Class IX – Science (Physics) Work, Energy and Power Chapter

Class IX – Science (Physics)
Work, Energy and Power
Chapter Notes
The term 'work' implies any activity resulting in muscular or mental exertion.
In physics, however, the term has a different meaning. It represents a physical quantity.
When a force acts on an object and the object moves in the direction of force, we say
that the force has done work on the object.
For example –
a) If you push a book lying on a table, you exert force on the book and the book moves in the direction of the force. We say that the force has done work. b) If you push a wall, the act will definitely tire you, but the wall does not move but, no work is done. The work done by a force depends on two factors:
i) Magnitude of the force ii) Distance through which the body moves in the direction of the force Definition – Work done by force acting on an object is equal to the product of the force
and the distance moved by the object in the direction of force
Units – Work = Force X Displacement
S.I Unit of Force and Displacement are Newton and metre respectively.
Thus, unit of work is Newton.metre, which is expressed as a separate unit ‘Joule’ in
honour of the British scientist James Prescott Joule. It is denoted by J.
When a force of 1 N acts on an object and the object moves by a distance of 1 m in the
direction of the force, then the work done is I joule.
Important - Both Force and Displacement have direction and are vector quantities but
their product, which is Work, does not have a direction and hence it is a Scalar quantity
Work done under different conditions
a) When displacement is in the direction of the force If Force is denoted by F and displacement is denoted by S, Work Done = F X S Examples –
1. When an object falls, the displacement is in the direction of the force of gravity. 2. When a boy pushes a book along a table, the displacement of the book is along the direction of the force. • Work done in such a case is Positive • Positive Work increases the velocity of the object. b) When displacement is in the opposite direction of the force If Force is denoted by F and displacement is denoted by S, If the direction of Force is taken as positive, direction of displacement will be negative Work Done = F X (‐S) = ‐FS Page 1
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Class IX – Science (Physics)
Work, Energy and Power
Chapter Notes
Example –
1. A football moving on a ground slows down and ultimately stops due to force of friction by ground. This force acts in the direction opposite to the direction of the moving ball. 2. When a ball is thrown up, the force of gravity acts in downward direction whereas the ball moves in upward direction. Also the velocity of the ball slows down and becomes zero before it starts falling down. • Work done in such a case is Negative • Negative Work decreases the velocity of the object. c) When displacement is at an angle to the direction of the force Let a constant force F acting on a body produce a displacement S as shown in the
figure. Let be the angle between the direction of the force and displacement.
Displacement in the direction of the force = Component of S along AX = AC
But Cos
=
=
Thus AC = S Cos
Thus
Work Done = F X S Cos
Important –
If = 0, Cos = 1
Thus if Force and displacement are same direction, angle is 0 degrees and thus
Work = F X S Cos (0) = F X S X 1 = F X S
Thus if Force and displacement are in opposite direction, angle is 0 degrees and thus
Work = F X S Cos (0) = F X(-S) X 1 = - F X S
If
= 30, Cos
=
3
If
= 45, Cos
= 1
If
= 90, Cos
=0
2
2
If
= 60, Cos
=
1
2
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Class IX – Science (Physics)
Work, Energy and Power
Chapter Notes
d) When displacement is perpendicular to the direction of the force If the displacement of an object is perpendicular to the force acting on it, the work
done by the force is
Work Done = F x S Cos
= F XS Cos (90)
=FXSX0=0
Thus the work done is such a situation is Zero.
Examples –
1. The force of gravity acts in downward direction whereas an aircraft’s
displacement is in horizontal direction. Thus, there is no displacement in
the direction of force and hence work done is Zero.
2. When a porter moves on a railway platform, carrying luggage on the head,
he applies force on the luggage in vertical direction while he moves in
horizontal direction. Since no displacement takes place in the direction of
the force, no work is done by the porter on the luggage.
3. Same porter when climbs stairs with luggage on his head, applies force in
upward direction and also moves in upward direction, he does Positive
work on the luggage
4. Same porter when comes down the stairs, applies force in upward
direction but moves in downward direction does Negative work on the
luggage.
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Class IX – Science (Physics)
Work, Energy and Power
Chapter Notes
Energy
Amount of energy possessed by a body is equal to the amount of work it can do when its
energy is released. Thus Energy can be defined as Capacity of an object to do work
•
•
Like Work, energy is also a scalar quantity Like Work, S.I unit of energy is Joules denoted by ‘J’ Kinetic Energy
Energy possessed by a moving body is called Kinetic energy.
Examples –
a) Winds can do work by moving blades of a wind mill b) Falling water can do work by moving turbines for generating electricity Consider these cases –
a) Two balls having same mass but thrown at different velocities – more work will be required to stop the ball thrown with higher velocity. Thus Kinetic energy of a moving object depends on its velocity. If velocity is zero, kinetic energy is zero. Thus object at rest does not possess any Kinetic energy. b) Two balls having different masses but thrown with the same velocities – more work will be required to stop the ball having more mass. Thus Kinetic energy of a moving object depends on its mass Formula
Suppose a ball of mass ‘M’ is kept at rest on a smooth horizontal surface.
Let a force ‘F’ is applied on it
Then the acceleration ‘a’ attained by the ball =
F
M
(by Newton’s second law of motion,
Force = mass X acceleration.
