WORKSHEET: KINETIC AND POTENTIAL ENERGY PROBLEMS Worksheet - Free Printable
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Step-by-step solution for: WORKSHEET: KINETIC AND POTENTIAL ENERGY PROBLEMS Worksheet
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Show Answer Key & Explanations
Step-by-step solution for: WORKSHEET: KINETIC AND POTENTIAL ENERGY PROBLEMS Worksheet
Let’s go step by step to solve each problem on the worksheet. We’ll start with potential energy (questions 1–10), then kinetic energy (questions 11–16).
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Potential Energy Basics:
Potential energy (PE) is stored energy due to position — usually height in gravity problems.
Formula:
PE = m × g × h
Where:
- m = mass (in kg)
- g = gravitational pull (on Earth, about 9.8 m/s²)
- h = height (in meters)
- PE is measured in Joules (J)
Units:
- Mass → kilograms (kg)
- Gravity → meters per second squared (m/s²)
- Height → meters (m)
- Energy → Joules (J)
---
Now let’s answer each question:
---
1. Stored energy or energy due to position is known as _potential_ energy.
✔ Simple definition.
---
2. The formula for calculating potential energy is _PE = mgh_.
✔ Standard formula.
---
3. The three factors that determine the amount of potential energy in an object are _mass_, _gravitational pull_, and _height_.
✔ From the formula: m, g, h.
---
4. Potential energy is measured in units of _Joules (J)_.
✔ SI unit for energy.
---
5. Mass must be measured in units of _kilograms (kg)_.
✔ Required for the formula to work with Joules.
---
6. Gravitational pull must be measured in units of _meters per second squared (m/s²)_.
✔ That’s acceleration due to gravity.
---
7. Height must be measured in units of _meters (m)_.
✔ Consistent with metric system used in physics.
---
8. Calculate the potential energy of a rock with a mass of 55 kg while sitting on a cliff that is 27 m high.
Use: PE = m × g × h
Assume g = 9.8 m/s² (standard on Earth)
PE = 55 kg × 9.8 m/s² × 27 m
First, 55 × 9.8 = 539
Then, 539 × 27:
Break it down:
539 × 20 = 10,780
539 × 7 = 3,773
Total = 10,780 + 3,773 = 14,553 J
✔ So, PE = 14,553 Joules
*(Note: Sometimes teachers use g = 10 for simplicity — if so, 55×10×27=14,850 J. But since not specified, we use 9.8.)*
---
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?
We know:
PE = mgh → rearrange to solve for h:
h = PE / (m × g)
Plug in:
h = 196 J / (5 kg × 9.8 m/s²)
= 196 / 49
= 4 meters
✔ So, the book is 4 meters above the floor.
---
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.
Again, PE = mgh → solve for m:
m = PE / (g × h)
m = 362,600 / (9.8 × 20)
First, 9.8 × 20 = 196
Then, 362,600 ÷ 196
Let’s divide:
196 × 1850 = ?
Well, 196 × 1000 = 196,000
196 × 800 = 156,800 → total 196,000 + 156,800 = 352,800
Subtract from 362,600: 362,600 - 352,800 = 9,800
196 × 50 = 9,800 → perfect!
So, 1000 + 800 + 50 = 1850 kg
✔ Mass = 1850 kg
---
Kinetic Energy Basics:
Kinetic energy (KE) is energy of motion.
Formula:
KE = ½ × m × v²
Where:
- m = mass (kg)
- v = velocity (m/s)
- KE is in Joules (J)
Units same as before: mass in kg, velocity in m/s, energy in J.
---
11. Energy of motion is known as _kinetic_ energy.
✔ Definition.
---
12. The formula for calculating kinetic energy is _KE = ½mv²_.
✔ Standard formula.
---
13. The two factors that determine the amount of kinetic energy in an object are _mass_ and _velocity_.
✔ From the formula.
---
14. Kinetic energy is measured in units of _Joules (J)_.
✔ Same as potential energy.
---
15. Mass must be measured in units of _kilograms (kg)_.
✔ Required for consistency.
---
16. Velocity must be measured in units of _meters per second (m/s)_.
✔ Because KE uses v², and we want Joules as output.
