Q: A 5 kg box is pulled across a horizontal floor by a force of 30 N at an angle of 60° above the horizontal for a distance of 10 m. What is the work done by the force on the box?

$$W = 30 \times 10 \times \cos 60^\circ = 150\ \mathrm{J}$$

Q: A 2 kg object is dropped from a height of 5 m. What is its gravitational potential energy relative to the ground before it is dropped? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

$$U_g = mgy = 2 \times 9.8 \times 5 = 98\ \mathrm{J}$$

Q: A spring with spring constant $$k = 200\ \mathrm{N/m} is $$compressed by $$0.1\ \mathrm{m}. $$What is the elastic potential energy stored in the spring?

$$U_s = \frac{1}{2}kx^2$ = \frac{1}{2} \times 200 \times (0.1)^2$ = 1\ \mathrm{J}$$

Q: A 1000 kg car accelerates from rest to a speed of $$20\ \mathrm{m/s}. $$What is the change in its kinetic energy?

$$\Delta K = \frac{1}{2}mv^2$ = \frac{1}{2} \times 1000 \times (20)^2$ = 200,000\ \mathrm{J}$$

Q: A dog pulls a sled with a force of 350 N for 4.9 m at constant speed. How much work does the dog do?

$$W = Fd = 350 \times 4.9 = 1700\ \mathrm{J}$$

Q: A 5000 kg canal boat is pulled from rest by a constant force of 1400 N until it reaches a speed of $$0.70\ \mathrm{m/s}. $$What distance did the horses pull the boat?

$$d = \frac{mv^2$}{2F} = \frac{5000 \times (0.70)^2$}{2 \times 1400} \approx 0.875\ \mathrm{m}$$

Q: A weightlifter lifts a 100 kg barbell from the ground to a height of 2 m. How much work is done against gravity?

$$W = mgh = 100 \times 9.8 \times 2 = 1960\ \mathrm{J}$$

Question 1

A 5 kg box is pulled across a horizontal floor by a force of 30 N at an angle of 60° above the horizontal for a distance of 10 m. What is the work done by the force on the box?

Accepted Answer

$$W = 30 	imes 10 	imes \cos 60^\circ = 150\ \mathrm{J}$$

Question 2

Which of the following best describes the change in energy when a child swings from the highest point to the lowest point of a playground swing?

Accepted Answer

Gravitational potential energy is transformed into kinetic energy: $$U_g \rightarrow K$$

Question 3

A 2 kg object is dropped from a height of 5 m. What is its gravitational potential energy relative to the ground before it is dropped? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$U_g = mgy = 2 	imes 9.8 	imes 5 = 98\ \mathrm{J}$$

Question 4

A spring with spring constant $$k = 200\ \mathrm{N/m} is $$compressed by $$0.1\ \mathrm{m}. $$What is the elastic potential energy stored in the spring?

Accepted Answer

$$U_s = \frac{1}{2}kx^2$ = \frac{1}{2} 	imes 200 	imes (0.1)^2$ = 1\ \mathrm{J}$$

Question 5

A 1000 kg car accelerates from rest to a speed of $$20\ \mathrm{m/s}. $$What is the change in its kinetic energy?

Accepted Answer

$$\Delta K = \frac{1}{2}mv^2$ = \frac{1}{2} 	imes 1000 	imes (20)^2$ = 200,000\ \mathrm{J}$$

Question 6

Which of the following forces does NO work on an object?

Accepted Answer

A force perpendicular to the displacement

Question 7

A dog pulls a sled with a force of 350 N for 4.9 m at constant speed. How much work does the dog do?

Accepted Answer

$$W = Fd = 350 	imes 4.9 = 1700\ \mathrm{J}$$

Question 8

A 5000 kg canal boat is pulled from rest by a constant force of 1400 N until it reaches a speed of $$0.70\ \mathrm{m/s}. $$What distance did the horses pull the boat?

Accepted Answer

$$d = \frac{mv^2$}{2F} = \frac{5000 	imes (0.70)^2$}{2 	imes 1400} \approx 0.875\ \mathrm{m}$$

Question 9

Which statement about the conservation of energy in an isolated system is correct?

Accepted Answer

The total energy remains constant, but energy can be transformed between different forms.

Question 10

A weightlifter lifts a 100 kg barbell from the ground to a height of 2 m. How much work is done against gravity?

Accepted Answer

$$W = mgh = 100 	imes 9.8 	imes 2 = 1960\ \mathrm{J}$$

Question 11

Which of the following is a correct statement about elastic potential energy in a spring?

Accepted Answer

It is given by $$U_s = \frac{1}{2}kx^2$, where x$ is the displacement from equilibrium.

Question 12

A suitcase is pulled at a constant speed by a force of 20 N at an angle of 45° for 120 m. What is the work done by the tension?

Accepted Answer

$$W = 20 	imes 120 	imes \cos 45^\circ = 1700\ \mathrm{J}$$

Question 13

Which of the following is NOT a conservative force?

Accepted Answer

Friction

Question 14

A ball of mass $$m is $$thrown vertically upward with initial speed $$v_0. At $$its highest point, what is its kinetic energy?

Accepted Answer

$$K = 0$$

Question 15

Which equation correctly relates the work done by a constant force $$F at an $$angle $$	heta to $$the displacement $$d$$?

Accepted Answer

$$W = Fd \cos 	heta$$

Question 16

A 3 kg object moves in a circle of radius 2 m at an angular velocity of $$4\ \mathrm{rad/s}. $$What is its rotational kinetic energy? (Assume $$I = mr^2$)

Accepted Answer

$$K_{rot} = \frac{1}{2}I\$$omega^2$$ = \frac{1}{2} 	imes 3 	imes 2^2$ 	imes 4^2$ = 192\ \mathrm{J}$$

Question 17

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

Accepted Answer

The net work done on a system equals the change in its kinetic energy: $$W_{net} = \Delta K$$

Lecture 16: Conservation Laws, Energy, and Work in Physics for Life Sciences

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