STUDY MATERIAL work and energy.pdf for 9

## Unveiling the Mysteries of Work and Energy: A Guide for Class 9 Science

Welcome to the fascinating world of Work and Energy! This chapter in your Class 9 Science curriculum unlocks the secrets behind seemingly everyday actions like lifting a box, pushing a swing, or even a car speeding down the road. This guide delves into the concepts of work and energy, equipping you with the knowledge to understand these fundamental forces that govern our physical world.

**Part 1: The Essence of Work**

* **Chapter 1: Understanding Work - Not Just Effort!**
* This chapter clarifies the scientific definition of work. You'll learn that work isn't simply exerting effort; it's about transferring energy from a force to an object, causing it to displace (move) in the direction of the applied force.
* We'll explore scenarios where work is done and differentiate it from situations where it isn't, like pushing against a wall or lifting an object without causing displacement.

* **Chapter 2: The Formula for Work - It's All About the Journey!**
* This chapter introduces the formula for calculating work: Work = Force x Displacement. We'll unpack this formula, understanding how the magnitude of the force applied and the distance the object moves in the direction of the force determine the amount of work done.
* You'll practice applying the formula to various scenarios, like lifting a bag of books or pushing a cart across the floor.

* **Chapter 3: Units of Work - Speaking the Language of Physics!**
* This chapter delves into the units used to measure work. We'll learn that the SI unit of work is the Joule (J), named after the scientist James Prescott Joule.
* You'll explore the relationship between Joules and other units of force (Newton) and distance (meter) and practice converting between these units.

**Part 2: Unveiling the Powerhouse - Energy!**

* **Chapter 4: The Power Within - What is Energy?**
* This chapter introduces the concept of energy, the ability to do work. We'll explore the different forms energy can take, like kinetic energy (energy of motion), potential energy (stored energy due to position or configuration), chemical energy (stored in the bonds of molecules), and many more.
* You'll understand how energy can transform from one form to another, like the chemical energy in food being converted to kinetic energy when we run.

* **Chapter 5: Kinetic Energy - The Energy of Action!**
* This chapter focuses on kinetic energy, the energy possessed by an object due to its motion. We'll delve into the formula for kinetic energy: Kinetic Energy = 1/2 * mass * velocity^2.
* You'll learn how the mass and velocity of an object influence its kinetic energy.
* Through examples and activities, you'll explore how kinetic energy increases with mass and the square of velocity (meaning, doubling the speed quadruples the kinetic energy!).

* **Chapter 6: Potential Energy - Ready, Set, Go!**

1. WORK AND ENERGY 1


Work
The physical meaning of the term ‘work’ is different from it means in the daily
life. e.g., a student learning his lesson, a person standing with a load kept on his head
and even a teacher teaching in a class, all are not doing any work.
Scientific Conception of Work
* In physics, “work is said to be done when the force applied on the body displaces
its position in the direction of the applied force”.
So, it is clear that for work to be done, the following two conditions need to
satisfied:
1. A force should act on the body.
2. The body must be displaced from it positions.
*If any of the above conditions is not satisfied, Then work is not considered done.
*Following are some of the examples from our daily life, where work is said to be
done.
1. When the bullock pulls a cart, the cart moves. The force is applied by the
bullock and the cart gets displaced. So, the work is done by the bullock on the cart.
2. A spring is stretched by hanging a weight to it. When the force is applied by
the hanging weight, the spring gets stretched. So the work is done by the hanging
weight on the spring.
3. When a gas is heated, the piston of the gas container lifts upward and the work
is done by the molecules of the gas on the piston.
Work Done By a constant Force
If a constant force F is applied to a body with the result that the body is displaced
through a distance s in the direction of the force, then the work done W by the force
F acting on the body is defined as the product o the force and the displacement of
the body from its initial position. Hence,
Work one = Force × Displacement in the direction of force
Or W = F × s


SI Unit of Work-
Work is a scalar quantity, i.e., it has only magnitude but no direction. The SI unit
of work is newton-metre (N-m) or Joule (J).

2. WORK AND ENERGY 2

W = F × s
If F = 1 newton and s = 1 metre, then
W = 1 N × 1m
= 1 N-m
or W = 1 J
*Thus, 1 joule is the amount of work done on an object when a force of 1N
displaces the objects through 1 m along the line of action of the force.
Nature of Work Done
Work done by the force when the direction of force subtends an angle 0 with the
direction of displacement on the direction of displacement.
1. Positive Work Done: If the force applied to a body and the displacement of
that body are in the same direction, then work done by the force is called
positive work done,
e.g., a boy pulls an object towards himself.



