Lesson 7 – Momentum & Collisions

Stage 1: Intermediate Complete Notes
Page 10 – Loss of Kinetic Energy in Collisions

In many collisions, momentum is conserved but kinetic energy is not. This page explains how to calculate the loss of kinetic energy in inelastic collisions.

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1️⃣ Why Kinetic Energy is Lost?

During an inelastic collision, some kinetic energy is converted into:

• Heat
• Sound
• Deformation energy

👉 Momentum is always conserved, but energy may be lost.

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2️⃣ Expression for Loss of Kinetic Energy

Consider two bodies of masses m₁ and m₂ with initial velocities u₁ and u₂, and final velocities v₁ and v₂.

Loss of kinetic energy:

Loss = Initial KE − Final KE

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3️⃣ Important Result (Very Important for Exams)

The loss of kinetic energy in a one-dimensional collision is given by:

Loss of KE = ½ × (m₁m₂ / (m₁ + m₂)) × (u₁ − u₂)² × (1 − e²)

where e is the coefficient of restitution.

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4️⃣ Special Cases

Elastic collision (e = 1)
Loss of KE = 0

Perfectly inelastic collision (e = 0)
Loss of KE is maximum

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5️⃣ Numerical Example

Two bodies of masses 2 kg and 3 kg move with velocities 5 m/s and 1 m/s respectively. If the coefficient of restitution is 0.5, find the loss of kinetic energy.

u₁ − u₂ = 4 m/s

Loss = ½ × (2×3 / 5) × (4)² × (1 − 0.25)

Loss of KE = 7.2 J

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6️⃣ Exam Tips & Shortcuts

✔ If e = 1 → no energy loss
✔ Larger (u₁ − u₂) → greater loss
✔ Loss depends on masses and nature of collision

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📌 Page 10 Summary

✔ Kinetic energy is not always conserved
✔ Loss depends on coefficient of restitution
✔ Maximum loss in perfectly inelastic collision
✔ Highly important for board & IIT exams

👉 Stage 1 (Intermediate Notes) Completed
Next: Stage 2 – Board Exam Questions & Answers