Class 11 Physics Work, Energy and Power Notes

Work

Work is said to be done when a force produces displacement in the direction of force.$$\text{Work} = \text{Force} \times \text{Displacement}$$Work=Force×Displacement

SI unit of work is joule (J).

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🔹 Types of Work

1. Positive Work – force and displacement in same direction
2. Negative Work – force and displacement in opposite direction
3. Zero Work – no displacement or force perpendicular to displacement

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🔹 Energy

Energy is the capacity to do work.

SI unit of energy is joule (J).

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🔹 Kinetic Energy

Energy possessed by a body due to its motion.$$KE = \frac{1}{2}mv^2$$KE=21​mv2

Where:

• $m$m = mass
• $v$v = velocity

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🔹 Work–Energy Theorem

The work done by a force on a body is equal to the change in its kinetic energy.

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🔹 Potential Energy

Energy possessed by a body due to its position or configuration.

Gravitational Potential Energy:

$$PE = mgh$$PE=mgh

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🔹 Conservative and Non-Conservative Forces

Conservative Forces:

• Path independent
• Energy conserved
  Example: gravitational force

Non-Conservative Forces:

• Path dependent
• Energy not conserved
  Example: friction

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🔹 Law of Conservation of Energy

Energy can neither be created nor destroyed; it can only be transformed from one form to another.

Example:

• Falling body
• Simple pendulum

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🔹 Power

Power is the rate of doing work.$$\text{Power} = \frac{\text{Work}}{\text{Time}}$$Power=TimeWork​

SI unit: watt (W)

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🔹 Average and Instantaneous Power

• Average Power = total work / total time
• Instantaneous Power = $F \cdot v$F⋅v

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🔹 Collision

Collision is an event where two bodies collide for a short time.

Types of Collision:

1. Elastic collision – kinetic energy conserved
2. Inelastic collision – kinetic energy not conserved

1. Elastic Collision

Definition:
A collision in which both momentum and kinetic energy are conserved.

Key Points:

• Momentum is conserved
• Kinetic energy is conserved
• Bodies regain their original shape after collision
• No energy lost as heat, sound, or deformation

Examples:

• Collision of gas molecules
• Collision of steel or glass balls (approximate)

Mathematical Conditions (1D):$$\text{Momentum: } m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$$Momentum: m1​u1​+m2​u2​=m1​v1​+m2​v2​ $$\text{Kinetic Energy: } \frac{1}{2}m_1u_1^2 + \frac{1}{2}m_2u_2^2 = \frac{1}{2}m_1v_1^2 + \frac{1}{2}m_2v_2^2$$Kinetic Energy: 21​m1​u12​+21​m2​u22​=21​m1​v12​+21​m2​v22​

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🔹 2. Inelastic Collision

Definition:
A collision in which momentum is conserved but kinetic energy is not conserved.

Key Points:

• Momentum is conserved
• Kinetic energy is partially lost as heat, sound, or deformation
• Bodies may stick together (perfectly inelastic) or separate (partially inelastic)

Examples:

• Car crashes
• Clay balls colliding

Special Case – Perfectly Inelastic Collision:

• Bodies stick together after collision
• Maximum kinetic energy is lost
• Move with a common velocity after collision

$$v_{\text{common}} = \frac{m_1u_1 + m_2u_2}{m_1 + m_2}$$vcommon​=m1​+m2​m1​u1​+m2​u2​​

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🔹 Quick Comparison Table

Feature	Elastic Collision	Inelastic Collision
Momentum	Conserved	Conserved
Kinetic Energy	Conserved	Not conserved
Bodies After Collision	Separate, retain shape	May stick or deform
Energy Lost	None	Yes (heat, sound, deformation)
Example	Gas molecules, steel balls	Clay balls, car crashes
Coefficient of Restitution (e)	e = 1	e < 1