Class 9th
Work And Energy (Potential Energy )
Student Learning Objectives
Potential Energy:-
Energy of a body due to its position or configuration relative to a reference in a force field is known as potential energy.
- Explanation:
In kinetic energy we see that when work is done on the object it moves and possesses kinetic energy equal to that work done. Now if we lift the book to a certain height and place it there we have done work on it but body has not moved . i.e it has not gained Kinetic energy. Now the work done in the body is stored in the body due to its position. This work done is stored in the form of potential energy.
- Nature of Potential energy:
Potential Energy is a scaler Quantity because it doesn’t need a direction same like other energies.
Mathematical form:
We see that more work is done on the body of greater mass and when lifted to a greater height , and high value of g . So potential energy depends upon mass , gravitational acceleration and height of object. Mathematically, Potential Energy is the product of mass , gravitational acceleration and height of object.
P.E = mgh …….(i)
If we lift an object of mass 5kg to a height of 4m then P.E will be ,
P.E = 5×9.8×4
P.E = 196 J
- Mathematical Proof:
Consider an object of mass ‘m’ which is vertically lifted to a height ‘h’ through the Earth’s gravitational field.
Now the work done to lift the object to this much height ‘h’ is given by,
w = F.s
Since the force here in this case is equal to weight of object ,
F = w = mg
As displacement here is equally to height of object,
s = h
As
w = F.s
Putting value of force and displacement, work done will be equal to
w = mgh
Since this work done is stored in the body in the form of Gravitational Potential Energy.
So ,
P.E = mgh
Forms of Potential Energy:
Potential energy is stored in the body in different forms .
- Gravitational Potential Energy:
When work is done against the force of gravity, this work is stored in the body in the form of Gravitational Potential Energy. If the object is released downwards , it will move downward and gain Kinetic energy thus gravitational potential energy will do work.
- Chemical Potential Energy:
The energy stored in the body due to chemical bonds between objects is called chemical Potential Energy. e.g Energy stored in the food or energy stored in gasoline.
- Elastic Potential Energy:
When an elastic object is stretched , elastic potential energy is stored in the object. e.g When an arrow is stretched it has elastic potential energy.
- Electrical Potential Energy:
The energy stored in the battery is electrical potential energy.
SLO Question:
What will be effect on the Potential Energy of body if it’s mass is doubled?
Answer:
As we know that gravitational potential energy is given by ,
P E = mgh ……(i)
When mass of object is changed , then potential energy also changes,
When mass is doubled , so m’ = 2m Potential energy is given by ,
P.E’ = m’gh
Putting value of m’ in above equation,
P.E’ = 2mgh
P.E’ = 2 ( mgh )
P.E’ = 2 P.E
So Potential Energy will be doubled when mass of an object is doubled.
What will be effect on the Potential Energy of body if it’s mass is halved?
Answer:
As we know that gravitational potential energy is given by ,
P E = mgh ……(i)
When mass of object is changed , then potential energy also changes,
When mass is halved , so m’ = 1/2m Potential energy is given by ,
P.E’ = m’gh
Putting value of m’ in above equation,
P.E’ = 1/2 (mgh)
P.E’ = 1/2 ( mgh )
P.E’ = 1/2 P.E
So Potential Energy will be halved when mass of an object is halved.
What will be effect on the P.E of body if height is doubled?
Answer:
As we know that gravitational potential energy is given by ,
P E = mgh ……(i)
When height of object is changed , then potential energy also changes,
When height is doubled , so h’ = 2h Potential energy is given by ,
P.E’ = mgh’
Putting value of h’ in above equation,
P.E’ = mg(2h)
P.E’ = 2 ( mgh )
P.E’ = 2 P.E
So Potential Energy will be doubled when height of an object is doubled.
What will be effect on the P.E of body if height is halved?
Answer:
As we know that gravitational potential energy is given by ,
P E = mgh ……(i)
When height of object is changed , then potential energy also changes,
When height is halved , so h’ = 1/2h Potential energy is given by ,
P.E’ = mgh’
Putting value of h’ in above equation,
P.E’ = mg(1/2h)
P.E’ = 1/2 ( mgh )
P.E’ =1/2 P.E
So Potential Energy will be halved when height of an object is halved.
Example 6.1
The maximum height a human can jump is about 60cm. By how much does the gravitational potential energy increase for 72kg person in such a jump? From where he gets this potential energy?
Given Data :
mass of human=m= 72 kg
height of object= h = 60 cm = 60/100 m = 0.6 m
gravitational acceleration= g = 9.8 m/s²
Required:
Potential Energy= P.E = ?
Solution:
As we know that Gravitational Potential Energy is given by,
P.E = mgh
Putting values ,
P.E = 72× 9.8 × 0.6
P.E = 423.6 J
Thus potential energy in this case will be 423.6 J .
This Gravitational Potential Energy comes from elastic potential energy of tensed muscles of Human.
Assignment 6.1
An object of mass 10kg is lifted to a vertical height of 5 m at a constant speed . What is the gravitational potential energy gained by object?
Given Data :
Mass of object= m = 10kg
Height of object= h = 5m
Gravitational acceleration= g = 9.8m/s²
Required:
Potential Energy= P.E = ?
Solution:
As we know that gravitational potential energy is given by,
P.E = mgh
P.E = 10kg × 9.8m/s² × 5 m
P.E = 490 J
The potential e energy in this case will be 490 J.
