Q: A person pushes a stalled car with a constant force of 400 N for a distance of 15 m in the direction of the force. How much work is done by the person on the car?

$$W = 400 \times 15 = 6000\ \mathrm{J}$$

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

$$K = \frac{1}{2} m v^2$ = \frac{1}{2} \times 2 \times 3^2$ = 9\ \mathrm{J}$$

Q: A 1,000 kg car accelerates from 10 m/s to 20 m/s. What is the change in its kinetic energy?

$$\Delta K = \frac{1}{2} m (v_f^2$ - v_i^2$) = \frac{1}{2} \times 1000 \times (20^2$ - 10^2$) = 150,000\ \mathrm{J}$$

Q: A person lifts a 20 kg box vertically upward a distance of 2 m at constant speed. What is the work done by the person against gravity? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

$$W = m g h = 20 \times 9.8 \times 2 = 392\ \mathrm{J}$$

Q: A cyclist applies a constant force of 100 N to move a bike 50 m along a straight path. If the force is at an angle of $$60^\circ to $$the direction of motion, what is the work done?

$$W = 100 \times 50 \times \cos 60^\circ = 2500\ \mathrm{J}$$

Question 1

A person pushes a stalled car with a constant force of 400 N for a distance of 15 m in the direction of the force. How much work is done by the person on the car?

Accepted Answer

$$W = 400 	imes 15 = 6000\ \mathrm{J}$$

Question 2

Which of the following situations results in zero work being done by the applied force?

Accepted Answer

A person holds a heavy box stationary above their head.

Question 3

A weightlifter lowers a barbell to the floor. What is the sign of the work done by the weightlifter's hands on the barbell?

Accepted Answer

Negative

Question 4

A force of $$F$$ acts at an angle $$	heta to $$the direction of displacement $$\vec{s}. $$What is the formula for the work done by this force?

Accepted Answer

$$W = F s \cos 	heta$$

Question 5

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

Accepted Answer

$$K = \frac{1}{2} m v^2$ = \frac{1}{2} 	imes 2 	imes 3^2$ = 9\ \mathrm{J}$$

Question 6

If the net work done on a particle is positive, what happens to its speed?

Accepted Answer

It increases

Question 7

A spring with spring constant $$k is $$stretched a distance $$x. $$What is the work done to stretch the spring?

Accepted Answer

$$W = \frac{1}{2} k x^2$

Question 8

Which of the following statements about kinetic energy is correct?

Accepted Answer

Kinetic energy depends only on mass and speed, not direction.

Question 9

A 1,000 kg car accelerates from 10 m/s to 20 m/s. What is the change in its kinetic energy?

Accepted Answer

$$\Delta K = \frac{1}{2} m (v_f^2$ - v_i^2$) = \frac{1}{2} 	imes 1000 	imes (20^2$ - 10^2$) = 150,000\ \mathrm{J}$$

Question 10

A force $$F_x$$ varies with position $$x. $$What is the general expression for the work done by this force as the object moves from $$x_1 to$$ $$x_2$$?

Accepted Answer

$$W = \int_{x_1$}^{x_2$} F_x\, dx$$

Question 11

A person lifts a 20 kg box vertically upward a distance of 2 m at constant speed. What is the work done by the person against gravity? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$W = m g h = 20 	imes 9.8 	imes 2 = 392\ \mathrm{J}$$

Question 12

Which of the following best describes the work-energy theorem?

Accepted Answer

The net work done on a particle equals the change in its kinetic energy.

Question 13

A cyclist applies a constant force of 100 N to move a bike 50 m along a straight path. If the force is at an angle of $$60^\circ to $$the direction of motion, what is the work done?

Accepted Answer

$$W = 100 	imes 50 	imes \cos 60^\circ = 2500\ \mathrm{J}$$

Question 14

A machine does 2000 J of work in 10 seconds. What is its average power output?

Accepted Answer

$$P = \frac{W}{\Delta t} = \frac{2000}{10} = 200\ \mathrm{W}$$

Question 15

Which of the following is the correct SI unit for power?

Accepted Answer

Watt ($$\mathrm{W})$$

Question 16

A car engine provides a constant force of 500 N to move the car at a constant velocity of 20 m/s. What is the instantaneous power delivered by the engine?

Accepted Answer

$$P = F v = 500 	imes 20 = 10,000\ \mathrm{W}$$

Question 17

A graph shows force as a function of position. What does the area under the curve between two positions represent?

Accepted Answer

The work done by the force over that displacement

Question 18

A runner of mass 70 kg increases her speed from 5 m/s to 8 m/s. How much work is required to achieve this change?

Accepted Answer

$$W = \Delta K = \frac{1}{2} m (v_f^2$ - v_i^2$) = \frac{1}{2} 	imes 70 	imes (8^2$ - 5^2$) = 1,365\ \mathrm{J}$$

Question 19

A box is lifted slowly and then quickly to the same height. Which statement is true about the work and power involved?

Accepted Answer

The work done is the same in both cases, but the power is greater when lifted quickly.

Work and Kinetic Energy: Concepts, Formulas, and Applications

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