By going through these CBSE Class 11 Physics Notes Chapter 6 Work, Energy and Power, students can recall all the concepts quickly.

## Work, Energy and Power Notes Class 11 Physics Chapter 6

→ The total work done in the uniform speed of a body is zero i.e. if work is done is zero then the speed of the body is uniform.

→ In doing work in stretching or compressing a spring and by a falling body, the variable forces involved are restoring force and force of gravitation.

→ Work is done by a force on a body over a certain displacement.

→ The change in kinetic energy of an object is equal to the work done on it by the net force.

→ No work is done by the force if it acts perpendicular to the displacement of the body.

→ The total mechanical energy of a system is conserved if the forces doing work on it are conservative.

→ Energy can exist in various forms such as mechanical energy, heat energy, light energy, sound energy, etc.

→ The motion of a simple pendulum is an example of the conversion of P.E. into K.E. and vice-versa.

→ A body possesses chemical energy due to the chemical bonding of its atoms.

→ A body possesses heat energy due to the disorderly motion of its molecules.

→ The mass-energy equivalence formula describes energies to all masses (E = mc^{2}) and masses to all energies (\(\frac{\mathrm{E}}{\mathrm{c}^{2}}\) = m)

→ The P.E. which an elevator loses in coming down from an upper story of the building to stop at the ground floor is used up to lift up the counter-poise weight.

→ When a very light body in motion collides with a heavy stationary body in an elastic collision, the lighter one rebounds back with the same speed without the heavy body being displaced.

→ When a body moving with some velocity undergoes elastic collision with another similar body at rest, then there is an exchange of their velocities after collision i.e. first one comes to rest and the second starts moving with the velocity of the first one.

→ 1 J = 10^{7} erg.

→ Joule (J) and erg are the S.I. and C.G.S. units of work and energy. Energy is the capacity of the body to do the work.

→ The area under the force-displacement graph is equal to the work done.

→ Work done by the gravitational or electric force does not depend on the nature of the path followed.

→ It depends only on the initial and final positions of the path of the body.

→ Power is measured in horsepower (h.p.). It is the fps unit of power used in engineering.

→ 1 h.p. = 746 W.

→ Watt (W) is the S.I. unit of power.

→ The area under the force-velocity graph is equal to the power dissipated. Body or external agency dissipates power against friction.

→ If the rails are on a plane surface and there is no friction, the power dissipated by the engine is zero.

→ When a body moves along a circular path with constant speed, its kinetic energy remains constant.

→ K.E. of a body can’t change if the force acting on a body is perpendicular to the instantaneous velocity. ,

→ K.E. is always positive.

→ If a machine gun fires n bullets per second with kinetic energy K, then the power of the machine gun is P = nK.

→ The force required to hold the machine gun in the above case is

F = nv = n \(\sqrt{2 \mathrm{mK}}\)

→ When work is done on a body, it’s K.E. or P.E. increases.

→ When work is done by a body, its P.E. or K.E. decreases.

→ Mass and energy are interconvertible.

→ K.E. can change into P.E. and vice-versa.

→ One form of energy can be changed into other forms according to the law of conservation of energy.

→ When a body falls, its P.E. is converted into its K.E.

→ The collision generally occurs for every small interval of time.

→ Physical contact between the colliding bodies is not essential for the collision.

→ The mutual forces between the colliding bodies are action and reaction pair.

→ Momentum and total energy are conserved during elastic collisions.

→ The collision is said to be elastic when the K.E. is conserved.

→ Inelastic collisions the forces involved are conservative.

→ Elastic collisions, the K.E. or mechanical energy is not converted into any other form of energy.

→ Elastic collisions produce no sound or heat.

→ There is no difference between the elastic and perfectly elastic collisions.

→ In the elastic collisions, the relative velocity before the collision is equal to the relative velocity after collision i.e. u_{1} – u_{2} = v_{2} – v_{1.}

→ The collision is said to be inelastic when the K.E. is not conserved.

→ Head-on collisions are called one-dimensional collisions.

→ When the momentum of a body increases by a factor n, then its K.E. is increased by a factor n^{2}.

→ If the speed of a vehicle is made n-times then its stopping distance becomes n^{2} times.

→ Work: Work is said to be done if a force acting on a body displaces it by some distance along the line of action of the force.

→ Energy: It is defined as the capacity of a body to do work.

→ K.E.: It is defined as the energy possessed by a body due to its motion.

→ P.E.: It is defined as the energy possessed by a body due to its position or configuration.

→ Gravitational P.E.: It is defined as the energy possessed by a body due to its position above the surface of death.

→ Power: It is defined as the time rate of doing work.

→ Work-energy theorem: It states that the work is done by a force acting on a body is equal to the change in its K.E.

→ Law of conservation of energy: Total energy of the universe always remains constant.

→ Instantaneous Power: It is the limiting value of the average power of an agent in a small time interval tending to zero.

→ Mass-energy Equivalence: E = mc^{2}.

→ Elastic collision: The collision is said to be elastic if both momentum and the K.E. of the system remain conserved.

→ Elastic collision in one dimension: The collision is said to be one-dimensional if the colliding bodies move along the same straight line after the collision.

→ In-elastic collision: It is defined as the collision in which K.E. does not remain conserved.

→ Transformation of energy: It is defined as the phenomena of change of energy from one form to the other.

→ Coefficient of restitution: It is defined as the ratio of the velocity of separation to the velocity of approach i.e.

e = \(\frac{v_{2}-v_{1}}{u_{1}-u_{2}}\)

→ Moderator: It is defined as a substance used in atomic reactors to slow down fast-moving neutrons to make them thermal neutrons. e.g. graphite and heavy water are moderators

→ 1 eV: It is defined as the energy acquired by an electron when a potential difference of 1 volt is applied

i. e. 1 eV = 1.6 × 10^{-19 }c × 1 V

= 1.6 × 10^{-19} J

**Important Formulae:**

→ Work done by F in moving a body by S is

W = F . S = FS cos θ

→ P = \(\frac{W}{t}\)

→ Instantaneous power is P = F.v

→ K.E. = \(\frac{1}{2}\)mv^{2}.

→ P.E. = mgh.

→ P.E. of a spring is given by = \(\frac{1}{2}\)kx^{2}.

where k = force constant, x = displacement i.e. extension or compression produced in the spring. .

→ E = mc^{2}.

→ Velocities of the two bodies after collisions are given by

v_{1} = \(\frac{m_{1}-\dot{m}_{2}}{m_{1}+m_{2}}\)u_{1} + \(\frac{2 m_{2}}{m_{1}+m_{2}}\)u_{2}

and

v_{2} = \(\frac{m_{2}-\dot{m}_{1}}{m_{1}+m_{2}}\)u_{2} + \(\frac{2 m_{2}}{m_{1}+m_{2}}\)u_{1}

→ Power of an engine pulling a train on rails having coefficient of friction p is given by:

P = μ mg v.

where μ = coefficient of friction.

m = mass of train,

v = velocity of train.

→ Power of engine on an inclined plane pulling the train up is

P = (μ cos θ + sin θ)mg v

→ And pulling down the inclined plane is

P = (μ cos θ – sin θ)mg v

→ Work against friction in above cases when the body moves down the inclined plane is W = m.g.(sin θ – μ cos θ)S

→ When body moves up the incline,

W = mg(μ cos θ + sin θ)S

→ % efficiency (n%) = \(\frac{\text { Poweroutput }}{\text { Powerinput }}\) × 100

= \(\frac{\text { Output energy }}{\text { Input energy }}\) × 100