Revision: Work and Energy Science English Medium Class 9 CBSE

The work done by a force on a body is equal to the product of the force applied and the distance moved by the body in the direction of force i.e.,

Work done = Force × distance moved in the direction of force

Work is said to be done only when the force applied on a body makes the body move (i.e., there is a displacement of the body). 

When a force acts on a rigid body which is free to move, the body starts moving in a straight line in the direction of the force. This is called translational motion.

“Capacity of doing work” is called Energy.

Energy, in physics, is the capacity for doing work. It may exist in potential, kinetic, thermal, electrical, chemical, nuclear, or other various forms. There are, moreover, heat and work-i.e., energy in the process of transfer from one body to another.

The SI unit of work is joule.
1 joule of work is said to be done when a force of 1 newton displaces a body through 1 metre in its own direction.

The ratio of the work done by the machine to the work done on the machine is called the efficiency of a machine

Efficiency =`"Output energy"/" Input energy"`

(Work done by a machine is called the output energy and the work done on a machine is called the input energy.)

The energy of a body is its capacity to do work.

The energy possessed by a body due to its state of rest or of motion, is called mechanical energy. It is the sum of potential energy and kinetic energy.

The energy possessed by a body due to its state of motion is called its kinetic energy.

The kinetic energy of the body due to motion in a straight line is called translational kinetic energy.

If a body rotates about an axis, the motion is called rotational motion.

The kinetic energy of the body due to rotational motion is called rotational kinetic energy or simply rotational energy.

If a body moves to and fro about its mean position, the motion is called vibrational motion.

The kinetic energy of the body due to its vibrational motion is called vibrational kinetic energy or simply vibrational energy.

The motion of a body in a straight line path is called translational motion.

The energy possessed by a body by virtue of its specific position (or changed configuration) is called the potential energy.

The energy possessed by a body due to its state of rest or of motion, is called mechanical energy.

The energy possessed by a body at rest due to its position or size and shape is called potential energy.

Energy can neither be created nor can it be destroyed. It only changes from one form to another.

1 watt is the power of an agent which does 1 joule of work in 1 second.

In other words, if the rate of energy use is 1 J s^-1, then the power is 1 W.

1 watt = `(1  "joule")/(1  "second")`

or 1 w = 1 Js^-1

K = \[\frac {1}{2}\] mv²

Kinetic Energy = \[\frac {1}{2}\] mass × (velocity)²

Gravitational Potential Energy U_h = mgh

Statement:

According to the work-energy theorem, the increase in kinetic energy of a moving body is equal to the work done by a force acting in the direction of the moving body.

Proof:

Let a body of mass m be moving with an initial velocity u. When a constant force F is applied to the body along its direction of motion, it produces an acceleration a, and the body's velocity increases from u to v over a distance S.

Force,

F = ma

Work done by the force,

W = F × S

From the equation of motion,

\[v^2=u^2+2aS\Rightarrow S=\frac{v^2-u^2}{2a}\]

Substituting equations (i) and (iii) into (ii):

W = \[ma\times\frac{v^2-u^2}{2a}=\frac{1}{2}m(v^2-u^2)\]

Now,
Initial kinetic energy, K_i = \[\frac {1}{2}\]mu²
Final kinetic energy, K_f = \[\frac {1}{2}\]mv²

Therefore,

W = K_f − K_i

Conclusion:

Work done on the body = Increase in its kinetic energy.
Hence, the work-energy theorem is proved.

• The S.I. unit of work is joule (J).
    1 joule = 1 newton × 1 metre, i.e., work done when a force of 1 N moves a body 1 m in its direction.
• The C.G.S. unit of work is erg.
    1 erg = 1 dyne × 1 cm, i.e., work done when a force of 1 dyne moves a body 1 cm in its direction.
• The relation between joule and erg is:
    1 joule = 10⁷ erg

• Energy and work are directly related — when work is done, energy is transferred; doing work decreases energy, and receiving work increases it.
• No energy transfer occurs when the applied force is perpendicular to the displacement (e.g., centripetal force in circular motion).
• Units of energy are the same as those of work:
    - S.I. unit: Joule (J)
    - C.G.S. unit: Erg
    - 1 J = 10⁷ erg
• Practical units of energy:
    - 1 Wh = 3600 J = 3.6 kJ
    - 1 kWh = 3.6 × 10⁶ J = 3.6 MJ
    - 1 calorie = 4.18 J, 1 kilocalorie = 4180 J
• Energy in atomic-scale processes is measured in electron volt (eV), where 1 eV = 1.6 × 10⁻¹⁹ J

• There are two main types of potential energy: gravitational and elastic.
• Gravitational potential energy is due to height and is given by U = mgh.
• It is zero at infinity and becomes less negative as the distance from Earth increases.
• Elastic potential energy is stored when an object is stretched or compressed.
• Lifting a body stores energy as gravitational potential energy by doing work against gravity.

• Mechanical energy → Electrical energy: In a generator, the kinetic energy of water rotates the turbine to produce electrical energy.
• Electrical energy → Mechanical energy: In an electric motor, electrical energy changes into mechanical energy.
• Electrical energy → Heat energy: In devices like a heater, oven, or geyser, current through a resistance wire produces heat energy.
• Heat energy → Electrical energy: A thermocouple converts heat energy into electrical energy.
• Electrical energy → Sound energy: In a loudspeaker or electric bell, electrical energy changes into sound energy.
• Sound energy → Electrical energy: A microphone converts sound energy into electrical energy.
• Chemical energy → Electrical energy: In an electric cell, chemical energy changes into electrical energy.
• Electrical energy → Light energy: In an electric bulb, electrical energy changes into heat and light energy.
• Light energy → Electrical energy: In a photoelectric cell or solar cell, light energy is converted into electrical energy.
• Chemical energy → Mechanical energy: In automobiles, chemical energy of petrol/diesel changes into mechanical energy.