Law of Conservation of Energy: The Big Picture

Physics · Work, Energy And Power · NEET

The law of conservation of energy says the total energy of an isolated system stays the same. Energy is never made and never destroyed; it only changes from one form to another (like potential to kinetic, or kinetic to heat). Memory hook: "Energy just changes clothes, it never leaves the room."
Conservation of Energy: a ball falling from height Hground123PE = mgH, KE = 0PE + KE = mgH(half PE, half KE)PE = 0, KE = mgHv = sqrt(2gH)Total energy = mgH (constant)
As the ball falls, potential energy turns into kinetic energy, but the total (PE + KE) stays fixed at mgH. This is conservation of mechanical energy, a special case of the law of conservation of energy.

Your doubts, answered

Is 'conservation of mechanical energy' the same as the 'law of conservation of energy'?

No, and this is the most common mix-up. The law of conservation of energy is the big rule: TOTAL energy (all forms) is always constant. Conservation of MECHANICAL energy (KE + PE = constant) is a smaller special case that only holds when just conservative forces (like gravity or spring force) do work. If friction or air drag acts, mechanical energy drops, but the missing part turns into heat, so TOTAL energy is still conserved.

Where does the energy go when friction or air resistance acts?

It does not disappear. Non-conservative forces like friction and air drag convert mechanical energy (KE + PE) into heat and sound. In the 2017 NEET raindrop question, gravity gives 10 J but the drop lands with only 1.25 J of KE. The 'missing' 8.75 J was turned into heat by air resistance. Total energy stays the same, so the law of conservation of energy still holds.

If a ball rolling on the floor slowly stops, is its energy destroyed?

No. The kinetic energy is not destroyed, it is transformed. Friction between the ball and floor changes the KE into thermal energy (the floor and ball warm up very slightly) and a little sound. Add up all forms and the total is unchanged. Energy is never destroyed, only converted.

Why do we say kinetic energy is 'not conserved' in some collisions if energy is always conserved?

In an inelastic collision, kinetic energy is not conserved because some KE turns into heat, sound, or deformation. But total energy IS conserved. When a book says 'energy is lost', it means mechanical energy is lost from the moving objects, not that energy vanished from the universe.

When can I safely write mgh = (1/2)mv squared?

Only when non-conservative forces do no work, for example a smooth (frictionless) slide or a free fall in vacuum. Then all PE becomes KE, so mgh = (1/2)mv squared, giving v = sqrt(2gh). If friction or air drag is present, you must add a work-against-friction term, or use energy conservation with a heat loss term.

⚠️ The NEET trap
Assuming mechanical energy is always conserved, so writing mgh = (1/2)mv squared even when air resistance or friction is mentioned.
Total energy is always conserved, but mechanical energy is conserved ONLY with conservative forces. With friction or air drag, use Work-energy theorem: W_gravity + W_resistance = change in KE, and the resistance work is negative (heat).
🧠 See the words 'air resistance', 'friction', or 'rough' -> mechanical energy is NOT conserved. Total energy still is.

Real NEET questions

2017

Consider a drop of rain water having mass 1 g falling from a height of 1 km. It hits the ground with a speed of 50 m/s. Take g constant with a value 10 m/s squared. The work done by the (i) gravitational force and the (ii) resistive force of air is:

A · (i) 1.25 J (ii) -8.25 J
B · (i) 100 J (ii) 8.75 J
C · (i) -10 J (ii) -8.25 J
D · (i) 10 J (ii) -8.75 J
Solution: Given m = 1 g = 10^-3 kg, h = 1 km = 1000 m, v = 50 m/s, g = 10 m/s squared. Step 1: Work by gravity W_grav = mgh = (10^-3)(10)(1000) = 10 J. Step 2: Change in kinetic energy = (1/2)mv squared = (1/2)(10^-3)(50 squared) = (1/2)(10^-3)(2500) = 1.25 J. Step 3: Work-energy theorem says W_grav + W_air = change in KE, so W_air = 1.25 - 10 = -8.75 J. The negative sign means air resistance removed energy (turned it into heat), which is exactly the conservation-of-energy big picture. Answer: (i) 10 J, (ii) -8.75 J.
2021

A particle is released from height S from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of the Earth and the speed of the particle at that instant are respectively:

A · 3S/4 , sqrt(3gS/2)
B · S/4 , sqrt(3gS/2)
C · S/4 , 3gS/2
D · 3S/4 , 3gS/2
Solution: Take the ground as reference. Total energy at start = mgS (all potential, released from rest). Step 1: At height h, PE = mgh and KE = 3(PE) = 3mgh. By conservation of mechanical energy (free fall, no air drag): total = KE + PE = 3mgh + mgh = 4mgh. Set equal to start: 4mgh = mgS, so h = S/4. Step 2: KE = 3mgh = 3mg(S/4) = 3mgS/4. Also KE = (1/2)mv squared, so (1/2)mv squared = 3mgS/4, giving v squared = 3gS/2, so v = sqrt(3gS/2). Answer: h = S/4, v = sqrt(3gS/2).

Solved Work, Energy And Power NEET PYQs

Try the real previous-year questions from this chapter — each with the answer and a full solution.

See all 26 Work, Energy And Power NEET PYQs ›
Next concept: Work, Energy and PowerKeep learning — 2 minFeeling ready? Solve the Work, Energy And Power NEET PYQs ›Or practice on your phone — get the free MedicNEET app ›

Frequently asked

What is the law of conservation of energy in simple words?

Energy can neither be created nor destroyed; it can only change from one form to another. The total energy of an isolated system stays constant over time.

Is the law of conservation of energy always true?

Yes. For NEET it holds in every situation. Even when mechanical energy seems to be 'lost', it has just converted into heat, sound, or another form, so the total is always the same. At a deeper level, mass itself is a form of energy (E = mc squared).

What is the difference between conservation of energy and conservation of mechanical energy?

Conservation of energy applies to total energy in all cases. Conservation of mechanical energy (KE + PE = constant) is a special case that holds only when non-conservative forces such as friction do no work.

Does conservation of energy hold when there is friction?

Yes, total energy is still conserved. Mechanical energy decreases, but the lost amount appears as heat and sound. Add up all forms and the total does not change.

How is the law of conservation of energy used in NEET numericals?

You equate the total energy at two points, usually KE + PE at start equals KE + PE at end. If a non-conservative force acts, include its work: change in KE = work by all forces, as in the raindrop PYQ.