# Mechanical Energy Formula

When a force operates on an object to displace it, it is said that work is performed. Work entails the use of a force to shift an object. The object will gather energy after the job is completed on it. Mechanical energy is the amount of energy acquired by a working object. The mechanical energy formula and examples will be discussed in this article, as well as the concept and components of mechanical energy.

### Mechanical Energy

The sum of kinetic and potential energy in an object is referred to as Mechanical energy. It builds up as a result of doing a specific task. To put it another way, we can characterize an object’s energy based on its velocity or position, or both.

Because of its location, we know that the object possesses potential energy. Because some labor will be required to set an object at a specific height. In addition, an object has kinetic energy because of the work it does in order to move. When an object moves, its potential energy is assumed to be zero. Its kinetic energy, on the other hand, will be 0 while it is at rest.

### Formula of Mechanical Energy

The formula of Mechanical Energy is as follows,

Mechanical Energy (M.E.) = Kinetic Energy (K.E.) + Potential Energy (P.E.)Where,

- Kinetic Energy (K.E.) = (1/2)mv
^{2}- Potential Energy (P.E.) = m × g × h

∴ Mechanical Energy (M.E.) = ((1/2)mv^{2}) + (m × g × h)Where,

- m = mass of object,
- v = velocity of object,
- g = acceleration due to gravity,
- h = height of object from ground.

### Sample Questions

**Question 1: Define Mechanical energy.**

**Answer**:

The sum of kinetic and potential energy in an object is referred to as mechanical energy. Kinetic energy of an object is related to its motion and potential energy is related to its position. If there is not motion in the object, the total mechanical energy will only be the potential energy present in it, similarly, if the object’s position is not changed, neither the object’s orientation, then the object has no potential energy.

**Question 2: A body flying at a specific altitude from the ground has 500 J of kinetic energy and 738 J of potential energy. Calculate the total mechanical energy that is involved.**

**Solution:**

Given: K.E. = 500 J, P.E. = 738 J

Since,

Mechanical Energy (M.E.) = Kinetic Energy (K.E.) + Potential Energy (P.E.)

∴ M.E. = 500 + 738

∴

M.E. = 1238 J

**Question 3: A person sits on a building with a height of 23 m and a mass of 150 kg. Determine how much mechanical energy there is.**

**Solution:**

Given: h = 23 m, m = 150 kg, K.E. = 0 (Person in static position)

Since,

Mechanical Energy (M.E.) = ((1/2)mv

^{2}) + (m × g × h)∴ M.E = 0 + 150 × 9.81 × 23

∴ M.E. = 150 × 9.81 × 23

∴

M.E. = 33810 J

**Question 4: Calculate the mechanical energy of a 21 kg item that is traveling at a 10 ms ^{-1} speed.**

**Solution:**

Given: m = 21 kg, v = 10 ms

^{-1}, P.E = 0 (Object is moving)Since,

Mechanical Energy (M.E.) = ((1/2)mv

^{2}) + (m × g × h)∴ M.E. = ((1/2) × 21 × 10

^{2})) + 0∴

M.E. = 1050 J

**Question 5: If the kinetic energy of an object is 230 J and the potential energy of an object is 300 J then find the Mechanical energy.**

**Solution:**

Given: K.E. = 230 J, P.E. = 300 J

Since,

Mechanical Energy (M.E.) = Kinetic Energy (K.E.) + Potential Energy (P.E.)

∴ M.E. = 230 + 300

∴

M.E. = 530 J

**Question 6: Calculate the mechanical energy when the car traveled at a speed of 18 m/s and its mass is 7 kg.**

**Solution:**

Given: m = 7 kg, v = 18 ms

^{-1}, P.E = 0 (car is moving)Since,

Mechanical Energy (M.E.) = ((1/2)mv

^{2}) + (m × g × h)∴ M.E. = ((1/2) × 7 × 18

^{2})) + 0∴

M.E. = 1134 J