Q: A block of mass $$m is $$pulled across a rough surface with a force $$F at an $$angle $$\theta$$ above the horizontal. The coefficient of kinetic friction is $$\mu_k. $$What is the net work done by the pulling force over a distance $$d$$?

$$W = F \cos \theta d - \mu_k m g d$$

Q: A block of mass $$m is $$sliding down an incline of angle $$\theta$$ and length $$L$$ with coefficient of kinetic friction $$\mu_k. $$What is the final speed at the bottom?

$$v = \sqrt{2gL(\sin \theta - \mu_k \cos \theta)}$$

Q: A block of mass $$m$$ slides down a rough incline of angle $$\theta$$ and length $$L. $$The coefficient of kinetic friction is $$\mu_k. $$What is the total work done by friction?

$$W_{friction} = -\mu_k m g \cos \theta \cdot L$$

Question 1

A box of mass $$m is $$pushed against a vertical wall with a horizontal force $$F. $$The coefficient of static friction between the box and the wall is $$\mu_s. $$What is the minimum value of $$F$$ required to keep the box from sliding down?

Accepted Answer

$$F = \frac{mg}{\mu_s}$$

Question 2

A car and a truck are both traveling at the same initial speed $$v_0$$ when they see a deer and slam on the brakes, locking their wheels. The coefficient of kinetic friction between the tires and the road is $$\mu_k. $$Which vehicle will stop in a shorter distance?

Accepted Answer

Both will stop in the same distance, independent of mass.

Question 3

A block slides down a frictionless incline of height $$h. $$What is its speed at the bottom?

Accepted Answer

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

Question 4

A horse pulls a cart forward. According to Newton's third law, the cart pulls back on the horse with an equal and opposite force. Why does the horse-cart system move forward?

Accepted Answer

Because the ground exerts a forward force on the horse due to friction.

Question 5

A bullet of mass $$m_b is $$fired from a rifle of mass $$M_r. If $$the bullet leaves the rifle with velocity $$v_b$$, what is the recoil velocity $$v_r of $$the rifle?

Accepted Answer

$$v_r = -\frac{m_b}{M_r} v_b$$

Question 6

A block of mass $$m is $$pulled across a rough surface with a force $$F at an $$angle $$	heta$$ above the horizontal. The coefficient of kinetic friction is $$\mu_k. $$What is the net work done by the pulling force over a distance $$d$$?

Accepted Answer

$$W = F \cos 	heta d - \mu_k m g d$$

Question 7

A ball of mass $$m is $$dropped from height $$h$$ and bounces elastically off a massive stationary surface. What is its velocity immediately after the bounce?

Accepted Answer

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

Question 8

A block of mass $$m is $$attached to a spring with spring constant $$k$$ and is compressed by a distance $$x. $$When released, what is the speed of the block as it passes through the equilibrium position?

Accepted Answer

$$v = \sqrt{\frac{k}{m}} x$$

Question 9

A cart of mass $$M at $$rest on a frictionless track throws a ball of mass $$m to $$the left with velocity $$v. $$What is the velocity of the cart after the throw?

Accepted Answer

$$v_{cart} = \frac{m}{M} v$$

Question 10

A block of mass $$m is $$sliding down an incline of angle $$	heta$$ and length $$L$$ with coefficient of kinetic friction $$\mu_k. $$What is the final speed at the bottom?

Accepted Answer

$$v = \sqrt{2gL(\sin 	heta - \mu_k \cos 	heta)}$$

Question 11

Two blocks, $$m_1$$ and $$m_2$$, collide and stick together (perfectly inelastic collision). If $$m_1 is $$moving at $$v_1$$ and $$m_2 is at $$rest, what is their final velocity?

Accepted Answer

$$v_f = \frac{m_1$ v_1$}{m_1$ + m_2$}$$

Question 12

A roller coaster starts from rest at height $$h_A$$ and descends to height $$h_B$$ with no friction. What is its speed at point B?

Accepted Answer

$$v_B = \sqrt{2g(h_A - h_B)}$$

Question 13

A block of mass $$m is at $$rest on a horizontal surface. A force $$F is $$applied horizontally. If the coefficient of static friction is $$\mu_s$$, what is the maximum value of $$F$$ before the block starts to move?

Accepted Answer

$$F_{max} = \mu_s m g$$

Question 14

A person lifts a box vertically upward at constant speed. What is the net work done by all forces on the box?

Accepted Answer

Zero

Question 15

A block of mass $$m is $$moving with velocity $$v$$ and collides elastically with a stationary block of mass $$M \gg m. $$What is the velocity of the small block after the collision?

Accepted Answer

$$v' = -v$$

Question 16

A block of mass $$m is $$pulled across a frictionless surface by a force $$F$$ over a distance $$d. $$What is its final kinetic energy?

Accepted Answer

$$K_f = F d$$

Question 17

A block of mass $$m is $$dropped from height $$h$$ with initial velocity $$v_0. $$What is its speed just before hitting the ground?

Accepted Answer

$$v = \sqrt{2gh + v_0$^2}$$

Question 18

A block of mass $$m$$ slides down a rough incline of angle $$	heta$$ and length $$L. $$The coefficient of kinetic friction is $$\mu_k. $$What is the total work done by friction?

Accepted Answer

$$W_{friction} = -\mu_k m g \cos 	heta \cdot L$$

Physics 211: Forces, Newton's Laws, Friction, Work, Energy, and Momentum – Midterm 2 Review

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