Work–Energy TheoremJEE Main

Net work equals the change in kinetic energy — interactive Physics simulation for IIT-JEE.

Concept

The work–energy theorem says the net work done by all forces equals the change in kinetic energy: $W_{net} = \Delta KE$ . It is Newton's second law integrated over distance — a scalar shortcut that skips acceleration and time entirely.

Key formula

W_{net} = \Delta KE = \tfrac{1}{2}mv^2 - \tfrac{1}{2}mu^2, \qquad W = \vec{F}\cdot\vec{d} = Fd\cos\theta

Derivation

Start from $F_{net} = ma$ and use $v\,dv = a\,dx$ :

$ $\int F_{net}\,dx = m\int_u^v v\,dv = \tfrac{1}{2}mv^2 - \tfrac{1}{2}mu^2$ $

Here the applied force does $+Fd$ , friction does $-\mu mg\,d$ , and normal force & gravity do zero work (perpendicular to motion).

Scenarios to explore

Work–Energy Theorem — Net work equals ΔKE — with friction eating its share.

Real-world applications

Stopping distances of vehicles (brakes do negative work).
Pile drivers and hammers — KE converted to deformation work.
Ballistics: muzzle energy vs penetration depth.

JEE exam tips

Work-energy is frame-dependent: apply it in one inertial frame throughout.
For variable forces, W = area under the F–x graph.
If KE hits zero mid-path, the block stops there — check before plugging d blindly.

Common mistakes

Counting only the applied force — the theorem needs the NET work.
Giving friction positive work (it opposes sliding, so its work is negative here).
Using cos θ with the wrong angle — θ is between force and displacement.

Exam traps to avoid

Normal reaction and centripetal forces do zero work — speed unchanged by them.
Negative net work means the block ends SLOWER, even if it still moves forward.