Work, energy and power (Class 11): theorem, collisions and conservation
Energy is the bookkeeping of physics: it changes form but the total stays the same. The labs let you push a block, compress a spring, crash two trolleys and a bullet into a pendulum, and check the energy and momentum before and after.
NCERT Class 11 Physics, Chapter 5 (Work, Energy and Power). Every lab below runs in 3D in your browser or on a phone, in English and Hindi.
Try the labs
Work-energy theorem on a rough track · plan · Chapter 5
To verify the work–energy theorem: net work done on a body equals its change in kinetic energy.
Elastic and inelastic collisions in 1D and 2D · plan · Chapter 5
To study elastic and inelastic collisions in one and two dimensions and verify conservation of linear momentum.
Ballistic pendulum: bullet speed from the swing · plan · Chapter 5
To use a ballistic pendulum to find the speed of a bullet and to study the energy lost in a perfectly inelastic collision.
Spring potential energy and power · plan · Chapter 5
To study elastic potential energy stored in a spring, work done by a variable force and its conversion to kinetic energy.
Newton's cradle: elastic collisions in a chain · plan · Chapter 5
To explain Newton's cradle using conservation of momentum and kinetic energy in elastic collisions of equal masses.
Power of an engine: P = Fv, top speed and acceleration · plan · Chapter 5
To understand mechanical power P = F·v and how the top speed of a vehicle is fixed by the balance of engine power and resistive forces.
Motion in a vertical circle (death-well / loop-the-loop) · plan · Chapter 5
To study motion in a vertical circle, find the minimum speeds needed to complete the circle and understand how tension/normal force vary along the path.
Work and the work–energy theorem
Work is the dot product of force and displacement. The net work done on a body equals its change in kinetic energy, even when the force varies.
W = F · s = F s cos θW = ΔK = ½mv² − ½mu²P = W/t = F · v
Potential energy and conservation
In a conservative field, such as gravity or a spring, the sum of kinetic and potential energy is constant. A spring stores ½kx²; a mass at height h stores mgh. In a vertical circle the body just completes the loop if the speed at the bottom is √(5gr).
U = mghU = ½ k x²vbottom = √(5 g r) for a string
Collisions
Momentum is conserved in every collision. In an elastic collision kinetic energy is also conserved; in an inelastic one some becomes heat and sound. In a perfectly inelastic collision the bodies move together. The coefficient of restitution e is 1 for elastic and 0 for perfectly inelastic.
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂e = (v₂ − v₁) / (u₁ − u₂)v = (m₁u₁ + m₂u₂)/(m₁ + m₂) (perfectly inelastic)
Frequently asked questions
Is work done by the centripetal force zero?
Yes. The force is perpendicular to the velocity, so it changes the direction but not the speed.
Is momentum conserved in an inelastic collision?
Yes, always, if no external force acts. Only kinetic energy is lost.
How does a ballistic pendulum measure bullet speed?
The bullet embeds in the block (momentum conserved, energy not). The block then swings up and the rise h gives the speed after impact, from which v = (M + m)√(2gh)/m.
What is the unit of power?
The watt, one joule per second. One horsepower is about 746 W.