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

These comprehensive RBSE Class 11 Physics Notes Chapter 6 Work, Energy and Power will give a brief overview of all the concepts.

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

Product of two vectors:
Product of two vectors is of two types:
(i) Scalar product of dot product: This product of two vectors is a scalar quantity therefore, it is called scalar product’ and it is denoted by symbol of dot (.), therefore it is also called ‘Dot product’. It is given by \(\vec{A} \cdot \vec{B}\) = AB cos θ, where θ is the angle between two vectors. Example of dot product is work
i.e.,W = \(\vec{F} \cdot \vec{d}\)

(ii) Vector product or cross-product: This product of vectors is a vector quantity, therefore, it is called ‘vector product’ and it is denoted by symbol of cross (X), hence it is also called ‘cross product.’ It is obtained by \(\vec{A} \times \vec{B}\) = AB sinθ n̂, where n is unit vector at right angles to plane of 2 and P, direction of which is decided by right hand screw rule. Example of cross product is torque, \(\vec{\tau}=\vec{r} \times \vec{F}\)

Work:
When a body gets displaced in the direction of applying force, then dot product of force (\(\vec{F}\)) and displacement (\(\vec{d}\)) provides the work done by the force i. e.,
W = \(\vec{F} \cdot \vec{d}\) = Fd cos θ

 

Work done by variable force:
Work done by variable force W = \(\int_{x_1}^{x_2}\)F dx = Area of F - x graph form x₁ to x₂.

Conservative and non-conservative forces:

• Conservative force: If the work done in displacing an object from one point to other point by a force does not depend upon the path adopted then the force is said to he conservative. For examples, gravitational force and all central forces.
• Non conservative force: If the work done by a force in displacing the object from one point to other point, depends upon adopted path, then force is called non-conservative. For examples; friction force, viscous force and ‘ all retarding forces.

Energy:
Capacity of doing work is called the energy.

Kinds of mechanical energy:

• Kinetic energy: The energy of an object due to its motion, is called its kinetic energy.
• Potential energy: The energy which is due to particular position of the body is called its potential energy.

Work-energy theorem:
According to this theorem, “the work done by a force in displacing the object on horizontal surface is equal to change in its kinetic energy.” i.e.,
W = K_f - K_i = ΔK

Conservation of energy:
According to this law, “neither energy can he created nor it can be destroyed, only its conversion from one form to other from is possible.”

Potential energy of spring:
Work done in expanding or compressing a spring is called the potential energy of the spring. Its value is
U = \(\frac{1}{2}\)kx².

Power:
Rate of doing work is called power i.e., P = \(\frac{W}{t}\)

Collision of bodies:
Mutual interaction between two bodies for short time is called collision. In collision, the momentum and energies of the bodies are changed. There are three types of collisions:

• Perfectly elastic collision: The collision in which the mechanical energy and momentum are conserved separately, is called perfectly elastic collision. For example, the collision of gas molecules.
• Non-elastic collision: The collision in which the momentum remains conserved but mechanical energy does not remain conserved, is called non-elastic collision. For example, the collision of two vehicles in road accident.
• Perfectly non-elastic collision: The collision in which the momentum remains conserved but energy does not remain conserved and after collision both bodies moves with same velocity in same direction, is called perfectly non-elastic collision. For example, a bullet fired on a wodden block enters in it and moves with block.

Newton’s law of collision:
According to this law, “in head on collisions of two bodies the ratio of relative velocities after the collision and before the collision remains constant and is equal to negative value of coefficient of restitution.” i.e.,
\(\frac{v_1-v_2}{u_1-u_2}\) = -e

Ballistic pendulum:
This is the apparatus with the help of which velocity of fast moving object can be determined.

→ Scalar or dot product of vectors.
\(\vec{A} \vec{B}\) = AB cos θ

→ Vector or cross product of vectors,
\(\vec{A} \times \vec{B}\) = AB sinBn̂

→ Work W = \(\vec{F} \cdot \vec{d}\)= Fd cos θ

→ Work done by variable force W = \(\int_{x_1}^{x_2}\)F dx

→ If F = (F_xî + F_yĵ + F_zk̂) and dr = d_xî + d_yĵ + d_zk̂ then dW = \(\vec{F} \vec{d}\) r = F_xdx + F_ydy + F_zdz
and W =\(\int_{r_1}^{r_2}\vec{F} \vec{d}\) r = \(\int_{x_1}^{x_2}\)F_xdx + \(\int_{y_1}^{y_2}\)F_ydy + \(\int_{z_1}^{z_2}\)F_zdz

→ Kinetic 'energy K = \(\frac{1}{2}\) mv²

→ Relation between kinetic energy and momentum
K = \(\frac{p^2}{2 m}\) and p = \(\sqrt{2 m K}\)

→ Work energy theorem W = ΔK = K_f - K_i

→ Gravitational potential energy U_(h) = mgh

→ Potential energy of spring U = \(\frac{1}{2}\) kx²

→ Mass energy equivalence E = mc²

→ Power P = \(\frac{W}{t}=\vec{F} \cdot \vec{v}\)

→ Velocities of bodies after collision:
v₁ = \(\frac{2 m_2 u_2-\left(m_1-m_2\right) u_1}{m_1+m_2}\)
and v₂ = \(\frac{2 m_1 u_1-\left(m_2-m_1\right) u_2}{m_2+m_1}\)

→ For two dimensional elastic collision

• m₁u₁ = m₁v₁ cosθ ₁ + m₂v₂ cosθ ₂
• m₁v₁ sinθ₁ = m₂v₂ sinθ₂
• m₁u₁ = m₁v₁ + m₂v₂

→ Coefficient of restitution,
e = \(\frac{v_2-v_1}{u_1-u_2}\)

• For perfectly elastic collision, e = 1
• For non-elastic collision, 0 < e < 1
• For perfectly non elastic collisions, e = 0

→ In perfectly non elastic collision
mu = (M + m) v.

→ Conservative forces: The forces by whom the work done in displacing a body from one point to other point does not depend on the path adopted, are called conservative forces.

→ Non conservative forces: The forces by whom the work done in displacing an object from one point to other point, depends upon path adopted, are, called non-conservative forces.

→ Collision: Mutual interaction between two bodies for short time, is called collision in which the energies and momentums of bodies are changed.

→ Ballistic pendulum: It is an apparatus which is used to measure the velocity of a fast moving body.