Q.A body of mass 1 kg is thrown upwards with a velocity $20\ \mathrm{m\,s^{-1}}$. It momentarily comes to rest after attaining a height of 18 m. How much energy is lost due to air friction? (Take $g = 10\ \mathrm{m\,s^{-2}}$) (AIPMT 2009)

Conservation of Mechanical Energy

The Intuition First

Imagine you're holding a heavy stone at shoulder height. Your arm is tired. That stone has potential energy — energy stored because of its position. Now let it go. As it falls, it speeds up. The potential energy is turning into kinetic energy — the energy of motion. Just before it hits the ground, all the original potential energy has become kinetic energy.

Now imagine the reverse: you throw a ball straight up. It leaves your hand fast (lots of kinetic energy), rises, slows down, stops for an instant at the top (zero kinetic energy), then falls back. At the top, all the kinetic energy you gave it has turned back into potential energy.

This back-and-forth transformation — potential ↔ kinetic — is the heart of the idea. Energy doesn't disappear; it just changes form. That's conservation.

The Precise Statement

Total mechanical energy is the sum of kinetic energy ($K$) and potential energy ($U$):

The law says:

Or, in symbols:

What This Means in Practice

Let's go back to the falling stone. Suppose you hold it 5 metres above the ground. Its mass is 2 kg. Take $g = 10\ \text{m/s}^2$.

• At the top (initial):

  $K_i = 0$ (not moving)

  $U_i = mgh = 2 \times 10 \times 5 = 100\ \text{J}$

  $E_{\text{mech}} = 0 + 100 = 100\ \text{J}$

• Just before hitting ground (final):

  $U_f = 0$ (height = 0)

  $K_f = \frac{1}{2}mv^2$

  Conservation says $K_f = 100\ \text{J}$, so $\frac{1}{2} \times 2 \times v^2 = 100$, giving $v = 10\ \text{m/s}$.

You never needed to know the time of fall or acceleration. Energy conservation gave you the speed directly.

The Two Critical Conditions

If friction is present, some mechanical energy turns into heat (thermal energy). The total energy of the universe is still conserved, but mechanical energy alone is not.

A Simple Example to Cement It

A pendulum swings. At the highest point on either side, it stops momentarily — all energy is potential. At the lowest point, it moves fastest — all energy is kinetic. In between, it's a mix. If there were no air resistance or friction at the pivot, the pendulum would swing forever, with the same maximum height each time. That's mechanical energy being perfectly conserved.

The Big Picture

Conservation of mechanical energy is a shortcut. Instead of analysing forces and accelerations (which can be messy), you just track two numbers — kinetic and potential — and set their sum equal at two moments. It works because energy is a scalar (no direction), so you don't need vectors or free-body diagrams.

Final takeaway: Mechanical energy is never created or destroyed — only converted between kinetic and potential forms, as long as no friction or other non-conservative forces interfere.

Searches for "Conservation Of Mechanical Energy notes class 11" and "Conservation Of Mechanical Energy important questions" both point back to this same core idea, since Conservation Of Mechanical Energy is a syllabus-aligned topic under Work, Energy and Power in NCERT Class 11 Physics, making it a natural fit for both board exams and JEE/NEET practice sets. The clearest way to build exam confidence here is to combine this explanation with the NCERT Physics textbook's own solved examples and chapter-end questions.