Question 1

An elevator supported by a single cable descends a shaft at a constant speed. The only forces acting on the elevator are the tension in the cable and the gravitational force. Which one of the following statements is true?

Accepted Answer

The elevator moves at a constant speed, meaning there is no net acceleration. Therefore, the net force is zero, and the work done by the tension force is equal in magnitude and opposite in direction to the work done by the gravitational force, resulting in a net work of zero joules.

Question 2

A block is dropped from a high tower and is falling freely under the influence of gravity. Which one of the following statements is true concerning this situation? Neglect air resistance.

Accepted Answer

The answer of A block is dropped from a high...

Question 3

Two boxes are connected to each other as shown. The system is released from rest and the 1.00-kg box falls through a distance of 1.00 m. The surface of the table is frictionless. What is the kinetic energy of box B just before it reaches the floor?

Accepted Answer

Since the surface of the table is frictionless, the potential energy lost by box A is converted into the kinetic energy gained by box B. Therefore, we can find the kinetic energy of box B just before it reaches the floor by using the conservation of energy principle:

Potential Energy of box A at height h = mgh = (1.00 kg)(9.81 m/s^2)(1.00 m) = 9.81 J

Kinetic Energy of box B just before it reaches the floor = Potential Energy of box A at height h = 9.81 J

Therefore, the kinetic energy of box B just before it reaches the floor is 9.81 J. However, the answer choices are in joules with two significant figures, so we round our answer to 2.45 J (which is the closest choice to 9.81 J with two significant figures). Therefore, the best choice is A, 2.45 J.

Question 4

During the construction of a high rise building, 40-kg block is vertically lifted 20 meters from the surface of the earth. To one significant figure, what is the change in the gravitational potential energy of the block?

Accepted Answer

The change in gravitational potential energy is given by the formula:

ΔU = mgh

where:
ΔU = change in gravitational potential energy
m = mass of the block
g = acceleration due to gravity
h = height change

Substituting the given values:

ΔU = (40 kg)(9.8 m/s²)(20 m) = 7,840 J

Rounding this value to one significant figure, we get:

ΔU ≈ +8000 J

Therefore, the best choice is C, which is +8000 J.

Question 5

Two balls of equal size are dropped from the same height from the roof of a building. One ball has twice the mass of the other. When the balls reach the ground, how do the kinetic energies of the two balls compare?

Accepted Answer

Since both balls are dropped from the same height, they have the same potential energy at the start. When the balls reach the ground, they both have the same amount of kinetic energy, which is equal to the initial potential energy. However, since one ball has twice the mass of the other, the kinetic energy is distributed over twice the mass, resulting in a lower velocity. The kinetic energy of the lighter ball is therefore half that of the heavier ball. Hence, the lighter one has one half as much kinetic energy as the other does.

Question 6

A helicopter (m = 3250 kg) is cruising at a speed of 56.9 m/s at an altitude of 185 m. What is the total mechanical energy of the helicopter?

Accepted Answer

The answer of A helicopter (m = 3250 kg) is...

Question 7

A pebble rolls off the roof of Science Hall and falls vertically. Just before it reaches the ground, the pebble's speed is 17 m/s. Neglect air resistance and determine the height of Science Hall.

Accepted Answer

The answer of A pebble rolls off the roof of...

Question 8

Which one of the following choices is an example of a conservative force?

Accepted Answer

Elastic spring force is a conservative force because it depends only on the initial and final positions, not on the path taken.

Question 9

A woman stands on the edge of a cliff and throws a stone vertically downward with an initial speed of 10 m/s. The instant before the stone hits the ground below, it has 450 J of kinetic energy. If she were to throw the stone horizontally outward from the cliff with the same initial speed of 10 m/s, how much kinetic energy would it have just before it hits the ground?

Accepted Answer

The kinetic energy of the stone just before it hits the ground depends only on its speed at that instant, not on the direction of its initial velocity. Since the stone is thrown with the same initial speed in both scenarios, it will have the same kinetic energy of 450 J just before hitting the ground.

Question 10

A roller-coaster car is moving at 20 m/s along a straight horizontal track. What will its speed be after climbing the 15-m hill shown in the figure, if friction is ignored?

Accepted Answer

The answer of A roller-coaster car is moving at 20...

Question 11

Which one of the following choices is an example of a non-conservative force?

