Mechanical Energy Formula

Mechanical Energy – 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.

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.

Check: Types of energy – Definition, Types, Examples, & Facts

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)mv²
• Potential Energy (P.E.) = m × g × h

∴ Mechanical Energy (M.E.) = ((1/2)mv²) + (m × g × h)

Where,

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

Running or Walking: When you run or walk, your body converts chemical energy from food into mechanical energy, propelling you forward.

Swinging Pendulum: A swinging pendulum exhibits mechanical energy as it oscillates back and forth between potential energy at the highest point of its swing and kinetic energy at the lowest point.

Moving Vehicles: Cars, trains, bicycles, and other vehicles convert fuel or human energy into mechanical energy to move from one place to another.

Stretching a Spring: When you stretch a spring, you are applying a force to displace it, storing potential mechanical energy within the spring.

Rotating Blades: Wind turbines and propellers on airplanes convert wind or engine power into mechanical energy to generate electricity or propel the aircraft forward.

Mechanical energy can be either potential or kinetic. Potential energy relates to an object’s position or condition, while kinetic energy is linked to its movement. Think of a raised weight (potential energy) versus a moving ball (kinetic energy).

• Converting mechanical energy to electrical energy involves transforming the physical motion or potential energy of mechanical systems into electrical power.
• This process is utilized in various technologies such as generators, where mechanical forces, such as wind or water currents, rotate turbines.
• Turbines convert mechanical energy into electrical energy through electromagnetic induction.
• Piezoelectric materials can also convert mechanical stress or vibration directly into electrical energy.
• Applications of this conversion include sensors, energy harvesting devices, and wearable technology.

Related Article

• How to calculate the Mechanical Energy?
• Energy Conversion
• Energy
• Kinetic Energy
• Law of Conservation of Energy
• Uses of Electricity in Daily Life

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)mv²) + (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)mv²) + (m × g × h)

∴ M.E. = ((1/2) × 21 × 10²)) + 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)mv²) + (m × g × h)

∴ M.E. = ((1/2) × 7 × 18²)) + 0

∴ M.E. = 1134 J

Mechanical energy is a fundamental concept in physics that encompasses both potential and kinetic forms. Whether it’s the stored energy of an object’s position or the energy of its movement, mechanical energy plays a crucial role in various natural phenomena and human-made technologies. Understanding how mechanical energy works allows us to harness it for practical applications, from generating electricity to powering everyday devices. This energy conversion process continues to drive innovation and shape our modern world.

What is mechanical energy?

Mechanical energy is the energy possessed by an object due to its motion (kinetic energy) or position (potential energy) or the combination of both.

How is mechanical energy calculated?

The total mechanical energy of an object is the sum of its kinetic energy (0.5 * mass * velocity^2) and its potential energy (mass * gravity * height), if applicable.

What are the types of mechanical energy?

There are two main types of mechanical energy: kinetic energy, which is associated with the motion of an object, and potential energy, which is associated with an object’s position or state.

What are some examples of mechanical energy?

Examples of mechanical energy include a swinging pendulum, a moving car, a stretched spring, a rolling ball, and many others where motion or position is involved.

How does mechanical energy relate to work?

Work is done on an object when a force causes it to move through a distance. Mechanical energy is related to work in that work can transfer energy to or from an object, changing its mechanical energy.

Can mechanical energy be converted into other forms of energy?

Yes, mechanical energy can be converted into other forms of energy, such as electrical energy in a generator, thermal energy through friction, or sound energy when an object vibrates.

Is mechanical energy conserved?

According to the principle of conservation of mechanical energy, in the absence of non-conservative forces like friction or air resistance, the total mechanical energy of a system remains constant.

How is mechanical energy used in everyday life?

Mechanical energy is used in countless ways in everyday life, from transportation (cars, bicycles) to household appliances (blenders, elevators) to sports (running, jumping).

What are some real-world applications of mechanical energy?

Real-world applications of mechanical energy include renewable energy sources like wind turbines and hydroelectric dams, as well as machinery and equipment used in manufacturing and construction.

How can mechanical energy be optimized or harnessed more efficiently?

Mechanical energy can be optimized by reducing friction and other sources of energy loss, improving the design and efficiency of machines, and utilizing advanced materials and technologies.