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The **gravitational potential energy formula**, denoted as PE_{G} = m g Δh, establishes a relationship between the gravitational potential energy (PE_{G}) of an object, its mass (m), gravitational acceleration (g), and the vertical displacement (Δh). By utilizing this formula, one can accurately calculate the magnitude of gravitational potential energy stored in an object, taking into account its mass, gravitational acceleration, and the vertical distance it has been raised.

## Practice problems

### Problem #1

Determine the gravitational potential energy of a 10 kg box that has been lifted to a height of 5 m above the ground. Use a gravitational acceleration value of g = 9.81 m/s^{2}.

**Solution**

Given data:

- Gravitational potential energy of a box, PE
_{G}= ? - Mass of a box, m = 10 kg
- Distance above the surface of ground, Δh = 5 m
- Gravitational acceleration, g = 9.81 m/s
^{2}

Applying the formula:

- PE
_{G}= m g Δh - PE
_{G}= 10 × 9.81 × 5 - PE
_{G}= 490.5 J

Therefore, the gravitational potential energy of a box is **490.5 J**.

### Problem #2

Calculate the gravitational potential energy of a trolley weighing 5 kg that has been lifted to a height of 15 m above the ground. Use a gravitational acceleration value of g = 9.81 m/s^{2}.

**Solution**

Given data:

- Gravitational potential energy of a trolley, PE
_{G}= ? - Mass of a trolley, m = 5 kg
- Distance above the surface of ground, Δh = 15 m
- Gravitational acceleration, g = 9.81 m/s
^{2}

Applying the formula:

- PE
_{G}= m g Δh - PE
_{G}= 5 × 9.81 × 15 - PE
_{G}= 735.75 J

Therefore, the gravitational potential energy of a trolley is **735.75 J**.

### Problem #3

Find the gravitational potential energy of a 24 kg wooden block that has been lifted to a height of 20 m above the floor. Use a gravitational acceleration value of g = 9.81 m/s^{2}.

**Solution**

Given data:

- Gravitational potential energy of a wooden block, PE
_{G}= ? - Mass of a wooden block, m = 24 kg
- Distance above the surface of ground, Δh = 20 m
- Gravitational acceleration, g = 9.81 m/s
^{2}

Applying the formula:

- PE
_{G}= m g Δh - PE
_{G}= 24 × 9.81 × 20 - PE
_{G}= 4708.8 J

Therefore, the gravitational potential energy of a wooden block is **4708.8 J**.

### Problem #4

Determine the gravitational potential energy of a football thrown upwards by a player to a height of 8 m above the ground. The football has a mass of 450 g. Use a gravitational acceleration value of g = 9.81 m/s^{2}.

**Solution**

Given data:

- Gravitational potential energy of a football, PE
_{G}= ? - Distance above the surface of ground, Δh = 8 m
- Mass of a football, m = 450 g = 0.45 kg
- Gravitational acceleration, g = 9.81 m/s
^{2}

Applying the formula:

- PE
_{G}= m g Δh - PE
_{G}= 0.45 × 9.81 × 8 - PE
_{G}= 35.31 J

Therefore, the gravitational potential energy of a football is **35.31 J**.

## Related

- Thermal energy equation
- Potential energy formula
**Gravitational potential energy formula**- Electric potential energy formula
- Elastic potential energy formula
- Kinetic energy formula
- Rotational kinetic energy formula
- Electrical energy equation
- Mechanical energy formula
- Photon Energy Equation
- Conservation of energy formula

## External links

- https://www.calculatorsoup.com/calculators/physics/gravitational-potential.php
- https://study.com/learn/lesson/gravitational-potential-energy-formula.html
- https://www.khanacademy.org/science/hs-physics/x215e29cb31244fa1:modeling-energy/x215e29cb31244fa1:calculating-energy/v/calculating-gravitational-potential-energy

Deep

Learnool.com was founded by Deep Rana, who is a mechanical engineer by profession and a blogger by passion. He has a good conceptual knowledge on different educational topics and he provides the same on this website. He loves to learn something new everyday and believes that the best utilization of free time is developing a new skill.