$F$$ and the force of kinetic friction $$F_k$$?

Accepted Answer

$$F = F_k$$

Question 19

Which of the following is the correct formula for the net force acting on an object according to Newton's 2nd Law?

Accepted Answer

$$F_{net} = m a$$

Forces, Newton's Laws, and Applications: Study Notes and Problem Solutions

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