2. Zero Work Done:
 If the force applied to a body and the displacement of that body are
perpendicular to each other, then work done by the force is called a zero work
done.
 For example, when a person holding a suitcase on his head moves on the
horizontal road, then work done is zero.
 This is because the force applied by the person to hold the suitcase on his
head is perpendicular to the horizontal distance travelled by the person.

3. Negative Work Done:
 If the force applied to a body and the displacement of the body is in
opposite direction to that of the force applied, then the work done is
called a negative work done i.e., work is done against the force,
 e.g., when a body of mass m is raised vertically upwards from a point A to
B through a height h, then the work done by the force of gravity is called a
negative work done.
W= - (Fx s)


W = + F × s

3. WORK AND ENERGY 3



ENERGY
Energy of a body is defined as the capacity or the ability of the body to do a work.

 For doing a work, energy is always consumed. When a body is capable of
doing more work, it is said to possess more energy and vice-versa.
 The body doing the work loses energy while that on which the work is done
gains energy.
 This is because energy is transferred from one body to the other while
exerting a force. So, work done against a force is stored in the form of energy.
e.g., a stump is displaced from its stationary position when a fast moving
cricket ball hits it.




 1 joule energy is the energy required to do 1 joule of work.
 The larger unit of energy is kilojoule (kJ) 1kj = 1000j
.
Forms of Energy
There exists various forms of energy such as potential energy, kinetic energy,
chemical energy, electrical energy and light energy. Among all these, kinetic energy
and potential energy hold much relevance.
Kinetic Energy
The energy due to the motion of an object is called kinetic energy.
 For example, a bullet can pierce a target, moving wind moves the blades of
wind mill, etc.

 Its SI unit is joule (J). Kinetic energy of a body moving with certain velocity is
equal to the work done on it to acquire that velocity.
 Kinetic energy of an object increases with its speed. The kinetic energy
possessed by an object of mass m, moving with a uniform velocity v is given by
(KE or Ek = ½ mv
2
)
Calculation of Kinetic Energy
Energy is a scalar quantity, i.e., it has only magnitude and no direction. Its SI unit is Joule (J). Joule is
a smaller unit of energy called ‘Joule’ is named after a British physicist James Prescott Joule.

4. WORK AND ENERGY 4

The kinetic energy of an object is measured by the amount of work which it can do
before it comes to rest. Let us consider an object of mass m moving with a uniform
velocity u.
A force F is applied on it which displaces it through a distance s and it attains a
velocity v.

According to the equation of motion, we have
v
2
– u
2
= 2as
s=v
2
– u
2
/ 2a
where a is uniform acceleration, u is initial velocity and v is final velocity.
Also, form F = ma
Substituting the values of F and s in eq. (i), we have
W = ma × v
2
– u
2
/ 2a
Or W = ½m (v
2
-u
2
)
*This is known as work-energy theorem (i.e., total work is equal to the change in
kinetic energy).
If initial velocity, u = 0
Then, W = ½ mv
2

*This work done is equal to the kinetic energy of the object.


* Hence, kinetic energy depends on the mass and speed of an object. This is the
reason why heavy objects which are moving with a high speed possess more kinetic
energy as compared to smaller objects moving.

*Some Important Result can be Derived from the Formula KE = ½ mv
2
. These are
given below:
(i) If the mass of an object is halved, its kinetic energy also gets halved.
(ii) If the mass of an object is doubled, its kinetic energy also gets doubled.
(iii) If the speed of an object is halved, its kinetic energy becomes one-fourth.
(iv) If the speed of an object is doubled, its kinetic energy becomes four times.
Potential Energy
 The energy possessed by a body due to its stationary position is called
potential energy.
KE or Ek = ½ mv
2

5. WORK AND ENERGY 5

 If we do some work on an object, then the energy transferred to the object
will be stored in it the form of potential energy.

For example, energy stored in a stretched spring, a stretched rubber band, etc.


