Dear students in 9th and 10th standard we have learnt about the energy, the forms of energy and law of conservation of energy. We categorised the mechanical energy in to following forms:
1.) Kinetic energy,
Kinetic energy is the energy that possesses by the body due to its motion. If body of mass ‘m’ moves with the velocity of ‘v’ then kinetic energy of body is given as,
- Kinetic energy = 1/2 mv2
2.) Potential energy.
Potential energy is the energy that body possesses due to its shape/size/mass etc.
Let’s learn the concept of potential energy in detail….!
Consider object of mass ‘m’ is placed on the table at height ‘h’ above the earth’s surface. The object is in influence of gravitational force exerted by the earth. The magnitude of gravitational force is acting in opposite to the position of object.
IF ‘F’ be the gravitational force acting on the object, then the amount of work done by object to stay against the impact of gravitational influence is given as,
W(h) = -Gravitational force × height of object
W(h) = – weight of object × height of object
W(h) = -mg × h
W(h) = -mgh
Negative sign indicates that the work is done against the gravitational force.
From above equation we can conclude that,
i.e. gravitational force is negative rate of work done with respect to height.
When object falls under influence of gravity, initial velocity of object is zero, and the acceleration is due to gravity i.e. ‘g’, then according to 3rd equation of motion we have,
Using third equation of motion we can write
∴v2 = u2 + 2 as
∴v2 = 0 + 2 gh
∴v2 = 2 gh ……………….(2)
The change in kinetic energy of the body is then given as,
Kinetic energy = 1/2 mv2
Kinetic energy = 1/2 m 2 gh
Kinetic energy = mgh
We know that according to the work energy theorem, change in kinetic energy is equal to work done by the force. Hence the work done here can be given as,
Work done, W = mgh
This work is stored in the object in the form of energy here known as potential energy.
∴ Potential energy = mgh
F = – V(h)/h
Or
F = -dV/dh
F .dh = -dV
Total work done then given as,
SI unit of potential energy is joule (J)
Dimensions are [M1L2T-2]
Examples of potential energy:
- The energy in stretched string of bow has potential energy, so that the arrow can get sufficient kinetic energy.
- Potential energy is stored in the springs of suspension of vehicles which absorbs the jerk that acts on the vehicle when falls in wholes on road.
- Water in the dam has potential energy stored in it, which then converted as kinetic energy to rotate the turbines.