Q: Jon pulls a box with a force of $$50.0\ \mathrm{N} at an $$angle of $$20.0^\circ$$ above the horizontal for a distance of $$3.0\ \mathrm{m}. $$What is the work done by Jon on the box?

$$W = 50.0 \times 3.0 \times \cos(20.0^\circ) = 140.9\ \mathrm{J}$$

Q: A $$7.00\ \mathrm{kg}$$ ball is held and then dropped from rest. What is its kinetic energy just before it hits the ground if it falls $$3.00\ \mathrm{m}$$?

$$KE = mgh = 7.00 \times 9.8 \times 3.00 = 205.8\ \mathrm{J}$$

Q: A $$2.00\ \mathrm{kg}$$ object is moving at $$3.00\ \mathrm{m/s}. $$What is its kinetic energy?

$$KE = \frac{1}{2} \times 2.00 \times (3.00)^2$ = 9.0\ \mathrm{J}$$

Q: If a force of $$60.0\ \mathrm{N} is $$applied over a distance of $$3.0\ \mathrm{m} at an $$angle of $$18^\circ to $$the direction of motion, what is the work done?

$$W = 60.0 \times 3.0 \times \cos(18^\circ) = 171.0\ \mathrm{J}$$

Q: A $$1.00\ \mathrm{kg}$$ object moves at $$3.00\ \mathrm{m/s}. $$What is its kinetic energy?

$$KE = \frac{1}{2} \times 1.00 \times (3.00)^2$ = 4.5\ \mathrm{J}$$

Q: A $$10.0\ \mathrm{kg}$$ object is lifted to a height of $$4.34\ \mathrm{m}. $$What is its gravitational potential energy?

$$PE = 10.0 \times 9.8 \times 4.34 = 425.3\ \mathrm{J}$$

Q: A spring with spring constant $$k = 200\ \mathrm{N/m} is $$compressed by $$0.08\ \mathrm{m}. $$What is the elastic potential energy stored in the spring?

$$PE = \frac{1}{2} \times 200 \times (0.08)^2$ = 0.64\ \mathrm{J}$$

Q: A $$3.00\ \mathrm{kg}$$ object is dropped from a height of $$5.00\ \mathrm{m}. $$What is its speed just before hitting the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

$$v = \sqrt{2gh} = \sqrt{2 \times 9.8 \times 5.00} = 9.9\ \mathrm{m/s}$$

Question 1

Jon pulls a box with a force of $$50.0\ \mathrm{N} at an $$angle of $$20.0^\circ$$ above the horizontal for a distance of $$3.0\ \mathrm{m}. $$What is the work done by Jon on the box?

Accepted Answer

$$W = 50.0 	imes 3.0 	imes \cos(20.0^\circ) = 140.9\ \mathrm{J}$$

Question 2

A $$7.00\ \mathrm{kg}$$ ball is held and then dropped from rest. What is its kinetic energy just before it hits the ground if it falls $$3.00\ \mathrm{m}$$?

Accepted Answer

$$KE = mgh = 7.00 	imes 9.8 	imes 3.00 = 205.8\ \mathrm{J}$$

Question 3

Which equation correctly expresses the work-energy theorem?

Accepted Answer

$$W = \Delta KE$$

Question 4

A $$2.00\ \mathrm{kg}$$ object is moving at $$3.00\ \mathrm{m/s}. $$What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} 	imes 2.00 	imes (3.00)^2$ = 9.0\ \mathrm{J}$$

Question 5

If a force of $$60.0\ \mathrm{N} is $$applied over a distance of $$3.0\ \mathrm{m} at an $$angle of $$18^\circ to $$the direction of motion, what is the work done?

Accepted Answer

$$W = 60.0 	imes 3.0 	imes \cos(18^\circ) = 171.0\ \mathrm{J}$$

Question 6

Which of the following best describes mechanical energy?

Accepted Answer

The sum of kinetic and potential energy in a system.

Question 7

A $$1.00\ \mathrm{kg}$$ object moves at $$3.00\ \mathrm{m/s}. $$What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} 	imes 1.00 	imes (3.00)^2$ = 4.5\ \mathrm{J}$$

Question 8

Which formula is used to calculate gravitational potential energy?

Accepted Answer

$$PE = mgh$$

Question 9

A $$10.0\ \mathrm{kg}$$ object is lifted to a height of $$4.34\ \mathrm{m}. $$What is its gravitational potential energy?

Accepted Answer

$$PE = 10.0 	imes 9.8 	imes 4.34 = 425.3\ \mathrm{J}$$

Question 10

A spring with spring constant $$k = 200\ \mathrm{N/m} is $$compressed by $$0.08\ \mathrm{m}. $$What is the elastic potential energy stored in the spring?

Accepted Answer

$$PE = \frac{1}{2} 	imes 200 	imes (0.08)^2$ = 0.64\ \mathrm{J}$$

Question 11

Which of the following scenarios best illustrates the conservation of mechanical energy?

Accepted Answer

A pendulum swinging without air resistance.

Question 12

A $$3.00\ \mathrm{kg}$$ object is dropped from a height of $$5.00\ \mathrm{m}. $$What is its speed just before hitting the ground? (Assume $$g = 9.8\ \mathrm{m/s^2$})$$

Accepted Answer

$$v = \sqrt{2gh} = \sqrt{2 	imes 9.8 	imes 5.00} = 9.9\ \mathrm{m/s}$$

Question 13

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

Accepted Answer

Kinetic energy

Question 14

A $$5.00\ \mathrm{kg}$$ object is moving at $$4.00\ \mathrm{m/s}. $$What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} 	imes 5.00 	imes (4.00)^2$ = 40.0\ \mathrm{J}$$

Question 15

A $$2.00\ \mathrm{kg}$$ ball is thrown vertically upward with a speed of $$6.00\ \mathrm{m/s}. $$What is its maximum height?

Accepted Answer

$$h = \frac{v^2$}{2g} = \frac{(6.00)^2$}{2 	imes 9.8} = 1.84\ \mathrm{m}$$

Question 16

Which of the following statements about the work-energy theorem is correct?

Accepted Answer

The net work done on an object equals its change in kinetic energy.

Question 17

A $$4.00\ \mathrm{kg}$$ object is lifted $$2.00\ \mathrm{m}$$ above the ground. What is its gravitational potential energy?

Accepted Answer

$$PE = 4.00 	imes 9.8 	imes 2.00 = 78.4\ \mathrm{J}$$

Question 18

A $$3.00\ \mathrm{kg}$$ object is moving at $$5.00\ \mathrm{m/s}. $$What is its kinetic energy?

Accepted Answer

$$KE = \frac{1}{2} 	imes 3.00 	imes (5.00)^2$ = 37.5\ \mathrm{J}$$

Work, Energy, and Mechanical Energy in Physics

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