Potential energy of an object at a height-
 The energy of an object increases when it is raised to a certain height from
the ground because of work done on it against gravity. This energy is termed
as gravitational potential energy and it depends on the ground level or the
level zero.
 Hence, an object in a given position can have a certain potential energy at
one level and a different value at another.
*Let us consider an object mass m, raised through a certain height from the
ground. The minimum force required to raise the object is equal to the weight of the
object mg .The work done in the process
we have, Work done = force × Displacement
*Since force acting on the body is the gravitational pull of the earth m × g acting in
downward direction.
W = mg × h (where g = acceleration due to gravity)







Since, work done on the object will be stored in it as potential energy i.e.,
Potential energy = Work done = mgh
i.e., PE or Ep = mgh
*It is also observed that the work done against the gravity depends on the
difference in vertical heights of the initial and the final position of the object and not
on the path along which the object is moved, as shown in figure.
W = mgh

6. WORK AND ENERGY 6







TRANSFORMATION OF ENERGY
 One form of energy can be converted to another as per the law of
conservation of energy. However, the total energy always remains constant
both before and after the transformation.
 Potential energy is converted into another in the nature. For example,
1. Green plants convert the light energy into the energy stored in the form of
food.
2. On rubbing the hands, the muscular energy gets converted into the heat
energy.
3. In a battery or cell, chemical energy gets converted into the electrical energy.
4. An electric motor converts electrical energy into mechanical energy.
5. Steam engine converts heat energy into kinetic energy
6. The solar cell converts light energy into electric energy.

LAW OF CONSERVATION OF ENERGY
*We know that the energy can be changed from its one form to another but the
total energy of a system during or after the process remains conserved. This is called
the law of converted from one form to another.
Conservation of Energy during the Free Fall of a Body
Consider a simple ex. Let an object of mass, m be made to fall freely from a height, h.
At the start, the potential energy is mgh and Kinetic energy is zero. The total energy
of the object is thus mgh. As it falls, its potential energy will change into Kinetic
energy.

7. WORK AND ENERGY 7



*The sum of Kinetic energy and potential energy of an object is its total mechanical
energy.
RATE OF DOING WORK OR POWER
 Power of a person or a machine measures the efficiently or the speed with
which that person or machine can do the work.
 It is defined as the rate of doing work or the rate of transfer of energy.
 A more powerful machine or a stronger person would do more work in a
shorter time as compared to the less powerful ones.
 If a body does W Work in time t, then the power of the body is given by
Power = Work/Time
(P= W/t)
 It is a ratio of two scalar quantities. So, power is also a scalar quantity.
 The SI unit of power is J s
-1
or watt.
 When a work of 1joule is done in 1 second, then the power is 1 watt.









The other units of power are as follows:
1 kilowatt (kW) = 1000 watt = 10 3W
1 megawatt (MW) = 1000000 watt = 106W
1 gigawatt (GW) = 1000,000,000 watt = 109W
Another unit of power is called horsepower (hp), which is equal to 746 watt. Thus,
1 horsepower = 746 watt
Or, 1 HP = 746 W
At point A,
K.E= 0, P.E + mgh
Total energy = K.E + P.E= 0 + mgh = mgh
At point B
K.E. =


mv
2
=



2mg(h-x)=mg(h-x)
P.E= mgx
Total energy = K.E + P.E
= mg(h-x) + mgx= mgh
At point C
K.E. =


mv
2
=


m2gh =mgh
P.E = 0
Total energy = K.E + P.E
= mgh + 0 = mgh
V
2
-u
2
= 2g(h-x)
V
2
-0= 2g(h-x)
V
2
= 2g(h-x)
V
2
-u
2
= 2gh
V
2
-0= 2gh
V
2
= 2gh

8. WORK AND ENERGY 8

Average Power
*The ratio of the total work done by the total time taken is called average power.
The power of an object or a person may vary with time depending on the energy
consumed.




Commercial Unit of Energy
 The SI unit of energy is joule which is a very small unit.
 The commercial unit of energy is kilowatt hour (kWh) or Board of Trade (BOT)
unit which is also equal to 1 unit.
 1 kilowatt hour is the amount of electric energy used in 1 hour at the rate of
1000 J s
-1
.

1 kWh = 1 kW × 1h
= 1000 W × 60 × 60 s
=3600000 J
=3.6 × 10
6
J
:. 1 kWh= 3.6 × 10
6
J
The electrical energy consumed in houses, commercial establishments and industries
is expressed in kilowatt hour, which is commonly referred to as one unit of
electricity.











Average power = Total energy consumed / Total time taken