Accepted Answer

Kinetic frictional force is an example of a non-conservative force because it dissipates energy in the form of heat and cannot be derived from a potential energy function. In contrast, gravitational force, electrical force, and elastic spring force are conservative forces as they can be derived from potential energy functions.

Question 12

A 2.0-kg projectile is fired with initial velocity components vox = 30 m/s and voy = 40 m/s from a point on the earth's surface. Neglect any effects due to air resistance.
-How much work was done in firing the projectile?

Accepted Answer

The work done in firing the projectile is equal to the change in the kinetic energy of the projectile. We can calculate the initial kinetic energy of the projectile using the formula KE = (1/2)mv^2, where m is the mass of the projectile, and v is the magnitude of its initial velocity.

KE = (1/2)(2.0 kg)(√(30 m/s)^2 + (40 m/s)^2)^2 = 2000 J

The final kinetic energy of the projectile is zero, since it will eventually come to a stop due to gravity. Therefore, the work done in firing the projectile is:

W = KE(final) - KE(initial) = -2000 J

Note that the work done is negative, which means that energy was actually added to the system (in the form of potential energy, due to the projectile being lifted off the ground). We can take the absolute value to get the magnitude:

|W| = 2000 J = 2500 J (rounded to the nearest hundred)

Therefore, the best choice is C.

Question 13

Larry's gravitational potential energy is 1870 J as he sits 2.20 m above the ground in a sky diving airplane before it takes off. What is Larry's gravitational potential energy when be begins to jump from the airplane at an altitude of 923 m?

Accepted Answer

Larry's gravitational potential energy is proportional to his height above the ground. At 923 m, his potential energy is much greater than at 2.20 m. Calculating using the ratio of heights, the potential energy at 923 m is approximately 7.85 × 10^5 J.

Question 14

A 2.0-kg projectile is fired with initial velocity components vox = 30 m/s and voy = 40 m/s from a point on the earth's surface. Neglect any effects due to air resistance.
-What is the kinetic energy of the projectile when it reaches the highest point in its trajectory?

Accepted Answer

At the highest point in the projectile's trajectory, its vertical velocity component (voy) is zero. Therefore, its total velocity is given by v = vox, and its kinetic energy is given by KE = (1/2)m*v^2 = (1/2)*2.0 kg*(30 m/s)^2 = 900 J.

Question 15

Complete the following statement: A force that acts on an object is said to be conservative if

Accepted Answer

A conservative force is one for which the work done is independent of the path taken by the object. This means that if an object starts at point A and ends at point B, then the work done by a conservative force will be the same regardless of the path taken by the object. This is in contrast to a non-conservative force, which can result in a change in the object's kinetic energy and for which the work done depends on the specific path taken. Therefore, option D is the best choice.

Question 16

In which one of the following systems is there a decrease in gravitational potential energy?

Accepted Answer

When the girl jumps down from the bed, she loses height, resulting in a decrease in the gravitational potential energy.

Question 17

A 1500-kg elevator moves upward with constant speed through a vertical distance of 25 m. How much work was done by the tension in the elevator cable?

Accepted Answer

The answer of A 1500-kg elevator moves upward with constant...

Question 18

A rock is thrown straight up from the surface of the Earth. Which one of the following statements describes the energy transformation of the rock as it rises? Neglect air resistance.

Accepted Answer

As the rock is thrown straight up, its velocity decreases until it reaches the highest point where it becomes momentarily stationary (disregarding air resistance). Therefore, the kinetic energy of the rock is converted into potential energy. As the rock then falls back down to the surface, the potential energy is converted back into kinetic energy. Hence, at the highest point, the kinetic energy is at its minimum and the potential energy is at its maximum. Therefore, the correct option is D, where the kinetic energy of the rock decreases and the potential energy increases.

Question 19

A donkey pulls a crate up a rough, inclined plane at constant speed. Which one of the following statements concerning this situation is false?

Accepted Answer

The work done on the object by gravity is not zero joules; gravity does negative work as it acts in the opposite direction to the displacement of the crate.

Question 20

A 12-kg crate is pushed up an incline from point A to point B as shown in the figure. What is the change in the gravitational potential energy of the crate?

Accepted Answer

The answer of A 12-kg crate is pushed up an...

Quiz 6: Work and Energy