Lesson 7 – Momentum & Collisions

Stage 1: Intermediate Complete Notes
Page 5 – Coefficient of Restitution

The coefficient of restitution is a quantity that tells us how elastic or inelastic a collision is. It is extremely important for both Intermediate exams and IIT-JEE.

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1️⃣ What is Coefficient of Restitution?

The coefficient of restitution (denoted by e) is defined as the ratio of relative velocity of separation to relative velocity of approach along the line of impact.

e = (Relative velocity of separation)
    / (Relative velocity of approach)

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2️⃣ Mathematical Expression (1-D Collision)

For two bodies moving along the same straight line:

e = (v₂ − v₁) / (u₁ − u₂)

where:

• u₁, u₂ → velocities before collision
• v₁, v₂ → velocities after collision

👉 Velocities must be taken along the line of collision.

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3️⃣ Values of Coefficient of Restitution

e = 1 → Perfectly elastic collision
0 < e < 1 → Inelastic collision
e = 0 → Perfectly inelastic collision

The value of e always lies between 0 and 1.

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4️⃣ Physical Meaning of Coefficient of Restitution

The value of e indicates how much kinetic energy is retained after collision.

• Higher value of e → More elastic collision
• Lower value of e → More energy loss

👉 e measures the bounciness of collision.

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5️⃣ Special Case: Perfectly Inelastic Collision

In a perfectly inelastic collision:

✔ Bodies stick together after collision
✔ Relative velocity of separation = 0
✔ Hence, e = 0

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6️⃣ Coefficient of Restitution & Conservation Laws

In all collisions:

• Momentum is conserved
• Energy may or may not be conserved

👉 Coefficient of restitution helps us distinguish between elastic and inelastic collisions.

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7️⃣ Important Exam Points

✔ e is dimensionless
✔ Depends on nature of materials
✔ Independent of masses of bodies
✔ Used with momentum conservation to solve problems

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📌 Page 5 Summary

✔ e = separation speed / approach speed
✔ e = 1 → elastic collision
✔ e = 0 → perfectly inelastic collision
✔ Key parameter in collision problems

👉 Next page: One-Dimensional Collision Problems (Solved Examples)