# Mechanical Energy Formula | Problems (With Solutions)

Mechanical energy (Emechanical) is the sum of kinetic energy (½ m v2) and the potential energy (m g h). Using the formula of mechanical energy: Emechanical = ½ m v2 + m g h, the value of mechanical energy of an object can be calculated.

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

## Mechanical Energy Practice Problems

Problem 1: Calculate the mechanical energy of a 20 kg stone resting on the top of a hill at a height of 50 m. (Take the value of gravitational acceleration, g = 9.81 m/s2)

Solution:

Given data:
Mechanical energy of a stone, Emechanical = ?
Mass of a stone, m = 20 kg
Velocity of a stone, v = 0 m/s (Because, a stone is at rest)
Height of a stone, h = 50 m
Gravitational acceleration, g = 9.81 m/s2

Using the formula of mechanical energy,
Emechanical = ½ m v2 + m g h
Emechanical = (0) + (20 × 9.81 × 50)
Emechanical = 20 × 9.81 × 50
Emechanical = 9,810 J

Therefore, the mechanical energy of a stone is 9,810 J.

Problem 2: A skydiver of mass 50 kg has the velocity of 20 m/s at a height of 100 m above the ground. Calculate the mechanical energy of a skydiver. (Take the value of gravitational acceleration, g = 9.81 m/s2)

Solution:

Given data:
Mass of a skydiver, m = 50 kg
Velocity of a skydiver, v = 20 m/s
Height of a skydiver, h = 100 m
Mechanical energy of a skydiver, Emechanical = ?
Gravitational acceleration, g = 9.81 m/s2

Using the formula of mechanical energy,
Emechanical = ½ m v2 + m g h
Emechanical = [(½ × 50 × 202) + (50 × 9.81 × 100)]
Emechanical = 10,000 + 49,050
Emechanical = 59,050 J

Therefore, the mechanical energy of a skydiver is 59,050 J.

Problem 3: A 10 kg ball is rolling down the hill with the velocity of 12 m/s at a height of 30 m above the ground. Calculate the mechanical energy of a ball. (Take the value of gravitational acceleration, g = 9.81 m/s2)

Solution:

Given data:
Mass of a ball, m = 10 kg
Velocity of a ball, v = 12 m/s
Height of a ball, h = 30 m
Mechanical energy of a ball, Emechanical = ?
Gravitational acceleration, g = 9.81 m/s2

Using the formula of mechanical energy,
Emechanical = ½ m v2 + m g h
Emechanical = [(½ × 10 × 122) + (10 × 9.81 × 30)]
Emechanical = 720 + 2943
Emechanical = 3,663 J

Therefore, the mechanical energy of a ball is 3,663 J.

Problem 4: A football player kicks a football to a height of 12 m above the ground. If the mass of a football is 450 gm and the velocity of a football is 8 m/s, then calculate the mechanical energy of a football. (Take the value of gravitational acceleration, g = 9.81 m/s2)

Solution:

Given data:
Height of a football, h = 12 m
Mass of a football, m = 450 gm = 0.45 kg
Velocity of a football, v = 8 m/s
Mechanical energy of a football, Emechanical = ?
Gravitational acceleration, g = 9.81 m/s2

Using the formula of mechanical energy,
Emechanical = ½ m v2 + m g h
Emechanical = [(½ × 0.45 × 82) + (0.45 × 9.81 × 12)]
Emechanical = 14.4 + 52.974
Emechanical = 67.37 J

Therefore, the mechanical energy of a football is 67.37 J.

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