Q: A person pushes a box of mass $$m up a $$ramp at constant speed. The ramp makes an angle $$\theta$$ with the horizontal and the coefficient of kinetic friction is $$\mu_k. $$What is the minimum force required to move the box up the ramp?

$$F = mg(\sin\theta + \mu_k \cos\theta)$$

Q: A ball of mass $$m is $$thrown horizontally from a cart of mass $$M at $$rest. After the ball is thrown, what is the velocity of the cart?

$$v_{\text{cart}} = -\dfrac{m}{M} v_{\text{ball}}$$

Question 1

A person carries a heavy box at a constant speed across a flat surface. According to the physics definition of work, is the person doing work on the box?

Accepted Answer

No, because the force is perpendicular to the direction of motion.

Question 2

In a free-body diagram, will there be any action-reaction pairs according to Newton's 3rd law?

Accepted Answer

No, because Newton's 3rd law applies to forces between different objects.

Question 3

You see an object sitting at rest on a flat and level table. You gradually apply an upward force on the object until just before it lifts off the table. What happens to the normal force between the table and the object as you increase the upward force?

Accepted Answer

The normal force decreases.

Question 4

A person stands on a cart that is initially at rest and throws a ball towards a rigid barrier mounted on the cart. After the ball bounces off the barrier, how will the cart be moving?

Accepted Answer

To the left, due to conservation of momentum.

Question 5

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

Accepted Answer

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

Question 6

A rollercoaster car starts from rest at a height $$h$$ and descends to a lower height. Ignoring friction, what is the speed $$v of $$the car at the bottom?

Accepted Answer

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

Question 7

A car of mass $$m is $$moving at speed $$v$$ and skids to a stop due to kinetic friction with coefficient $$\mu_k. $$What is the stopping distance $$\Delta x$$?

Accepted Answer

$$\Delta x = \dfrac{v^2$}{2\mu_k g}$$

Question 8

If the mass of a vehicle increases, how does the stopping distance due to friction change, assuming all other factors remain constant?

Accepted Answer

The stopping distance remains unchanged.

Question 9

A car of mass $$m$$ collides inelastically with a stationary truck of mass $$M. If$$ $$M is $$much larger than $$m$$, what fraction of the car's initial kinetic energy is lost in the collision?

Accepted Answer

100% of the kinetic energy is lost.

Question 10

Which of the following statements about Newton's 2nd law is correct?

Accepted Answer

The net force on an object is equal to the product of its mass and acceleration: $$\vec{F}_{	ext{net}} = m\vec{a}.$$

Question 11

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

Accepted Answer

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

Question 12

A box of mass $$m is at $$rest on a horizontal surface. The coefficient of kinetic friction is $$\mu_k. $$What is the force required to keep the box moving at constant velocity?

Accepted Answer

$$F = \mu_k mg$$

Question 13

Which of the following best describes the work done by gravity when lifting an object of mass $$m to a $$height $$h at $$constant speed?

Accepted Answer

Negative work equal to $$-mgh.$$

Question 14

A person pushes a box of mass $$m up a $$ramp at constant speed. The ramp makes an angle $$	heta$$ with the horizontal and the coefficient of kinetic friction is $$\mu_k. $$What is the minimum force required to move the box up the ramp?

Accepted Answer

$$F = mg(\sin	heta + \mu_k \cos	heta)$$

Question 15

A ball of mass $$m is $$thrown horizontally from a cart of mass $$M at $$rest. After the ball is thrown, what is the velocity of the cart?

Accepted Answer

$$v_{	ext{cart}} = -\dfrac{m}{M} v_{	ext{ball}}$$

Question 16

A car of mass $$m$$ moving at velocity $$v$$ collides inelastically with another car of equal mass at rest. What is the final velocity of the combined mass after the collision?

Accepted Answer

$$v_f = \dfrac{v}{2}$$

Question 17

Which of the following is true about the normal force acting on an object at rest on a horizontal surface?

Accepted Answer

It is equal in magnitude and opposite in direction to the gravitational force.

Question 18

A car of mass $$m$$ moving at velocity $$v$$ collides inelastically with a stationary truck of mass $$9m. $$What fraction of the car's initial kinetic energy is lost in the collision?

Accepted Answer

90% of the kinetic energy is lost.

Question 19

Which of the following is a correct statement of the work-energy theorem?

Accepted Answer

The net work done on an object is equal to its change in kinetic energy: $$W_{	ext{net}} = \Delta K$$

Physics 211: Forces, Motion, Work, Energy, and Momentum – Midterm 2 Review Study Notes

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