Question 1

A 4.0-kg object is moving with speed 2.0 m/s. A 1.0-kg object is moving with speed 4.0 m/s. Both objects encounter the same constant braking force and are brought to rest. Which object travels the greater distance before stopping?

Accepted Answer

The 1.0-kg object

Question 2

Two objects, one of mass $$m$$ and the other of mass $$2m$$, are dropped from the top of a building. When they hit the ground, which statement about their kinetic energy is correct?

Accepted Answer

The heavier one will have twice the kinetic energy of the lighter one.

Question 3

Two stones, one of mass $$m$$ and the other of mass $$2m$$, are thrown directly upward with the same velocity at the same time from ground level and feel no air resistance. Which statement about their motion is true?

Accepted Answer

At their highest point, the heavier stone will have twice as much gravitational potential energy as the lighter stone because its mass is heavier.

Question 4

Which of the following statements about the conservation of mechanical energy is correct?

Accepted Answer

No, because this would have no physical meaning.

Question 5

A box of mass $$m is $$pressed against (but not attached to) an ideal spring of force constant $$k$$ and negligible mass, compressing the spring a distance $$x. $$After it is released, the box slides up a frictionless incline as shown in the figure and eventually stops. If we repeat this experiment with a box of mass $$2m$$, which statement is correct?

Accepted Answer

Both boxes will have the same speed just as they move free of the spring.

Question 6

A 50-cm$$^3$$ block of wood is floating partially submerged in water, and a 50-cm$$^3$$ block of iron is totally submerged in water. Which block has the greater buoyant force on it?

Accepted Answer

The iron

Question 7

As a rock is under water in a shallow lake, as the rock sinks deeper and deeper into water, the buoyant force on it:

Accepted Answer

Remains constant.

Question 8

A bucket is lifted at constant speed to the top of a building. The bucket is initially at rest, but is traveling at 4.0 m/s when it reaches the top of the building. What is the minimum amount of work that the worker did in lifting the bucket?

Accepted Answer

$$W = mgh + \frac{1}{2}mv^2$

Question 9

How much energy is needed to change the speed of a 1600 kg sport utility vehicle from 15.0 m/s to 40.0 m/s?

Accepted Answer

$$E = \frac{1}{2}m(v_f^2$ - v_i^2$)$$

Question 10

A spring-loaded dart gun is used to shoot a dart straight up into the air, and the dart reaches a maximum height of 24 meters above its point of release. The same dart is shot up a second time from the same gun, but this time the spring is compressed only half as far (compared to the first shot). How far up does the dart go this time?

Accepted Answer

6 m

Question 11

In the figure, an open tank contains a layer of oil floating on top of a layer of water (of density $$1000\ \mathrm{kg/m^3$}) $$that is 3.00 m thick, as shown. What must be the thickness of the oil layer if the gauge pressure at the bottom of the tank is to be $$5.0 	imes 10^4$ Pa? (The density of the oil is 510$$\ \mathrm{$$kg/m^3$$}$$.)

Accepted Answer

$$h_{oil} = \frac{P_{gauge} - \$$rho_{water}$$gh_{water}}{\$$rho_{oil}$$g}$$

Question 12

Spring 1 connects block A to a frictionless peg at O and spring 2 connects block A and block B. When the blocks are in uniform circular motion about O, the springs have lengths of 0.60 m and 0.40 m, as shown. The springs are ideal and massless, and the linear speed of block B is 2.0 m/s. If the distance that spring 2 stretches is 0.060 m, what is the spring constant of spring 2?

Accepted Answer

$$k = \frac{mv^2$}{x}$$

Question 13

A 60.0-kg person drops from rest a distance of 1.20 m to a platform of negligible mass supported by an ideal stiff spring of negligible mass. The platform drops 6.00 cm before the person comes to rest. What is the spring constant of the spring?

Accepted Answer

$$k = \frac{mg}{x}$$

Question 14

A block is projected with a velocity $$v_1$$ from a spring, descends a ramp, and enters a rough section with coefficient of kinetic friction $$\mu_k. $$The velocity of the block is $$v_3 at C. $$What is the work done by friction between points B and C?

Accepted Answer

$$W_{fric} = \mu_k mg s$$

Question 15

A rock is suspended from a scale and reads 200 N. A beaker of water (density $$1000\ \mathrm{kg/m^3$}) is $$raised up so the rock is totally submerged in the water. The scale now reads 125 N. What is the density of the rock?

Accepted Answer

$$\rho_{rock} = \frac{W_{air}}{W_{air} - W_{water}} \rho_{water}$$

Question 16

A board that is 20.0 cm wide, 5.00 cm thick, and 3.00 m long has a density of 350 kg/m$$^3. $$The board is floating partially submerged in water of density 1000 kg/m$$^3. $$What fraction of the volume of the board is above the surface of the water?

Accepted Answer

$$f = 1 - \frac{\rho_{board}}{\rho_{water}}$$

Question 17

A dart gun is used to shoot a dart straight up into the air. If the spring is compressed by $$x$$, the dart reaches a height $$h. If $$the spring is compressed by $$2x$$, what is the new height reached by the dart (neglecting air resistance)?

Accepted Answer

$$h_{new} = 4h$$

Question 18

A block of mass $$m is $$released from rest at height $$h$$ above the ground and slides down a frictionless ramp. What is its speed at the bottom?

Accepted Answer

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

Question 19

A block of mass $$m is $$attached to a spring of constant $$k$$ and compressed a distance $$x. $$What is the maximum speed of the block when released on a frictionless surface?

Accepted Answer

$$v_{max} = \sqrt{\frac{k}{m}}x$$

Physics Exam Review: Work, Energy, Fluids, and Circular Motion

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