Q: A car of mass 1500 kg is towed from rest over 200 m. The tension in the rope decreases linearly from 5000 N to 0 N. What is the final speed of the car after being towed?

$$v = \sqrt{\frac{2W}{m}} = \sqrt{\frac{2 \times 500,000}{1500}} \approx 25.8\ \mathrm{m/s}$$

Q: A weightlifter slowly lifts a 50 kg barbell by 1.5 m. What is the work done by the weightlifter's applied force?

$$W = 50 \times 9.8 \times 1.5 = 735\ \mathrm{J}$$

Q: A force of 10 N acts at an angle of $$60^\circ to $$the direction of displacement of 5 m. What is the work done by the force?

$$W = 10 \times 5 \times \cos 60^\circ = 25\ \mathrm{J}$$

Q: If a child pulls a wagon with a force of 30 N at an angle of $$0^\circ to $$the direction of motion for 10 m, what is the work done?

$$W = 30 \times 10 \times \cos 0^\circ = 300\ \mathrm{J}$$

Question 1

Which of the following best describes the dot product of two vectors $$\vec{A}$$ and $$\vec{B}$$?

Accepted Answer

$$\vec{A} \cdot \vec{B} = AB \cos \phi$$

Question 2

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

Accepted Answer

$$K = \frac{1}{2}mv^2$ = \frac{1}{2}(2)(3^2$) = 9\ \mathrm{J}$$

Question 3

Which of the following statements about work is correct?

Accepted Answer

Work is the energy transferred to or from an object as the result of the action of a force.

Question 4

A person lifts a 10 kg box vertically upward by 2 m. What is the work done by gravity?

Accepted Answer

$$W = -mgh = -(10)(9.8)(2) = -196\ \mathrm{J}$$

Question 5

If a force acts perpendicular to the direction of displacement, what is the work done by the force?

Accepted Answer

The work is zero.

Question 6

A car of mass 1500 kg is towed from rest over 200 m. The tension in the rope decreases linearly from 5000 N to 0 N. What is the final speed of the car after being towed?

Accepted Answer

$$v = \sqrt{\frac{2W}{m}} = \sqrt{\frac{2 	imes 500,000}{1500}} \approx 25.8\ \mathrm{m/s}$$

Question 7

Which equation correctly expresses the work done by a variable force $$F$$ along a path from $$r_{initial} to$$ $$r_{final}$$?

Accepted Answer

$$W = \int_{r_{initial}}^{r_{final}} F \cdot d\vec{r}$$

Question 8

A basketball is tossed straight up with an initial speed $$v_i. $$What is the work done by gravity when the ball reaches its maximum height $$h$$?

Accepted Answer

$$W = -mgh$$

Question 9

Which of the following is NOT a form of mechanical energy?

Accepted Answer

Thermal energy

Question 10

A weightlifter slowly lifts a 50 kg barbell by 1.5 m. What is the work done by the weightlifter's applied force?

Accepted Answer

$$W = 50 	imes 9.8 	imes 1.5 = 735\ \mathrm{J}$$

Question 11

Which of the following best describes the energy principle for a system?

Accepted Answer

$$\Delta E_{sys} = W_{ext}$$

Question 12

A force of 10 N acts at an angle of $$60^\circ to $$the direction of displacement of 5 m. What is the work done by the force?

Accepted Answer

$$W = 10 	imes 5 	imes \cos 60^\circ = 25\ \mathrm{J}$$

Question 13

If a child pulls a wagon with a force of 30 N at an angle of $$0^\circ to $$the direction of motion for 10 m, what is the work done?

Accepted Answer

$$W = 30 	imes 10 	imes \cos 0^\circ = 300\ \mathrm{J}$$

Question 14

Which of the following is true about the work done by the gravitational force when an object is lowered slowly by a weightlifter?

Accepted Answer

The work done by gravity is positive.

Question 15

A force $$\vec{F}$$ acts on an object causing a displacement $$\Delta \vec{r}. $$Which formula gives the work done by the force?

Accepted Answer

$$W = \vec{F} \cdot \Delta \vec{r}$$

Question 16

Which of the following best describes the change in kinetic energy of a system when work is done by an external force?

Accepted Answer

$$\Delta K = W_{ext}$$

Question 17

A 5 kg object is dropped from a height of 10 m. What is the work done by gravity as it falls?

Accepted Answer

$$W = mgh = (5)(9.8)(10) = 490\ \mathrm{J}$$

Question 18

Which of the following is a correct statement about energy transformation in a system?

Accepted Answer

Energy can be transformed between kinetic, potential, thermal, and chemical forms.

Work and Kinetic Energy: Principles, Calculations, and Applications

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