Comprehensive WBBSE Class 9 Physical Science Notes Chapter 5 Work, Power and Energy can help students make connections between concepts.

## Work, Power and Energy Class 9 WBBSE Notes

The temperature of the deeper layers of the water in the pond remains nearly at 4°C and falls gradually to 0°C upwards till the layer of ice is reached. The marine life in water is thus saved.

Work = Force x displacement of the point of application in the direction of the force

WF x d (W Work done;

F Force acting on body

d = displacement of the body from the point of application of the force)

Sometimes the direction of force is placed as an angle to the horizontal vector will be taken suppose F is acting as θ angle with horizontal plane. So, the horizontal vector Fcosθ.

∴ work done,

W = Fcosθ.d = Fdcosθ ………………………… (i)

Note :

(i) If θ = 0°, cosθ = 1, then W = Fd

(ii) If θ = 90°, cosθ 1, then W = 0

(iii) If θ = 180°, cosθ = -1, then I W = – Fd

Work done by the force : If the displacement of the point of application of the force takes place in the direction of the force then the force is said to have done the work.

Example : If a body is dropped vertically, the gravitational force attracts it downward. The displacement of the body takes place in the direction of gravitational force. Here, work is done by the gravitational force.

Work done against the force: When the displacement of the point of application of the force takes place in the direction opposite to the applied force, then work is said to be done against the force.

Example: If a body is lifted vertically upward, displacement of the body is in the direction opposite to the gravitational force and work is done against the gravitational force.

No work force : When a force acts perpendicularly to the direction of displacement of the particle, then the force does not do any work and is known as no work force.

Example : If a man moves along a horizontal place road with a suitcase in his hand, force of gravity does no work on the suitcase. Because in this case weight of suitcase and its displacement are at right angles to each other.

Unit of work:

Absolute unit :

(i) CGS : erg

1 erg 1 dyne x 1cm

(ii) SI : Joule

1 Joule = 1 Newton x 1 meter

= 10^{5} dyne × 10

^{2} cm

= 10^{7} dyne × cm

∴ Joule = 10^{7}erg

Gavitational unit of work :

(i) CGS : g-cm

1g-cm = 1 g-wt × 1 cm

= 981 dyne × 1 cm

1 g-cm = 981 erg

(ii) SI : kg-m

1kg-m = 1 kg-wt x 1m

= 9.8 Newton x 1m

1 kg-m = 9.8 Joule

Practical unit of work : Joule

1 Joule 10^{7 } erg

Power : Rate of work done by an agent is called its power, i.e. work done in unit time is known as power. If any work W done by applying ‘p’ force in ‘p’ time then

N.B : Some work done is less time by an agent means it has greater power. Power does not depend on the total amount of work done but on the time required to do the work. Power is a scalar quantity.

Unit of power:

Absolute unit:

- CGS : erg s
^{-1} - SI: Watt or Js
^{-1}

Gravitational unit:

- CGS : g-cms
^{-1} - SI: kg-ms
^{-1}

Practical unit : The practical unit of power in both CGS and SI units is Watt.

Watt : The power of doing 1 erg of work in 1 second is known as 1 watt.

1 Watt 1 Joule second^{-1 } = 10^{-7}erg s^{-1
}1 Kilowatt 10^{3 } watt

1 Megawatt 10^{6 }watt

Horsepower: In FPS system, practical unit of power.

Definition of Horse Power (hp) : The power to work at the rate of 550ft-lb per second is called 1 horse power 1 horse power = 746 Watt

Energy : The capacity of an object to do work is called the energy of the object.

N.B. Since by energy we mean some amount of work, so we express energy in the unit of work.

Energy is a scalar quantity.

Types of energy :

(1) Potential energy : The energy of an object because of its position or shape is called its potential energy. Examples of potential energy :

- When a weight is raised through a certain height, work is done against gravity, which is retained in the body in this new position as potential energy and is now capable of doing some work if allowed to fall down to its former position.
- When a spring wound, stretched or compressed it gains potential energy, as it is now capable to do work while it comes back to its normal shape.

(2) Kinetic energy : It is the energy acquired by a body by virtue of its motion.

Examples of Kinetic energy :

- Kinetic energy of a bullet fired from a gun helps it to pierce a target.
- Kinetic energy of blowing air and running water are used to run a windmill and a water mill respectively.

Kinetic energy of a hammer is used in driving a nail into a block of wood.

Calculation of kinetic energy: If a body of mass m be moving with velocity v, then it can be shown that,

i.e. Kinetic energy = 1/2 x mass x (velocity)^{2}

∴ Kinetic energy = 1/2 mv^{2}

Mechanical energy: The sum of the kinetic energy and the potential energy of an object is called its mechanical energy.

Law of conservation of energy: Energy cannot be created or destroyed. Only one form of energy is transformed to other type of energy. The total amount of energy is constant in the universe.

Examples of conservation of energy :

(i) Snow deposited at high altitudes melts and the water so formed flows down to the seas. In the process, the potential energy of the water is converted into kinetic energy. We convert this kinetic energy of water to electrical energy in hydroelectric power plants.

(ii) The food we eat comes from plants and animals that eat plants or plant products. When we eat food, several chemical processes take place, and energy in the form needed by the body is produced from the energy contained in the food. When we walk, run, exercise, this energy is used to provide kinetic energy.

m Conservation of energy in a freely falling body : Suppose a ball of mass ‘m’ is kept at rest at a point A, which is at a height ‘h’ above the ground. We take the potential energy at the ground to be zero. The potential energy of the ball at A’ is then,

U_{A} = mgh

The ball is at rest at A, so its kinetic energy here is

K_{A}= o

The total energy is, U_{A} + K_{A} = mgh (1)

The ball is now allowed to fall. The only force on it during the fall is gravity (free fall), and hence, its acceleration is a = g downwards. Consider any point B in its path.

Suppose its distance from A is x. The height of the point B from the ground is (h – x). When the ball reaches point B, its potential energy is,

U_{A} = mg (h- x).

The velocity of the ball at point B is given by

v^{2} = u^{2} + 2gx = 2gx.

The kinetic energy of the ball at point ‘B’ is :

K_{B} – \(\frac{1}{2}\) mv^{2} = \(\frac{1}{2}\) m(2gx) = mgx

The total energy at point B is

U_{B} + K_{B} = mg(h-x) + mgx = mgh …………..(2)

Comparing (1) and (2), we see that

U_{A} + K_{A} = U_{B} + K_{B}

The point B was chosen to be any point in the path of the ball. The total energy here turned out to be equal to the initial energy. Thus, the energy at all points during the fall is the same, that is, remains conserved as the ball falls.

The potential energy is gradually converted into kinetic energy.

This result is also true if a ball is thrown upwards or at some angle with the vertical. During the upward movement of a ball, its kinetic energy gets gradually converted to potential energy.