---
Final Answer:
1. potential
2. PE = mgh
3. mass, gravitational pull, height
4. Joules (J)
5. kilograms (kg)
6. meters per second squared (m/s²)
7. meters (m)
8. 14,553 J
9. 4 meters
10. 1850 kg
11. kinetic
12. KE = ½mv²
13. mass, velocity
14. Joules (J)
15. kilograms (kg)
16. meters per second (m/s)
---
Potential Energy Basics:
Potential energy (PE) is stored energy due to position — usually height in gravity problems.
Formula:
PE = m × g × h
Where:
- m = mass (in kg)
- g = gravitational pull (on Earth, about 9.8 m/s²)
- h = height (in meters)
- PE is measured in Joules (J)
Units:
- Mass → kilograms (kg)
- Gravity → meters per second squared (m/s²)
- Height → meters (m)
- Energy → Joules (J)
---
Now let’s answer each question:
---
1. Stored energy or energy due to position is known as _potential_ energy.
✔ Simple definition.
---
2. The formula for calculating potential energy is _PE = mgh_.
✔ Standard formula.
---
3. The three factors that determine the amount of potential energy in an object are _mass_, _gravitational pull_, and _height_.
✔ From the formula: m, g, h.
---
4. Potential energy is measured in units of _Joules (J)_.
✔ SI unit for energy.
---
5. Mass must be measured in units of _kilograms (kg)_.
✔ Required for the formula to work with Joules.
---
6. Gravitational pull must be measured in units of _meters per second squared (m/s²)_.
✔ That’s acceleration due to gravity.
---
7. Height must be measured in units of _meters (m)_.
✔ Consistent with metric system used in physics.
---
8. Calculate the potential energy of a rock with a mass of 55 kg while sitting on a cliff that is 27 m high.
Use: PE = m × g × h
Assume g = 9.8 m/s² (standard on Earth)
PE = 55 kg × 9.8 m/s² × 27 m
First, 55 × 9.8 = 539
Then, 539 × 27:
Break it down:
539 × 20 = 10,780
539 × 7 = 3,773
Total = 10,780 + 3,773 = 14,553 J
✔ So, PE = 14,553 Joules
*(Note: Sometimes teachers use g = 10 for simplicity — if so, 55×10×27=14,850 J. But since not specified, we use 9.8.)*
---
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?
We know:
PE = mgh → rearrange to solve for h:
h = PE / (m × g)
Plug in:
h = 196 J / (5 kg × 9.8 m/s²)
= 196 / 49
= 4 meters
✔ So, the book is 4 meters above the floor.
---
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.
Again, PE = mgh → solve for m:
m = PE / (g × h)
m = 362,600 / (9.8 × 20)
First, 9.8 × 20 = 196
Then, 362,600 ÷ 196
Let’s divide:
196 × 1850 = ?
Well, 196 × 1000 = 196,000
196 × 800 = 156,800 → total 196,000 + 156,800 = 352,800
Subtract from 362,600: 362,600 - 352,800 = 9,800
196 × 50 = 9,800 → perfect!
So, 1000 + 800 + 50 = 1850 kg
✔ Mass = 1850 kg
---
Kinetic Energy Basics:
Kinetic energy (KE) is energy of motion.
Formula:
KE = ½ × m × v²
Where:
- m = mass (kg)
- v = velocity (m/s)
- KE is in Joules (J)
Units same as before: mass in kg, velocity in m/s, energy in J.
---
11. Energy of motion is known as _kinetic_ energy.
✔ Definition.
---
12. The formula for calculating kinetic energy is _KE = ½mv²_.
✔ Standard formula.
---
13. The two factors that determine the amount of kinetic energy in an object are _mass_ and _velocity_.
✔ From the formula.
---
14. Kinetic energy is measured in units of _Joules (J)_.
✔ Same as potential energy.
---
15. Mass must be measured in units of _kilograms (kg)_.
✔ Required for consistency.
---
16. Velocity must be measured in units of _meters per second (m/s)_.
✔ Because KE uses v², and we want Joules as output.
---
Final Answer:
1. potential
2. PE = mgh
3. mass, gravitational pull, height
4. Joules (J)
5. kilograms (kg)
6. meters per second squared (m/s²)
7. meters (m)
8. 14,553 J
9. 4 meters
10. 1850 kg
11. kinetic
12. KE = ½mv²
13. mass, velocity
14. Joules (J)
15. kilograms (kg)
16. meters per second (m/s)
Parent Tip: Review the logic above to help your child master the concept of kinetic and potential energy worksheet answers key.
