Q: A spring of constant $$k is $$attached to a block of mass $$M on a $$frictionless ramp inclined at angle $$\theta. $$The spring stretches parallel to the ramp. What is the equilibrium stretch $$x of $$the spring?

$$x = \dfrac{Mg \sin \theta}{k}$$

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 $$a of $$the block?

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

Question 1

A block of mass $$M is at $$rest on a frictionless ramp inclined at an angle $$	heta to $$the horizontal. The block is attached to a wall by a string parallel to the ramp. What is the tension $$T in $$the string?

Accepted Answer

$$T = Mg \sin 	heta$$

Question 2

A car with initial velocity $$v_0 = 30$$\,\mathrm{m/s}$$ skids to a stop over a distance d = 51.0$$\,\mathrm{m}$$ on a flat road. What is the coefficient of kinetic friction $$\mu_k$$ between the tires and the road?

Accepted Answer

$$\mu_k = 0.70$$

Question 3

A block of mass $$M is $$released from rest at the top of a frictionless ramp inclined at $$	heta = 30^\circ. $$What is the acceleration $$a of $$the block down the ramp?

Accepted Answer

$$a = g \sin 30^\circ$$

Question 4

A spring of constant $$k is $$attached to a block of mass $$M on a $$frictionless ramp inclined at angle $$	heta. $$The spring stretches parallel to the ramp. What is the equilibrium stretch $$x of $$the spring?

Accepted Answer

$$x = \dfrac{Mg \sin 	heta}{k}$$

Question 5

A car of mass $$M$$ moves with constant speed $$v = \sqrt{3gR}$$ through a dip of radius $$R. $$What is the normal force $$N on $$the car at the bottom of the dip?

Accepted Answer

$$N = 4Mg$$

Question 6

A block is pushed to the right with constant velocity on a horizontal surface. Which of the following free-body diagrams best describes the forces acting on the block?

Accepted Answer

A rightward force equal in magnitude to the leftward kinetic friction force, and upward and downward forces of equal magnitude.

Question 7

A block of mass $$M is at $$rest on a horizontal table. Which of the following statements is true?

Accepted Answer

The normal force from the table equals the gravitational force on the block.

Question 8

A cart of mass $$M_c$$ rolls on a frictionless horizontal ground. A block of mass $$M_b is $$pressed against the vertical front of the cart. An applied force $$F_{app}$$ causes the cart to accelerate, keeping the block from falling due to static friction. What is the minimum coefficient of static friction $$\mu_s$$ required between the cart and the block?

Accepted Answer

$$\mu_s = \dfrac{a}{g}$$

Question 9

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

Accepted Answer

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

Question 10

A solid sphere of mass $$M$$ and radius $$R$$ rolls without slipping down an incline of height $$h. $$What is its speed $$v at $$the bottom?

Accepted Answer

$$v = \sqrt{\dfrac{10gh}{7}}$$

Question 11

A block of mass $$M is $$attached to a horizontal spring of constant $$k$$ and oscillates with amplitude $$A. $$What is the maximum speed $$v_{max} of $$the block?

Accepted Answer

$$v_{max} = A \sqrt{\dfrac{k}{M}}$$

Question 12

A rod of length $$L$$ and mass $$M$$ rotates about its center. What is its moment of inertia $$I$$?

Accepted Answer

$$I = \dfrac{1}{12}ML^2$

Question 13

A block of mass $$M is $$pushed up a frictionless ramp inclined at angle $$	heta$$ with initial speed $$v_0. $$What is the maximum height $$h_{max}$$ reached by the block?

Accepted Answer

$$h_{max} = \dfrac{v_0$^2}{2g}$$

Question 14

A block of mass $$M is $$attached to a spring of constant $$k$$ and oscillates with period $$T. $$What is the period $$T$$?

Accepted Answer

$$T = 2\pi \sqrt{\dfrac{M}{k}}$$

Question 15

A block of mass $$M is $$dropped from height $$h$$ onto a spring of constant $$k. $$What is the maximum compression $$x_{max} of $$the spring?

Accepted Answer

$$x_{max} = \sqrt{\dfrac{2Mh}{k}}$$

Question 16

A block of mass $$M is $$pulled at constant velocity $$v$$ across a rough horizontal surface with coefficient of kinetic friction $$\mu_k. $$What is the work $$W$$ done by the pulling force over distance $$d$$?

Accepted Answer

$$W = \mu_k M g d$$

Question 17

A block of mass $$M is $$attached to a string and whirled in a horizontal circle of radius $$R at $$constant speed $$v. $$What is the tension $$T in $$the string?

Accepted Answer

$$T = \dfrac{Mv^2$}{R}$$

Question 18

A block of mass $$M is $$released from rest at the top of a frictionless ramp of height $$h. $$What is its speed $$v at $$the bottom?

Accepted Answer

$$v = \sqrt{2gh}$$

Question 19

A block of mass $$M is $$attached to a spring of constant $$k$$ and oscillates with amplitude $$A. $$What is the total mechanical energy $$E of $$the system?

Accepted Answer

$$E = \dfrac{1}{2}kA^2$

Physics I: Mechanics – Quiz Study Guide (Forces, Motion, Energy, Rotational Dynamics)

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