Work, Energy and Power
CBSE Class 11 Physics • Chapter 05
Chapter Overview
This chapter covers the fundamental concepts of Work, Energy and Power. Ensure you
understand the definitions and derivations thoroughly.
05.1 Work & Kinetic Energy
- Work ($W$): Scalar product of Force and Displacement. $W = \vec{F} \cdot \vec{d} = Fd \cos \theta$.
- SI Unit: Joule (J). [Dimensional Formula: $M L^2 T^{-2}$].
- Types of Work:
- Positive: $0 \le \theta < 90^\circ$ (Force favours motion).
- Negative: $90^\circ < \theta \le 180^\circ$ (Force opposes motion, e.g., Friction).
- Zero: $\theta = 90^\circ$ (e.g., Centripetal force).
05.6 Work-Energy Theorem
Statement: Work done by all forces on a body equals change in its Kinetic Energy.
$$ W_{net} = \Delta K = K_f - K_i $$
Proof (Constant Force): $v^2 - u^2 = 2as \Rightarrow \frac{1}{2}mv^2 - \frac{1}{2}mu^2 = ma \cdot s = Fs = W$.
For Variable Force: $W = \int_{x_i}^{x_f} F(x) dx$. (Area under F-x graph).
05.7 Potential Energy & Conservation
- Potential Energy ($U$): Energy possessed by virtue of position or configuration.
- Gravitational PE: $U = mgh$ (near Earth surface).
- Spring PE: $U = \frac{1}{2}kx^2$ (where $k$ is spring constant).
Conservation of Mechanical Energy: For conservative forces, total mechanical energy ($E = K + U$) is constant.
$\Delta K + \Delta U = 0 \Rightarrow K_i + U_i = K_f + U_f$.
Example (Free Fall): At height $H$, $E=mgH$. At ground, $E = \frac{1}{2}mv^2$. Since $v^2=2gH$, $E$ is conserved.
05.1 Work & Kinetic Energy
- Work ($W$): Scalar product of Force and Displacement. $W = \vec{F} \cdot \vec{d} = Fd \cos \theta$.
- SI Unit: Joule (J). [Dimensional Formula: $M L^2 T^{-2}$].
- Types of Work:
- Positive: $0 \le \theta < 90^\circ$ (Force favours motion).
- Negative: $90^\circ < \theta \le 180^\circ$ (Force opposes motion, e.g., Friction).
- Zero: $\theta = 90^\circ$ (e.g., Centripetal force).
05.6 Work-Energy Theorem
Statement: Work done by all forces on a body equals change in its Kinetic Energy.
$$ W_{net} = \Delta K = K_f - K_i $$
Proof (Constant Force): $v^2 - u^2 = 2as \Rightarrow \frac{1}{2}mv^2 - \frac{1}{2}mu^2 = ma \cdot s = Fs = W$.
For Variable Force: $W = \int_{x_i}^{x_f} F(x) dx$. (Area under F-x graph).
05.7 Potential Energy & Conservation
- Potential Energy ($U$): Energy possessed by virtue of position or configuration.
- Gravitational PE: $U = mgh$ (near Earth surface).
- Spring PE: $U = \frac{1}{2}kx^2$ (where $k$ is spring constant).
Conservation of Mechanical Energy: For conservative forces, total mechanical energy ($E = K + U$) is constant.
$\Delta K + \Delta U = 0 \Rightarrow K_i + U_i = K_f + U_f$.
Example (Free Fall): At height $H$, $E=mgH$. At ground, $E = \frac{1}{2}mv^2$. Since $v^2=2gH$, $E$ is conserved.
05.10 Power & Collisions
- Power ($P$): Rate of doing work. $P = \frac{dW}{dt} = \vec{F} \cdot \vec{v}$.
- SI Unit: Watt (W). 1 HP = 746 W.
Collisions:
- Elastic: Momentum and Kinetic Energy both conserved. (e.g., Atomic collisions).
- Inelastic: Only Momentum conserved. KE is lost. (e.g., Mud ball hitting wall).
- Coefficient of Restitution ($e$): $e = \frac{|v_2 - v_1|}{|u_1 - u_2|} = \frac{\text{Separation Speed}}{\text{Approach Speed}}$.
- Elastic: $e=1$. Perfectly Inelastic: $e=0$.
1D Elastic Collision Velocities:
$v_1 = \left( \frac{m_1 - m_2}{m_1 + m_2} \right) u_1 + \left( \frac{2m_2}{m_1 + m_2} \right) u_2$.
$v_2 = \left( \frac{2m_1}{m_1 + m_2} \right) u_1 + \left( \frac{m_2 - m_1}{m_1 + m_2} \right) u_2$.
Q: A body of mass 2kg moving at 10 m/s collides head-on elastically with a stationary body of mass 3kg. Find final velocities.
Ans: $m_1=2, u_1=10, m_2=3, u_2=0$.
$v_1 = \left( \frac{2-3}{2+3} \right)(10) + 0 = \frac{-1}{5}(10) = \mathbf{-2 \text{ m/s}}$. (Rebounds)
$v_2 = \left( \frac{2(2)}{2+3} \right)(10) + 0 = \frac{4}{5}(10) = \mathbf{8 \text{ m/s}}$.
Study Tip: Master the derivations in this chapter as they are frequently asked in exams.
Practice numericals based on the formulas.