Let the velocity of the ball be ‘V’ after it has covered a distance ‘S’
2
2
V =u +2aS
V2 = 0 + 2 (
F
M
)S
2
M XV =2FXS
Or F X S =
1
2
M X V2
But F XS is force times displacement which is work done
Since Kinetic energy is defined as capacity to do work,
K.E =
1
2
M X V2
Thus, if mass of an object is doubled (velocity remaining same), kinetic energy is
doubled
Thus, if mass of an object is halved (velocity remaining same), kinetic energy is halved
Thus, if velocity of an object is doubled (mass remaining same), kinetic energy becomes
4 times
Page 4
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Class IX – Science (Physics)
Work, Energy and Power
Chapter Notes
Thus, if velocity of an object is halved (mass remaining same), kinetic energy becomes
1
th.
4
Potential Energy
Energy of an object due to its Position or Shape is called Potential energy
a) Potential energy due to position of an object •
•
•
•
Suppose a stone of mass ‘m’ is lying on the ground It is now lifted to a height of ‘h’ by applying a force ‘F’ The work done against gravity gets stored in the object as its potential energy (gravitational potential energy) = F X H But F = mg [Newton's second law of motion] Therefore, Potential energy = mg x h Example –
1. First a stone is raised to a height and is allowed to fall. As it falls it attains more velocity and when it hits the ground creates a depression (in case of soil). If it is raised further and allowed to fall, it will hit the ground with more velocity creating deeper depression. Thus if height is increased, the stone acquires more potential energy which gets released in the form of Kinetic energy when allowed to fall. 2. Water storage tanks are constructed at a height. Reason, water at that height possesses more potential energy (gravitational potential energy). When valve of the tank is opened, the stored potential energy gets released in the form of kinetic energy and water reaches the residential areas with a pressure. b) Potential energy due to shape of an object When rubber strings of a catapult is stretched, work done in doing so gets stored
in the form of Potential energy (Elastic Potential energy). When the string is
released, the stored elastic potential energy gets released in the form of kinetic
energy, which is used to throw a stone placed between the strings.
In toy cars, when we wind-up the spring by using a key, some work is done on
spring and elastic potential energy gets stored in it. When wound-up spring is
released, the stored elastic potential energy gets released in the form kinetic
energy and the cars starts moving.
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Class IX – Science (Physics)
Work, Energy and Power
Chapter Notes
Law of Conservation of Energy
Steam engine: The coal burns. Heat generated due to the combustion of coal converts
water into steam. The force exerted by the steam on the piston of the engine moves the
engine. In this case, Chemical energy (from coal) is converted to heat energy, heat
energy is used to generate steam. This steam moves the piston and generates kinetic
energy.
Hydroelectric power plant: Water stored in a reservoir is made to fall on turbines which
are kept at a lower level and which in turn are connected to coils of an a.c. generator. In
this case, Potential energy of the water in the reservoir changes to kinetic energy, kinetic
energy of the falling water to kinetic energy of the turbines, which in turn changes to
electrical energy.
Thus, whenever energy in one form disappears, an equivalent amount of energy in
another form reappears, so that the total energy remains constant.
Law of Conservation of Energy
Law of conservation of energy states that the energy can neither be created nor
destroyed but can be transformed from one form to another.
Example – A ball of mass ‘m’ is allowed to fall from a height of ‘h’
At position A
Potential energy = mgh
Kinetic energy = 0
Total energy = mgh + 0 = mgh ………………………….Equation 1
At position B
Potential energy = mg(h-x)
Velocity at B is given by
V2 = u2 + 2gx
= 0 + 2gx
= 2gx
V = 2gx
Kinetic energy = 1 m V2 = 1 m ( 2 gx )2 = 1 m (2gx) = mgx
2
2
2
Total energy = mg (h-x) + mgx
=mgh –mgx +mgx
Total energy
= mgh …………………………………..Equation 2
Page 6
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Class IX – Science (Physics)
Work, Energy and Power
Chapter Notes
At position C
Potential energy = 0
Velocity at C is given by
V2 = u2 + 2gh
= 0 + 2gh
= 2gh
V = 2gh
Kinetic energy at C = 1 m V2 = 1 m ( 2 gh )2 = 1 m (2gh) = mgh
2
Total energy
2
2
= mgh ……………………………………..Equation 3
It is clear from equations 1, 2 and 3 that the total energy of the body remains constant at
every point. Thus, we conclude that law of conservation of energy holds good in the case
of a freely falling body.
Page 7
Neela Bakore Tutorials
Class IX – Science (Physics)
Work, Energy and Power
Chapter Notes
Power
Suppose two people are given a task of shifting 1 block of stone from ground floor of a
building to the top floor. In both the cases work done is same. But if one person takes
less time in doing the work, it means that the rate at which the work is done or energy is
spent is more.
Definition –
Power is defined as the rate at which work is done or energy is consumed.
•
Power is a scalar quantity •
SI unit of power is – Watt •
1 Watt is the power which does work at the rate of 1 Joule per second •
1 Watt is the power which consumes energy at the rate 1 Joule per second Thus power of an electric appliance tells us the rate at which electric energy is consumed.
For example, a bulb of 60 watt, consumes electric energy at the rate of 60 Joules per
second.
•
•
•
Higher unit of power is Kilo watt denoted by kW = 1000 W Mega Watt denoted by MW = 1000000 W Horse power = 746 Watt Commercial unit of energy
Power = Electric energy consumed / time (in seconds)
Thus electric energy consumed = Power X time in (seconds).
Since this is a very small unit, for commercial purposes a higher unit is for calculating
energy consumption.
1 commercial unit = Power (in kW) X time (in hrs). This is written as kWh
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