Q: A block of mass $$m is $$sliding down a rough ramp inclined at angle $$\theta. $$The friction force is $$f. $$What is the equation for the acceleration $$a of $$the block down the ramp?

$$a = \frac{mg \sin \theta - f}{m}$$

Question 1

A box of mass $$m is $$sliding to the right on a rough horizontal surface. Which free body diagram correctly represents all the forces acting on the box?

Accepted Answer

D. The diagram with upward normal force, downward gravity, rightward force, and leftward force.

Question 2

A box of mass $$m is $$sliding up a frictionless ramp. Which free body diagram correctly represents all the forces acting on the box?

Accepted Answer

A. The diagram with normal force perpendicular to the ramp and gravity straight down.

Question 3

A box of mass $$m is $$compressing a spring on a horizontal surface. Which free body diagram correctly represents all the forces acting on the box?

Accepted Answer

B. The diagram with upward normal force, downward gravity, and leftward spring force.

Question 4

A block of mass $$m is at $$rest on the ground. What is the magnitude of the normal force $$N$$ acting on the block?

Accepted Answer

$$N = mg$$

Question 5

A block of mass $$m is $$being pulled by a string to the right on a frictionless surface with tension $$T. $$What is the acceleration $$a of $$the block?

Accepted Answer

$$a = \frac{T}{m}$$

Question 6

A block of mass $$m is $$being pulled by a string to the right on a rough surface. The string pulls perfectly horizontal. The block is moving to the right. If the magnitude of the tension is $$T$$ and the kinetic friction force is $$f_k$$, what is the acceleration $$a of $$the block?

Accepted Answer

$$a = \frac{T - f_k}{m}$$

Question 7

A block of mass $$m is $$being pulled by a string at an angle $$	heta to $$the right on a rough surface. Friction exerts a force $$f on $$the block. What is the equation for the tension $$T in $$the rope if the acceleration of the block is $$a_x$$?

Accepted Answer

$$T \cos 	heta = ma_x + f$$

Question 8

A block of mass $$m is $$sliding down a rough ramp inclined at angle $$	heta. $$The friction force is $$f. $$What is the equation for the acceleration $$a of $$the block down the ramp?

Accepted Answer

$$a = \frac{mg \sin 	heta - f}{m}$$

Question 9

Which of the following statements about static and kinetic friction is correct?

Accepted Answer

Static friction can vary up to a maximum value, while kinetic friction is constant.

Question 10

A block of mass $$10\ \mathrm{kg} is at $$rest on a horizontal surface. If the coefficient of static friction is $$\mu_s = 0.2$$, what is the minimum force required to start moving the block?

Accepted Answer

$$F = 20\ \mathrm{N}$$

Question 11

A spring with spring constant $$k is $$stretched by $$x$$ meters. What is the force exerted by the spring according to Hooke's Law?

Accepted Answer

$$F = -kx$$

Question 12

A steel rod of length $$L_0$$ and cross-sectional area $$A is $$stretched by a force $$F$$ causing an extension $$\Delta L. $$What is the Young's modulus $$Y of $$the material?

Accepted Answer

$$Y = \frac{F L_0$}{A \Delta L}$$

Question 13

A block of mass $$m is $$pulled by a constant force $$F$$ over a displacement $$d at an $$angle $$	heta$$ above the horizontal. What is the work done by the force?

Accepted Answer

$$W = Fd \cos 	heta$$

Question 14

A 5 kg object on a frictionless table is pulled by a constant tension of 10 N directly to the right. If the mass started at rest, how far does it go after 3 seconds?

Accepted Answer

$$x = 9\ \mathrm{m}$$

Question 15

A block of mass $$m$$ slides across a frictionless floor with initial speed $$v_i$$, goes up a ramp of height $$y$$, and continues on a frictionless table. What is the final speed $$v_f on $$the table?

Accepted Answer

$$v_f = \sqrt{v_i^2$ - 2gy}$$

Question 16

A block of mass $$m is $$sliding across a frictionless floor with initial speed $$v_i. It $$slides up a ramp of height $$y$$ and onto a rough table with coefficient of kinetic friction $$\mu_k. $$How far $$d$$ does the block travel on the table before coming to rest?

Accepted Answer

$$d = \frac{v_i^2$ - 2gy}{2\mu_k g}$$

Question 17

A 100 kg weightlifter raises a 190 kg bar from the ground to a height of 1.9 m in 1.8 s. What is his output power?

Accepted Answer

$$P = 2078\ \mathrm{W}$$

Question 18

A block of mass $$m is $$sliding across a frictionless floor with initial speed $$v_i. It $$slides up a ramp of height $$y$$ and is brought to rest by compressing a spring by $$x$$ meters. What is the spring constant $$k$$?

Accepted Answer

$$k = \frac{m v_i^2$ - 2 m g y}{x^2$}$$

Free Body Diagrams, Newton’s Laws, Friction, Springs, and Circular Motion

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