Gravitational Potential Energy Formula | Problems

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Gravitational Potential Energy Formula

Gravitational potential energy or gravitational energy (PEG) is the product of mass (m), gravitational acceleration (g) and the distance (Δh). Using the formula of gravitational potential energy: PEG = m g Δh, the value of gravitational potential energy of an object can be calculated.

Let’s solve some problems based on this formula, so you’ll get a clear idea.

Gravitational Potential Energy Practice Problems

Problem 1: Calculate the gravitational potential energy of a 10 kg box which is lifted to a height of 5 m above the ground. (Take the value of gravitational acceleration, g = 9.81 m/s2)

Solution:

Given data:
Gravitational potential energy of a box, PEG = ?
Mass of a box, m = 10 kg
Distance above the surface of ground, Δh = 5 m
Gravitational acceleration, g = 9.81 m/s2

Using the formula of gravitational potential energy,
PEG = m g Δh
PEG = 10 × 9.81 × 5
PEG = 490.5 J

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

Problem 2: A 5 kg trolley is lifted to a height of 15 m above the ground. Calculate the gravitational potential energy of a trolley. (Take the value of gravitational acceleration, g = 9.81 m/s2)

Solution:

Given data:
Mass of a trolley, m = 5 kg
Distance above the surface of ground, Δh = 15 m
Gravitational potential energy of a trolley, PEG = ?
Gravitational acceleration, g = 9.81 m/s2

Using the formula of gravitational potential energy,
PEG = m g Δh
PEG = 5 × 9.81 × 15
PEG = 735.75 J

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

Problem 3: What is the gravitational potential energy of a 24 kg wooden block which is lifted to a height of 20 m above the floor. (Take the value of gravitational acceleration, g = 9.81 m/s2)

Solution:

Given data:
Gravitational potential energy of a wooden block, PEG = ?
Mass of a wooden block, m = 24 kg
Distance above the surface of ground, Δh = 20 m
Gravitational acceleration, g = 9.81 m/s2

Using the formula of gravitational potential energy,
PEG = m g Δh
PEG = 24 × 9.81 × 20
PEG = 4708.8 J

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

Problem 4: A player throws a football in the upward direction to the height of 8 m above the ground. Calculate the gravitational potential energy of a football, if the mass of a football is 450 gm. (Take the value of gravitational acceleration, g = 9.81 m/s2)

Solution:

Given data:
Distance above the surface of ground, Δh = 8 m
Gravitational potential energy of a football, PEG = ?
Mass of a football, m = 450 gm = 0.45 kg
Gravitational acceleration, g = 9.81 m/s2

Using the formula of gravitational potential energy,
PEG = m g Δh
PEG = 0.45 × 9.81 × 8
PEG = 35.31 J

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

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