Q: A construction worker lifts a 20 kg bag of cement to the third floor, as shown in the second and third images. If the vertical distance between each floor is 3 m, what is the total work done against gravity to lift the bag from the ground to the third floor? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

$$W = mgh = 20 \times 9.8 \times 6 = 1176\ \mathrm{J}$$

Q: In the sixth image, a car is lifted by a hydraulic lift. If the car has a mass of 1000 kg and is raised 2 meters, what is the increase in gravitational potential energy? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

$$\Delta PE = mgh = 1000 \times 9.8 \times 2 = 19600\ \mathrm{J}$$

Q: A 2 kg object is moving at 3 m/s. What is its kinetic energy?

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} \times 2 \times 3^2$ = 9\ \mathrm{J}$$

Question 1

A person pushes against a stationary wall for several minutes, as shown in the first image. According to the definition of work in physics, how much work is done on the wall?

Accepted Answer

No work is done because the wall does not move.

Question 2

A construction worker lifts a 20 kg bag of cement to the third floor, as shown in the second and third images. If the vertical distance between each floor is 3 m, what is the total work done against gravity to lift the bag from the ground to the third floor? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$W = mgh = 20 	imes 9.8 	imes 6 = 1176\ \mathrm{J}$$

Question 3

A weightlifter raises a barbell from the floor to above their head, as shown in the fourth image. Which of the following best describes the energy transformation that occurs?

Accepted Answer

Chemical energy in the muscles is converted to gravitational potential energy of the barbell.

Question 4

A rocket launches vertically, as shown in the fifth image. Which of the following statements is true regarding the work done by the rocket engines?

Accepted Answer

The engines do work on the rocket by exerting a force over the distance the rocket travels upward.

Question 5

In the sixth image, a car is lifted by a hydraulic lift. If the car has a mass of 1000 kg and is raised 2 meters, what is the increase in gravitational potential energy? (Use $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$\Delta PE = mgh = 1000 	imes 9.8 	imes 2 = 19600\ \mathrm{J}$$

Question 6

Refer to the seventh image. A 10-N ball is raised to a height of 3 m by three different paths: straight up, along a ramp, and up a staircase. Which statement is correct about the work done against gravity?

Accepted Answer

The work done is the same in all three cases.

Question 7

A car drives off a cliff, as shown in the eighth image. Which form of energy is primarily converted as the car falls?

Accepted Answer

Gravitational potential energy is converted to kinetic energy.

Question 8

In the ninth image, a weight is dropped from a height. If the potential energy at the top is 100 J and the kinetic energy just before impact is 90 J, what happened to the missing energy?

Accepted Answer

10 J was transformed into heat and sound due to air resistance and friction.

Question 9

A bow is drawn, as shown in the tenth image. If the potential energy stored in the bow is 60 J and the arrow leaves with 50 J of kinetic energy, what can be concluded?

Accepted Answer

10 J of energy was transformed into heat and sound.

Question 10

A 2 kg object is moving at 3 m/s. What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} 	imes 2 	imes 3^2$ = 9\ \mathrm{J}$$

Question 11

A car of mass 1000 kg is moving at 20 m/s. How much work must be done by the brakes to bring it to a stop?

Accepted Answer

$$W = \Delta KE = \frac{1}{2}mv^2$ = \frac{1}{2} 	imes 1000 	imes 20^2$ = 200,000\ \mathrm{J}$$

Question 12

If the speed of a moving object is doubled, how does its kinetic energy change?

Accepted Answer

It becomes four times greater.

Question 13

Which of the following best describes the law of conservation of energy?

Accepted Answer

Energy cannot be created or destroyed; it can only be transformed from one form to another.

Question 14

A 5 kg object is lifted vertically upward at constant speed through a height of 4 m. What is the work done by the lifting force?

Accepted Answer

$$W = mgh = 5 	imes 9.8 	imes 4 = 196\ \mathrm{J}$$

Question 15

A machine does 500 J of work in 10 seconds. What is its power output?

Accepted Answer

$$P = \frac{W}{t} = \frac{500}{10} = 50\ \mathrm{W}$$

Question 16

A 10 kg object slides across a rough floor and comes to a stop after 5 m. If the friction force is 20 N, what was the object's initial kinetic energy?

Accepted Answer

$$KE = Fd = 20 	imes 5 = 100\ \mathrm{J}$$

Question 17

Which of the following statements is true about kinetic energy and momentum?

Accepted Answer

Kinetic energy is a scalar and cannot be canceled; momentum is a vector and can be canceled.

Chapter 7: Energy – Physics with Calculus Study Notes

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