“No time, use energy”
Choosing between kinematics and energy
If the question mentions speed and height but never time, the energy method is shorter. If it asks about time, go back to the equations of motion.
Class 11 Physics · Gujarat Board, CBSE, GUJCET and JEE
Work, Energy and Power formulas
Work, energy and power gives you a second way to solve mechanics problems, and it is usually the shorter one. When a question gives speeds and heights but no time, the energy method will beat the equations of motion every time.
17 formulas, 3 memory hooks, and the 5 mistakes that cost the most marks.
Work
| What | Formula | Symbols and notes |
|---|---|---|
| Work by a constant force | W = Fs cosθ | θ is the angle between force and displacement |
| Work by a variable force | W = ∫F dx | the area under a force-displacement graph |
| Work by a spring | W = ½kx² | the work done against the spring in stretching it by x |
| Work by gravity | W = −mgh going up, +mgh coming down | depends only on the height difference, not the path |
Energy
| What | Formula | Symbols and notes |
|---|---|---|
| Kinetic energy | KE = ½mv² = p²/2m | always positive; p is momentum |
| Gravitational potential energy | PE = mgh | near the Earth's surface, measured from a chosen level |
| Elastic potential energy | U = ½kx² | k is the spring constant, x the extension or compression |
| Work-energy theorem | Wnet = ΔKE = ½mv² − ½mu² | net work equals the change in kinetic energy, always |
| Conservation of mechanical energy | KE + PE = constant | only when no friction or other non-conservative force acts |
Power
| What | Formula | Symbols and notes |
|---|---|---|
| Average power | Pav = W/t | one watt is one joule per second |
| Instantaneous power | P = F·v = Fv cosθ | the dot product of force and velocity |
| Power of a pump | P = mgh/t = ρVgh/t | lifting a volume V of liquid of density ρ through height h |
Collisions
| What | Formula | Symbols and notes |
|---|---|---|
| Coefficient of restitution | e = (v₂ − v₁)/(u₁ − u₂) | relative speed after, over relative speed before |
| Perfectly elastic collision | e = 1, KE conserved | for equal masses the velocities are simply exchanged |
| Perfectly inelastic collision | e = 0, bodies move together | v = (m₁u₁ + m₂u₂)/(m₁ + m₂) |
| Elastic collision, unequal masses | v₁ = ((m₁ − m₂)u₁ + 2m₂u₂)/(m₁ + m₂) | momentum and kinetic energy both conserved |
| Height after n bounces | hn = e2nh | for a ball dropped from height h |
Taught by Darshit Bhatt, founder and lead faculty at Darshit Sir Institute. Instrumentation and Control engineer, with a master's degree and a chartered degree, teaching in Paldi, Ahmedabad since 2006.
Know the formula but not when to use it?
Darshit Sir has taught this in Paldi since 2006, in the classroom and live online.
Memory hooks
How to remember this chapter.
“Momentum always, energy sometimes”
Collisions
Momentum is conserved in every collision. Kinetic energy is conserved only if the collision is elastic. Write the momentum equation first, always.
“Perpendicular means no work”
When work is zero
A force at 90° to the displacement does no work. That is why the normal reaction, the tension in a circular path and the magnetic force on a moving charge all do zero work.
Where marks go
The mistakes that cost the most.
- Calling work a vector. Work is a scalar, and it can be negative, as friction always shows.
- Using conservation of mechanical energy on a rough surface. With friction present, the loss equals the work done against friction.
- Assuming kinetic energy is conserved in every collision. It is not, unless the collision is stated to be elastic.
- Writing potential energy without saying from where. PE is measured from a reference level you must choose and state.
- Mixing up average and instantaneous power in a question that gives a velocity at one instant.
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