**Mechanical energy** (E_{mechanical}) is the sum of **kinetic energy **(½ m v^{2}) and the **potential energy** (m g h). Using the formula of mechanical energy: **E**_{mechanical}** = ½ m v**^{2}** + 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/s^{2})

Solution:

Given data:

Mechanical energy of a stone, E_{mechanical} = ?

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/s^{2}

Using the formula of mechanical energy,

E_{mechanical} = ½ m v^{2} + m g h

E_{mechanical} = (0) + (20 × 9.81 × 50)

E_{mechanical} = 20 × 9.81 × 50

E_{mechanical} = 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/s^{2})

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, E_{mechanical} = ?

Gravitational acceleration, g = 9.81 m/s^{2}

Using the formula of mechanical energy,

E_{mechanical} = ½ m v^{2} + m g h

E_{mechanical} = [(½ × 50 × 20^{2}) + (50 × 9.81 × 100)]

E_{mechanical} = 10,000 + 49,050

E_{mechanical} = 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/s^{2})

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, E_{mechanical} = ?

Gravitational acceleration, g = 9.81 m/s^{2}

Using the formula of mechanical energy,

E_{mechanical} = ½ m v^{2} + m g h

E_{mechanical} = [(½ × 10 × 12^{2}) + (10 × 9.81 × 30)]

E_{mechanical} = 720 + 2943

E_{mechanical} = 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/s^{2})

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, E_{mechanical} = ?

Gravitational acceleration, g = 9.81 m/s^{2}

Using the formula of mechanical energy,

E_{mechanical} = ½ m v^{2} + m g h

E_{mechanical} = [(½ × 0.45 × 8^{2}) + (0.45 × 9.81 × 12)]

E_{mechanical} = 14.4 + 52.974

E_{mechanical} = 67.37 J

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

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**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
- Photon Energy Equation
- Conservation of Energy Formula

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