Physics · Class 11

Momentum after release

The spring pushes both carts internally. With no external impulse, total momentum remains its initial value, even while spring energy becomes kinetic energy. From rest, momenta are opposite. With an initial common drift, the centre of mass continues moving at that drift velocity.

Open the interactive experiment →

Track momentum through an internal release.

வெளிப்புற உந்தம் இல்லாத அமைப்பின் மொத்த உந்தம் மாறாது. சுருள் ஆற்றல் இயக்க ஆற்றலாக மாறினாலும் நிறை மைய வேகம் மாறாது.

Key notes, relationships and model limits

Key relationship

mAvA + mBvB = (mA + mB)U; ½μ(vB − vA)² = Espring; μ = mAmB/(mA + mB).

Remember

Common trap

Zero total momentum does not mean both carts are stationary.

Model limits

Massless spring releases all stored energy instantaneously at t = 0. No external horizontal impulse or friction. Cart velocities include the initial common drift.

What you will learn

Conserve system momentum and distinguish it from kinetic-energy conservation during release.

Try the experiment

Compare rest and moving-platform presets. Change one mass and inspect momenta and kinetic energy.

Think of it this way

Two riders push apart on a moving train; their separation changes while their shared centre follows the train.

Worked example

For masses 2 and 4 kg and spring energy 12 J, relative speed is √18 = 4.24 m/s; final speeds from rest are −2.83 and +1.41 m/s.

Why this matters

Momentum and energy constrain different parts of a many-body problem; use both only when their assumptions hold.

Before you start

Vector components · velocity · SI units

Check your understanding

A spring releases two carts from rest without external impulse. Their final momenta are…

Equal and in the same direction
Equal in magnitude and opposite
Zero for each cart

Read the explanation

The initial total momentum is zero, so pA + pB = 0 after release.

Course connection: CBSE XI Chapter 4; NEET/Main Unit 3; JEE Advanced Mechanics. Apply each exam’s stated assumptions.