Q: A 2 kg object is dropped from a height of 5 m. What is its speed just before it hits the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5} \approx 9.9\ \mathrm{m/s}$$

Question 1

A 1.5 kg block is sliding down a 30° ramp at a constant speed of 7.5 m/s. What is the value of the frictional force acting on the block?

Accepted Answer

$$5.8\ \mathrm{N}$$

Question 2

A circus performer on a skateboard is launched by a spring initially compressed a distance $$\Delta x as $$shown below. His speed on the horizontal portion of the ramp is $$v$$, and he rises to a height $$H$$ after he leaves the ramp. If the performer is moved launch with the spring initially compressed a distance $$2.5\Delta x$$, how high will he rise?

Accepted Answer

$$6.25H$$

Question 3

Two boxes are tied together by a string and are sitting at rest in the middle of a long frictionless table. Between the two boxes is an ideal compressed spring. The string is cut, releasing the boxes. If the boxes have equal mass, which box will have the largest change in velocity after the string is cut?

Accepted Answer

Both boxes will have the same change in velocity.

Question 4

An identical force is applied for the same amount of time to each of the following. Which would have the largest change in velocity?

Accepted Answer

A 2 kg ball moving at $$7\ \mathrm{m/s}$$

Question 5

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

Accepted Answer

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

Question 6

A spring with spring constant $$k is $$compressed by a distance $$x. $$What is the potential energy stored in the spring?

Accepted Answer

$$U = \frac{1}{2}kx^2$

Question 7

A block of mass $$m is $$pulled across a rough surface with a constant velocity. If the coefficient of kinetic friction is $$\mu_k$$, what is the magnitude of the frictional force?

Accepted Answer

$$f = \mu_k mg$$

Question 8

A 2 kg object is dropped from a height of 5 m. What is its speed just before it hits the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 5} \approx 9.9\ \mathrm{m/s}$$

Question 9

A force $$F is $$applied to a mass $$m$$ for a time $$t. $$What is the change in momentum of the mass?

Accepted Answer

$$\Delta p = Ft$$

Question 10

A block of mass $$m is $$released from rest at the top of a frictionless ramp of height $$h. $$What is the kinetic energy of the block at the bottom?

Accepted Answer

$$K = mgh$$

Question 11

A spring with spring constant $$k is $$compressed by $$x$$ and launches a mass $$m$$ horizontally. What is the speed of the mass after leaving the spring?

Accepted Answer

$$v = \sqrt{\frac{kx^2$}{m}}$$

Question 12

A block slides down a ramp at constant speed. What does this tell you about the net force acting on the block?

Accepted Answer

The net force is zero.

Question 13

If a force is applied to two objects of different masses for the same amount of time, which object will experience the greater change in velocity?

Accepted Answer

The object with the smaller mass.

Question 14

A block of mass $$m is $$pulled up a frictionless ramp of angle $$	heta at $$constant speed. What is the required force parallel to the ramp?

Accepted Answer

$$F = mg\sin	heta$$

Question 15

A compressed spring launches a mass $$m$$ vertically upward. If the spring is compressed twice as much, by what factor does the maximum height increase?

Accepted Answer

Four times higher.

Question 16

A block of mass $$m is $$sliding down a ramp at constant speed. If the angle of the ramp is increased, what happens to the required frictional force?

Accepted Answer

It increases.

Question 17

A spring with spring constant $$k is $$compressed by $$x$$ and launches a mass $$m$$ horizontally. If the mass is doubled, what happens to the speed of the mass after leaving the spring?

Accepted Answer

It decreases by a factor of $$\sqrt{2}.$$

Question 18

A block of mass $$m is $$pulled across a rough surface with a constant velocity. If the coefficient of kinetic friction is $$\mu_k$$, what is the work done by friction after moving a distance $$d$$?

Accepted Answer

$$W = -\mu_k mg d$$

Question 19

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

Accepted Answer

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

Newtonian Mechanics and Impulse: Exam Study Notes

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