Revision: Force, Work, Power and Energy >> Work, Energy and Power Physics (English Medium) ICSE Class 10 CISCE

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). 

“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 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

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.

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 amount of work done by a force is equal to the product of the force and the displacement of the point of application of the force in the direction of force.

The S.I. unit of work is newton-metre or joule (J).

1 Joule = 1 N × 1 m.

1 J of work is said to be done by a force of 1 N if it displaces a body by 1 m in the direction of the force.

The unit of force in the S. I. system is Newton (N). Newton is defined as the force which, when applied on a body of mass 1 kg produces in it an acceleration of 1 ms².

Power is defined as the rate of doing work or work done per second.

i.e., Power = `("Work done in joule")/("Times in second")`

or,  p = `("W (in joule)")/("t (in second)")`

The rate of doing work is called power.

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.

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 at rest due to its position or size and shape is called potential energy.

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

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 energy radiated out by the Sun is called solar energy.

The energy released on burning coal, oil, wood, or gas is called heat energy.

It is a form of energy in the presence of which other objects are seen.

The energy possessed by the fossil fuels such as coal, petroleum and natural gas is called chemical energy (or fuel energy). 

The energy possessed by fast-moving water is called hydro energy.

When two dry bodies are rubbed together, they get charged due to the movement of free electrons from one body to the other body, so they possess electrical energy.

The energy released due to loss in mass during the processes of nuclear fission and fusion is called nuclear (or atomic) energy.

OR

The energy released when nuclei undergo a nuclear reaction (change in structure, forming new nuclei) is called nuclear energy.

The energy released in nuclear disintegrations in the interior of Earth gets stored deep inside the Earth and is called geo thermal energy.

The energy possessed by the fast-moving air is called wind energy.

Vibrating body possesses mechanical energy capable of producing sound energy.

The energy possessed by a magnet due to which it can attract iron filings, is called magnetic energy.

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.

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

W = F × S cosθ

• W = Work done
• F = Magnitude of force
• θ = Angle between force and displacement
• S = Displacement of the object

W = FS = mgh

• W = Work done
• F = Force = mg (weight of the object)
• $S=h$ = Vertical displacement
• m = Mass of the object
• g = Acceleration due to gravity
• h = Height moved

Power P = \[\frac{\text{Work done }W}{\text{Time taken }t}\]

or

P = \[\frac {W}{t}\]

Gravitational Potential Energy U_h = mgh

K = \[\frac {1}{2}\] mv²

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

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.

Statement:

For a freely falling body, the sum of kinetic energy (K) and potential energy (U) remains constant, i.e.,

K + U = constant

Explanation / Proof:

Let a body of mass m fall from a height h.

• At position A (height = h):
  K = 0, U = mgh
  Total energy = mgh

• At position B (fallen through distance x):
  K = mgx, U = mg(h − x)
  Total energy = mgx + mg(h − x) = mgh

• At position C (on the ground):
  K = mgh, U = 0
  Total energy = mgh

• 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

• Work depends on two factors: the magnitude of the force applied and the displacement produced in the direction of the force.
• Greater force or greater displacement results in more work being done.
• Work is calculated as the product of force and displacement in the direction of the force.
• If displacement is zero, even when a force is applied, the work done is zero.
• Work is a scalar quantity, meaning it has magnitude but no direction.

• S.I. unit: If 1 joule of work is done in 1 second, the power spent is said to be 1 watt.
• C.G.S. unit: The C.G.S. unit of power is erg per second (erg s^-1).
• Relationship between S.I. and C.G.S. units:
   1 W = 1 J s^-1 = 10⁷ erg s^-1
• 1 horse power (H.P.) = 746 W = 0.746 kW

• Work does not depend on time, while power depends on the time at which work is done.
• S.I. unit of work is joule (J), and S.I. unit of power is watt (W).

• 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.

• Potential energy is due to a change in position or shape, while kinetic energy is due to a state of motion.
• Potential energy does not depend on speed, but kinetic energy depends on the speed of the body.

• 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.