How to calculate the Mechanical Energy?

The mechanical energy is calculated by adding both kinetic energy and potential energy. The formula for calculating mechanical energy is M.E. = K.E. + P.E., where M.E. is mechanical energy, K.E. is kinetic energy and P.E. is potential energy.

Mechanical Energy

Mechanical energy refers to the total energy possessed by an object or system due to its motion and/or position. It is the sum of the kinetic energy, which is associated with the object’s motion, and the potential energy, which is associated with its position relative to a force field, such as gravity.

The total mechanical energy E (total) of a system is the sum of its kinetic energy and potential energy:

E(total) = KE + PE

If there are no non-conservative forces (like friction or air resistance) acting on the system, the total mechanical energy remains constant (conservation of mechanical energy).

Types of Mechanical Energy

There are two types of mechanical energy.

• Potential Energy
• Kinetic Energy

Potential Energy

Potential energy is defined as the energy stored in a body due to its physical properties like the mass of the object or the position of the object. It is the force that a body could potentially develop when it is put into motion.

P.E. = m × g × h

Where, 

• PE is the potential energy,
• m is the mass of the object (kg or g),
• g is the gravity (9.8 m/sec²) and 
• h is the height of the object (cm or m).

The SI Unit of P.E is Joules or J.

Kinetic Energy

Kinetic energy is defined as the energy of motion or movement of an object, rather than in its position. The faster the motion of an object, the higher will be the kinetic energy.

K = 1/2 m×v²

where, 

K is the Kinetic energy,

m is the mass of the object (kg or g), and

v is the velocity of the object (m/sec).

The SI Unit of K.E. is Joules or J.

Mechanical Energy Formula

The mechanical energy (M.E.) is calculated as:

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

OR

M.E. = K.E. + P.E. 

OR

M.E. = 1/2 mv² + (m . g . h)

Where

• m is the mass of an object,
• v is the velocity of that object,
• g is the acceleration due to gravity
• h is the height of an object.
• The SI Unit of M
• E is Joules or J

How to Calculate Mechanical Energy?

Mechanical energy is the sum of kinetic energy and potential energy in a system. Thus, it can be calculated by adding kinetic and potential energy for any system. If K.E. is kinetic energy of system and P.E. is potential energy of system, then mechanical energy of system is K.E. + P.E.

to calculate the mechanical energy of a system, you need to determine the kinetic and potential energy components based on the motion and configuration of the objects involved. Then, sum these energies to obtain the total mechanical energy.

Sample Questions

Question 1: A man is sitting on a building of 30 m in height and his mass is 60 kg. Calculate the mechanical energy?

Answer: 

Given that, 

Mass of the man = 60 kg

Height of the building = 30m

The man is not moving, he is rest position, therefore, K. E = 0

The formula of mechanical energy 

M.E = K. E + P.E

Since K.E is 0, the equation becomes,

M.E =  P.E

⇒ M.E = m . g . h

⇒ M.E = 60Kg × 9.8m/s² × 30m

⇒ M.E = 17658 J

Question 2: If the potential energy of an object is 600 J and its mechanical energy is 1500 J, calculate its kinetic energy?

Answer: 

Given that,

P.E = 600J

M.E = 1500J

M.E = P.E + K.E

⇒ K.E = M.E – P.E

⇒ K.E = 1500 J – 600 J

⇒ K.E = 900 J

Therefore kinetic energy of the object is 900 J.

Question 3: A car is traveling at a speed of 12m/s and its mass is 20 kg. Calculate the mechanical energy?

Answer: 

Given that,

Mass of the car, m= 20 kg

velocity of the car, v = 12m/s

The car is moving, so the P.E. = 0

M.E = P.E + K.E

⇒ M.E = 0 + ½mv²

⇒ M.E= ½ × 20 × 12 × 12

⇒ M.E= 1440 J

Question 4: An object of mass 400 g is at a height 10 m above the ground. Calculate its potential energy at this height. If the object is fallen, what will be its kinetic energy halfway down? Take g=10 ms².

Answer: 

Given that,

Mass of the object (m)= 400g = 400/1000 = 0.4 kg

Height of the object (h )= 10m

Acceleration due to gravity is g=10ms²

The potential energy of the object at the height (h=10m) is

P.E = mgh = 0.4 × 10 × 10 = 40J

Now, halfway down, the kinetic energy of the body can be calculated using the law of conservation of mechanical energy. At this position, the kinetic energy gained will be equal to the potential energy lost which will be half of 40J.

Thus, the kinetic energy of the object will be K.E = P.E/2 = 40/2 = 20J. 

Therefore the potential energy = 40J and its kinetic energy halfway down = 20 J.

Question 5: A body with a mass of 15 kg is projected vertically upwards with a speed of 4 m/s. What will be its kinetic energy?

Answer:

Given :

Mass(m) = 15 kg

Velocity (v) = 4 m/s

Kinetic energy of the body while throwing is K.E = ½mv² 

K.E  = ½ ×15×(4)² 

⇒ K.E  = ½ ×15×16 

⇒ K.E  =  120 J

Therefore, kinetic energy of the body K E = 120 J.

FAQs

What is mechanical energy?

Mechanical energy is the energy associated with the motion and position of objects. It includes both kinetic energy, related to motion, and potential energy, related to position or configuration.

How is mechanical energy calculated?

Mechanical energy is calculated by taking sum of potential energy and kinetic energy

What is potential energy, and give an example?

Potential energy is the energy stored in an object due to its position or configuration within a gravitational or elastic field. An example is gravitational potential energy, which is the energy stored in an object due to its height above the ground.

How is gravitational potential energy calculated?

Gravitational potential energy is calculated using the formula: PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height of the object above a reference point.