Introduction
Mechanical energy refers to the total of kinetic energy and potential energy possessed by an object that is used to do a particular work. In other words, it describes the energy of an object because of its motion or position, or both.
If K E and P E refers to the kinetic and potential energies of a body, its mechanical energy is given by,
M.E = K.E + P.E
For an object thrown upwards, its total mechanical energy is given by:
E = ½ mv2 + mgh
Where,m is the mass of an object, v , the velocity of that object, g, the acceleration due to gravity and h tells at what height the object is from the ground.
Example: The kinetic energy of a body flying at a certain height from the ground is 4500 J and its potential energy is 8000 J. Find the total mechanical energy associated with it.
Solution:
KE = 4500 J, PE = 8000 J, ME=?
ME = KE + PE = 4500 + 8000 = 12500 J
Example: An object of mass 2 kg has been projected vertically upwards with a kinetic energy of 100 J. Find the maximum height it can reach (take g = 10 m/s2 and PE of the object at the point of projection is zero).
Solution: In motion under gravity, total mechanical energy is conserved.
Total Mechanical energy at the point of projection = total mechanical energy at the maximum height.
At the point of projection: KE1 = 100 J, PE1 = 0
At the maximum height: KE2 = 0, PE2 = mgh
Now, KE1 + PE1 = KE2 + PE2
Therefore, 100 + 0 = 0 + mgh
⇒h=100mg=1002×10=5m
The object will reach upto a maximum height of 5 m.
Question: A ball thrown up with certain kinetic energy can reach a maximum height of 8 m. An identical ball thrown up with four times kinetic energy can reach a maximum height of:
Options:
(a) 8 m
(b) 32 m
(c) 64 m
(d) 128 m
Answer: (d)
Kinetic Energy and Potential Energy
The energy that a body possesses when it is in motion is defined as kinetic energy, Irrespective of the direction of the motion (horizontal or vertical).
The types of kinetic energy can be classified into vibrational kinetic energy, rotational kinetic energy, and translational kinetic energy based on its movement.
e.g: Any object falling from a height.
Potential Energy
The stored energy that the body has when it is not in motion is defined as potential energy.
The types of potential energy can be classified into gravitational potential energy and elastic potential energy.
e.g: A ball resting in its position.
The four kinds of kinetic energy include:
Electrical Energy: The energy produced by electricity is known as electrical energy.
Radiant Energy: The energy produced by the light waves is called radiant energy.
Sound Energy: The energy produced by the sound waves is known as sound energy.
Thermal Energy: The energy produced by the heat is called thermal energy.
Conversion of Energy
The energy can never be created or destroyed, rather converted and transferred.
Any kind of energy that is transferred if it causes an object or thing to move is an example of the conversion of energy.
Below are some of the examples of how various kinds of energy are converted into mechanical energy:
The gasoline in cars and engines converts chemical energy into mechanical energy.
The steam in the train converts the thermal energy into mechanical energy.
In the eardrum, any music that can be heard is converted from sound energy to mechanical energy.
The human body converts chemical energy to mechanical energy from nutrients into movement.
When plugged in, the power drill converts the electrical energy into mechanical energy.
On the other hand, mechanical energy can also be converted into various other kinds of energy.
Below are some examples of how mechanical energy is converted into various kinds of energy.
The windmills convert the mechanical energy into electrical energy for electricity.
Hitting the drums converts the mechanical energy into sound energy.
Rubbing the hands together converts mechanical energy into thermal energy.
Turning a switch on converts the mechanical energy into electrical energy and later on to radiant energy.
The human body digesting food converts mechanical energy into chemical energy.
Mechanical Energy and its Origin
Mechanical energy is found everywhere in the world and around us. Any object or a thing that moves or doesn't move consists of some of the other forms of mechanical energy in it. The mechanical energy comes from the position as well as the speed of the moving object. The two energies, that is, kinetic and potential energies are still there and are combined.
For example, the car moving at the speed of 40km/h still has some potential energy left that needs to be released on the gas pedal.
Fact: Imagine the amount of mechanical energy the mountains store in them, The landslides are examples of how much energy they can release.
The Law of Conservation of Mechanical Energy
According to the law of conservation of mechanical energy, in a given closed system, the amount of mechanical energy remains the same. There is no change in the total energy, and it can only convert from potential energy to kinetic energy and vice versa. The outside external forces cannot dissipate the mechanical energy. The total amount of mechanical energy can neither be destroyed nor created.
FAQs on Mechanical Energy Formula
1. Distinguish between kinetic energy and potential energy?
In kinetic energy, the force is applied. Whereas, in potential energy, the force is stored. Hence, this is the major difference between both energies. The potential energy of the thing is equal to the amount of work that has to be done. A man jumping down with a parachute from the plane has maximum potential energy and as soon as he/she jumps, that energy is converted into kinetic energy. In the scenario, the kinetic energy increases as the parachute comes down, while the potential energy decreases. Supposing the parachute doesn't open, then the kinetic energy is at its maximum and the potential energy is nearly zero. To avoid this, the opening of the parachute is crucial as it prevents any injuries from occurring. To learn more in detail, visit Vedantu.
