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Potential Energy worksheet

Grades 8–9 · CCSS HSA.CED.A.4

Solve each problem and show your work. Round answers to 2 decimal places where needed.

1.
Problem 1.
- Solve for: Height
- Mass (m): 90 kg
- Potential energy (PE): 6,250 J
- Gravity (g): Earth: 9.80665 m/s² (standard)
- Show height in: Feet (ft)
Find: Height
Answer
2.
Problem 2.
- Solve for: Mass
- Height above the reference level (h): 8 m
- Potential energy (PE): 5,000 J
- Gravity (g): Earth: 9.80665 m/s² (standard)
- Show mass in: Grams (g)
Find: Mass
Answer
3.
Problem 3.
- Solve for: Potential energy
- Mass (m): 65 kg
- Height above the reference level (h): 10 m
- Gravity (g): Moon: 1.62 m/s²
- Show energy in: Kilocalories (kcal)
Find: Potential energy
Answer
4.
Problem 4.
- Solve for: Mass
- Height above the reference level (h): 9 m
- Potential energy (PE): 3,750 J
- Gravity (g): Custom value
- Custom gravitational acceleration: 8 m/s²
- Show mass in: Metric tonnes (t)
Find: Mass
Answer
5.
Problem 5.
- Solve for: Height
- Mass (m): 85 kg
- Potential energy (PE): 7,000 J
- Gravity (g): Custom value
- Custom gravitational acceleration: 14.5 m/s²
- Show height in: Centimeters (cm)
Find: Height
Answer
6.
Problem 6.
- Solve for: Potential energy
- Mass (m): 90 kg
- Height above the reference level (h): 11 m
- Gravity (g): Custom value
- Custom gravitational acceleration: 10 m/s²
- Show energy in: Kilojoules (kJ)
Find: Potential energy
Answer
7.
Problem 7.
- Solve for: Mass
- Height above the reference level (h): 9 m
- Potential energy (PE): 4,750 J
- Gravity (g): Moon: 1.62 m/s²
- Show mass in: Pounds (lb)
Find: Mass
Answer
8.
Problem 8.
- Solve for: Gravity (g)
- Mass (m): 66 kg
- Height above the reference level (h): 6 m
- Potential energy (PE): 5,000 J
- Show gravity in: Meters per second squared (m/s²)
Find: Gravitational acceleration
Answer
9.
Problem 9.
- Solve for: Height
- Mass (m): 90 kg
- Potential energy (PE): 2,750 J
- Gravity (g): Earth: 9.80665 m/s² (standard)
- Show height in: Inches (in)
Find: Height
Answer
10.
Problem 10.
- Solve for: Mass
- Height above the reference level (h): 9 m
- Potential energy (PE): 4,400 J
- Gravity (g): Mars: 3.71 m/s²
- Show mass in: Metric tonnes (t)
Find: Mass
Answer

Answer key: Potential Energy worksheet

1. Height: 23.23 ft
1. Use the surface gravity of Earth (standard gravity)
  $g$ $= 9.80665 m/s²$
2. To find the height, divide the energy by mass times gravity
  $\frac{6,250}{90 \times 9.80665}$ $= 7.081363 m$
3. Change the answer to ft, the unit you picked: divide by 0.3048
  $\frac{7.081363}{0.3048}$ $= 23.232817 ft$
2. Mass: 63,732.26 g
1. Use the surface gravity of Earth (standard gravity)
  $g$ $= 9.80665 m/s²$
2. To find the mass, divide the energy by gravity times height
  $\frac{5,000}{9.80665 \times 8}$ $= 63.732263 kg$
3. Change the answer to g, the unit you picked: divide by 0.001
  $\frac{63.732263}{0.001}$ $= 63,732.263311 g$
3. Potential energy: 0.25 kcal
1. Use the surface gravity of the Moon
  $g$ $= 1.62 m/s²$
2. Multiply the mass, the pull of gravity (g) and the height. In kilograms, m/s² and meters, that gives joules
  $65 \times 1.62 \times 10$ $= 1,053 J$
3. Change the answer to kcal, the unit you picked: divide by 4,184
  $\frac{1,053}{4,184}$ $= 0.251673 kcal$
4. Mass: 0.05 t
1. Use the gravity value you entered
  $g$ $= 8 m/s²$
2. To find the mass, divide the energy by gravity times height
  $\frac{3,750}{8 \times 9}$ $= 52.083333 kg$
3. Change the answer to t, the unit you picked: divide by 1,000
  $\frac{52.083333}{1,000}$ $= 0.052083 t$
5. Height: 567.95 cm
1. Use the gravity value you entered
  $g$ $= 14.5 m/s²$
2. To find the height, divide the energy by mass times gravity
  $\frac{7,000}{85 \times 14.5}$ $= 5.679513 m$
3. Change the answer to cm, the unit you picked: divide by 0.01
  $\frac{5.679513}{0.01}$ $= 567.951318 cm$
6. Potential energy: 9.9 kJ
1. Use the gravity value you entered
  $g$ $= 10 m/s²$
2. Multiply the mass, the pull of gravity (g) and the height. In kilograms, m/s² and meters, that gives joules
  $90 \times 10 \times 11$ $= 9,900 J$
3. Change the answer to kJ, the unit you picked: divide by 1,000
  $\frac{9,900}{1,000}$ $= 9.9 kJ$
7. Mass: 718.24 lb
1. Use the surface gravity of the Moon
  $g$ $= 1.62 m/s²$
2. To find the mass, divide the energy by gravity times height
  $\frac{4,750}{1.62 \times 9}$ $= 325.788752 kg$
3. Change the answer to lb, the unit you picked: divide by 0.45359237
  $\frac{325.788752}{0.45359237}$ $= 718.241252 lb$
8. Gravitational acceleration: 12.63 m/s²
1. To find the gravity, divide the energy by mass times height
  $\frac{5,000}{66 \times 6}$ $= 12.626263 m/s²$
9. Height: 122.67 in
1. Use the surface gravity of Earth (standard gravity)
  $g$ $= 9.80665 m/s²$
2. To find the height, divide the energy by mass times gravity
  $\frac{2,750}{90 \times 9.80665}$ $= 3.1158 m$
3. Change the answer to in, the unit you picked: divide by 0.0254
  $\frac{3.1158}{0.0254}$ $= 122.669273 in$
10. Mass: 0.13 t
1. Use the surface gravity of Mars
  $g$ $= 3.71 m/s²$
2. To find the mass, divide the energy by gravity times height
  $\frac{4,400}{3.71 \times 9}$ $= 131.775981 kg$
3. Change the answer to t, the unit you picked: divide by 1,000
  $\frac{131.775981}{1,000}$ $= 0.131776 t$