Worksheet covering kinetic and potential energy concepts, including formulas, units, and problem-solving exercises.

Worksheet: Kinetic and Potential Energy Problems

#### Section 1: Potential Energy

1. Stored energy or energy due to position is known as ________ energy.
- Answer: Potential energy

2. The formula for calculating potential energy is ________.
- Answer: \( PE = m \cdot g \cdot h \)
- Where:
- \( PE \) = Potential Energy
- \( m \) = Mass of the object
- \( g \) = Gravitational acceleration (approximately \( 9.8 \, \text{m/s}^2 \))
- \( h \) = Height above a reference point

3. The three factors that determine the amount of potential energy in an object are ________, ________, and ________.
- Answer: Mass, gravitational pull, height

4. Potential energy is measured in units of ________.
- Answer: Joules (J)

5. Mass must be measured in units of ________.
- Answer: Kilograms (kg)

6. Gravitational pull must be measured in units of ________.
- Answer: Meters per second squared (\( \text{m/s}^2 \))

7. Height must be measured in units of ________.
- Answer: Meters (m)

8. Calculate the potential energy of a rock with a mass of 55 kg while sitting on a cliff that is 27 m high.
- Formula: \( PE = m \cdot g \cdot h \)
- Given:
- \( m = 55 \, \text{kg} \)
- \( g = 9.8 \, \text{m/s}^2 \)
- \( h = 27 \, \text{m} \)
- Calculation:
\[
PE = 55 \cdot 9.8 \cdot 27
\]
\[
PE = 55 \cdot 264.6
\]
\[
PE = 14553 \, \text{J}
\]
- Answer: \( 14553 \, \text{J} \)

9. What distance is a book from the floor if the book contains 196 Joules of potential energy and has a mass of 5 kg?
- Formula: \( PE = m \cdot g \cdot h \)
- Rearrange for height (\( h \)):
\[
h = \frac{PE}{m \cdot g}
\]
- Given:
- \( PE = 196 \, \text{J} \)
- \( m = 5 \, \text{kg} \)
- \( g = 9.8 \, \text{m/s}^2 \)
- Calculation:
\[
h = \frac{196}{5 \cdot 9.8}
\]
\[
h = \frac{196}{49}
\]
\[
h = 4 \, \text{m}
\]
- Answer: \( 4 \, \text{m} \)

10. An automobile is sitting on a hill which is 20 m higher than ground level. Find the mass of the automobile if it contains 362,600 J of potential energy.
- Formula: \( PE = m \cdot g \cdot h \)
- Rearrange for mass (\( m \)):
\[
m = \frac{PE}{g \cdot h}
\]
- Given:
- \( PE = 362,600 \, \text{J} \)
- \( g = 9.8 \, \text{m/s}^2 \)
- \( h = 20 \, \text{m} \)
- Calculation:
\[
m = \frac{362,600}{9.8 \cdot 20}
\]
\[
m = \frac{362,600}{196}
\]
\[
m = 1850 \, \text{kg}
\]
- Answer: \( 1850 \, \text{kg} \)

#### Section 2: Kinetic Energy

11. Energy of motion is known as ________ energy.
- Answer: Kinetic energy

12. The formula for calculating kinetic energy is ________.
- Answer: \( KE = \frac{1}{2} \cdot m \cdot v^2 \)
- Where:
- \( KE \) = Kinetic Energy
- \( m \) = Mass of the object
- \( v \) = Velocity of the object

13. The two factors that determine the amount of kinetic energy in an object are ________ and ________.
- Answer: Mass, velocity

14. Kinetic energy is measured in units of ________.
- Answer: Joules (J)

15. Mass must be measured in units of ________.
- Answer: Kilograms (kg)

16. Velocity must be measured in units of ________.
- Answer: Meters per second (\( \text{m/s} \))

---

Final Answers:

1. Potential energy
2. \( PE = m \cdot g \cdot h \)
3. Mass, gravitational pull, height
4. Joules (J)
5. Kilograms (kg)
6. Meters per second squared (\( \text{m/s}^2 \))
7. Meters (m)
8. \( \boxed{14553 \, \text{J}} \)
9. \( \boxed{4 \, \text{m}} \)
10. \( \boxed{1850 \, \text{kg}} \)
11. Kinetic energy
12. \( KE = \frac{1}{2} \cdot m \cdot v^2 \)
13. Mass, velocity
14. Joules (J)
15. Kilograms (kg)
16. Meters per second (\( \text{m/s} \))