PhysicsWork, energy and powerClass 11

Work, energy and power: interactive simulation

Energy is the bookkeeping of mechanics. Work moves energy in or out; inside a system it shifts between kinetic and potential forms, and friction turns some of it into heat that never comes back.

Useful for: JEE Main, JEE Advanced, NEET, CBSE Boards, AP Physics 1, A-level Physics, IB Physics · 4 modes in one lab

What you can explore

  1. 1

    Potential energy curve

    Double well, molecular bond and hill potentials with turning points, force and stable/unstable equilibrium.
  2. 2

    Loop-the-loop

    Release height, speed and normal force around a vertical loop, and where the ball leaves the track.
  3. 3

    Spring & friction

    Spring energy turning into kinetic energy and then heat, with energy bars.
  4. 4

    Work & power

    Work as the area under an F–x graph, and motion at constant power.

Try this

Watch a particle roll in a potential energy landscape, find the lowest start for a loop-the-loop, follow every joule from a spring into heat, and measure work as an area.

  1. 1

    In the double well, start from x = −1.5.

    What you should see

    The particle crosses the central hill because its energy is above the unstable equilibrium at x = 0.

  2. 2

    Turn on friction.

    What you should see

    Each swing is lower; it ends up trapped in one of the two stable minima at x = ±1.

  3. 3

    In Loop-the-loop with R = 1 m, release from 2.7 m and then from 2 m.

    What you should see

    From 2.7 m it completes the loop with about 3.7 m/s at the top; from 2 m it leaves the track before the top.

  4. 4

    In Spring & friction, use k = 200 N/m, x₀ = 0.2 m, m = 1 kg, μ = 0.2.

    What you should see

    4 J is stored, and the block slides about 4 / (0.2 × 1 × 9.8) ≈ 2.04 m in total before stopping.

  5. 5

    In Work & power, choose F = kx and drag x.

    What you should see

    The shaded triangle grows as x², matching W = ½kx².

Formulas behind it

Work–energy theorem

Wnet=ΔKW_{net} = \Delta K

Force from potential energy

F=−dUdxF = -\frac{dU}{dx}

Stable equilibrium

dUdx=0,d2Udx2>0\frac{dU}{dx} = 0,\quad \frac{d^2U}{dx^2} > 0

Loop-the-loop (frictionless)

hmin=52Rh_{min} = \tfrac{5}{2}R

Spring energy

U=12kx2U = \tfrac{1}{2}kx^2

Work by a variable force

W=∫F dxW = \int F\,dx

Constant power from rest

v=2Ptmv = \sqrt{\frac{2Pt}{m}}

Common mistakes

  • Saying the normal force or tension always does no work. They do no work only when they are perpendicular to the motion.
  • Forgetting that friction acts during the whole motion, including while a spring is still pushing.
  • Using h = 2R as the minimum height for a loop. The ball also needs speed √(gR) at the top, so h must be 2.5R.
  • Calling a maximum of U(x) a stable equilibrium.
Practise 183 questionsCheck your answer instantly, with a worked solution.Stuck on a work, energy and power question?Snap it and get a whiteboard video solution.

FAQ

Can kinetic energy be negative?

No. K = ½mv² is never negative, which is why a particle can only be found where its total energy is at least the potential energy.

Is work done by friction always negative?

Kinetic friction on a sliding body does negative work relative to the surface. But friction can do positive work on a body — for example on a box sitting on an accelerating truck.

Why does the speed grow more slowly under constant power?

P = Fv, so as v rises the available force P/v falls, and the acceleration P/(mv) keeps decreasing.

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