Work, Energy & Power – SRMJEEE Physics Study Notes
(Prepared for quick revision & in‑depth understanding)
1. Simple Explanation
| Concept | What it means | When it is used |
|---|---|---|
| Work | The transfer of energy that occurs when a force moves an object in the direction of the force. | Whenever a force acts over a distance. |
| Energy | The capacity to do work. It comes in many forms (kinetic, potential, thermal, etc.). | To explain why objects move or change state. |
| Power | The rate at which work is done or energy is transferred. | When we care about how fast work is performed. |
2. Key Points
2.1 Work
-
Definition:
[ W = \vec{F}\cdot\vec{s} = Fs\cos\theta ] where ( \vec{F} ) is the applied force, ( \vec{s} ) is the displacement, and ( \theta ) is the angle between them. -
Units: Joule (J) = N·m.
-
Work by a variable force:
[ W = \int_{s_1}^{s_2} \vec{F}(s)\cdot d\vec{s} ] -
Work–Energy Theorem:
[ W_{\text{net}} = \Delta K = K_f - K_i ]
2.2 Kinetic Energy (KE)
- Definition: Energy of motion.
[ K = \frac{1}{2}mv^2 ] - Change in KE equals net work done on the object.
2.3 Potential Energy (PE)
| Type | Formula | Remarks |
|---|---|---|
| Gravitational (near Earth) | ( U_g = mgh ) | (h) is height above reference level |
| Elastic (spring) | ( U_s = \frac{1}{2}kx^2 ) | (k) = spring constant, (x) = extension/compression |
| General potential | ( U = -\int \vec{F}_\text{conservative}\cdot d\vec{s} ) | Work done by conservative forces is negative change in PE |
2.4 Mechanical Energy (ME)
- Definition: Sum of kinetic and potential energies.
[ E_{\text{mech}} = K + U ] - Conservation Law:
If only conservative forces act, (E_{\text{mech}}) remains constant.
[ K_i + U_i = K_f + U_f ] - Non‑conservative work:
[ W_{\text{nc}} = \Delta E_{\text{mech}} ]
2.5 Power
- Instantaneous Power:
[ P = \frac{dW}{dt} = \vec{F}\cdot\vec{v} ] - Average Power:
[ P_{\text{avg}} = \frac{W_{\text{total}}}{\Delta t} ] - Electrical Power (useful for SRMJEEE):
[ P = I^2R = \frac{V^2}{R} = VI ] (All in watts, W)
3. Worked Example
Problem (Typical SRMJEEE style)
A 2‑kg mass is pulled horizontally on a frictionless table by a constant force of 12 N for a distance of 5 m. The force is applied at an angle of (30^\circ) above the horizontal. Calculate:
- Work done by the force.
- Change in kinetic energy of the mass.
- Final speed of the mass.
- Average power delivered by the force if the displacement took 4 s.
Solution
-
Work Done
[ \theta = 30^\circ,\quad F = 12,\text{N},\quad s = 5,\text{m} ] [ W = Fs\cos\theta = 12 \times 5 \times \cos 30^\circ ] [ \cos 30^\circ = \frac{\sqrt{3}}{2} \approx 0.866 ] [ W \approx 12 \times 5 \times 0.866 = 52.0,\text{J} ] -
Change in Kinetic Energy
By Work–Energy Theorem:
[ \Delta K = W = 52,\text{J} ] -
Final Speed
Initial speed (v_i = 0) (mass