Q: A construction worker lifts a 20 kg bag of cement to a height of 3 meters. What is the gravitational potential energy gained by the bag? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

$$PE = mgh = 20 \times 9.8 \times 3 = 588\ \mathrm{J}$$

Q: A person pushes a stalled car with a force of $$300\ \mathrm{N}$$ for $$10\ \mathrm{m}. $$How much work is done on the car?

$$W = Fd = 300 \times 10 = 3000\ \mathrm{J}$$

Q: A 2 kg object is moving at $$5\ \mathrm{m/s}. $$What is its kinetic energy?

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} \times 2 \times 5^2$ = 25\ \mathrm{J}$$

Q: A machine is 40% efficient. If you input $$500\ \mathrm{J} of $$energy, how much useful work output do you get?

$$\text{Useful work} = 0.4 \times 500 = 200\ \mathrm{J}$$

Q: A 1000 kg car is moving at $$20\ \mathrm{m/s}. $$What is the minimum work required to bring it to a stop?

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

Q: A worker uses a pulley system to lift a 200 N load by applying a force of 50 N. If the worker pulls the rope 2 meters, how high is the load lifted?

$$\text{Height} = \frac{50 \times 2}{200} = 0.5\ \mathrm{m}$$

Q: A 10 kg box slides across a floor and comes to a stop due to friction. If the friction force is $$20\ \mathrm{N}$$ and the box's initial speed is $$4\ \mathrm{m/s}$$, what is the stopping distance?

$$Fd = \frac{1}{2}mv^2$ \Rightarrow d = \frac{\frac{1}{2} \times 10 \times 4^2$}{20} = \frac{80}{20} = 4\ \mathrm{m}$$

Q: A solar panel receives $$1000\ \mathrm{J} of $$solar energy and converts $$150\ \mathrm{J}$$ into electricity. What is its efficiency?

$$\text{Efficiency} = \frac{150}{1000} = 0.15 = 15\%$$

Question 1

A construction worker lifts a 20 kg bag of cement to a height of 3 meters. What is the gravitational potential energy gained by the bag? (Take $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$PE = mgh = 20 	imes 9.8 	imes 3 = 588\ \mathrm{J}$$

Question 2

A person pushes a stalled car with a force of $$300\ \mathrm{N}$$ for $$10\ \mathrm{m}. $$How much work is done on the car?

Accepted Answer

$$W = Fd = 300 	imes 10 = 3000\ \mathrm{J}$$

Question 3

A 2 kg object is moving at $$5\ \mathrm{m/s}. $$What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2}mv^2$ = \frac{1}{2} 	imes 2 	imes 5^2$ = 25\ \mathrm{J}$$

Question 4

If you double the speed of a car, by what factor does its kinetic energy increase?

Accepted Answer

It increases by a factor of 4.

Question 5

A machine is 40% efficient. If you input $$500\ \mathrm{J} of $$energy, how much useful work output do you get?

Accepted Answer

$$	ext{Useful work} = 0.4 	imes 500 = 200\ \mathrm{J}$$

Question 6

A 1000 kg car is moving at $$20\ \mathrm{m/s}. $$What is the minimum work required 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 7

A worker uses a pulley system to lift a 200 N load by applying a force of 50 N. If the worker pulls the rope 2 meters, how high is the load lifted?

Accepted Answer

$$	ext{Height} = \frac{50 	imes 2}{200} = 0.5\ \mathrm{m}$$

Question 8

A 10 kg box slides across a floor and comes to a stop due to friction. If the friction force is $$20\ \mathrm{N}$$ and the box's initial speed is $$4\ \mathrm{m/s}$$, what is the stopping distance?

Accepted Answer

$$Fd = \frac{1}{2}mv^2$ \Rightarrow d = \frac{\frac{1}{2} 	imes 10 	imes 4^2$}{20} = \frac{80}{20} = 4\ \mathrm{m}$$

Question 9

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 10

A solar panel receives $$1000\ \mathrm{J} of $$solar energy and converts $$150\ \mathrm{J}$$ into electricity. What is its efficiency?

Accepted Answer

$$	ext{Efficiency} = \frac{150}{1000} = 0.15 = 15\%$$

Question 11

A runner does $$6000\ \mathrm{J} of $$work in $$50\ \mathrm{s}. $$What is the average power output?

Accepted Answer

$$P = \frac{W}{t} = \frac{6000}{50} = 120\ \mathrm{W}$$

Question 12

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

Accepted Answer

Momentum is a vector and can be canceled; kinetic energy is a scalar and cannot be canceled.

Question 13

A bow stores $$60\ \mathrm{J} of $$potential energy when drawn. When the arrow is released, it leaves with $$50\ \mathrm{J} of $$kinetic energy. What happens to the remaining energy?

Accepted Answer

It is transformed into heat and sound in the bow.

Question 14

A hydroelectric dam converts the gravitational potential energy of water into electrical energy. Which energy transformation occurs first?

Accepted Answer

Potential energy to kinetic energy as water falls.

Question 15

If a car's speed triples, by what factor does its stopping distance increase, assuming the same braking force?

Accepted Answer

It increases by a factor of 9.

Question 16

Which of the following is NOT a source of energy ultimately derived from the Sun?

Accepted Answer

Nuclear energy from uranium.

Question 17

A lever allows a small force to lift a heavy load by increasing the distance over which the force is applied. Which principle does this illustrate?

Accepted Answer

Conservation of energy.

Chapter 7: Energy – Physics with Calculus Study Notes

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