Coefficient of Restitution and Rebounds
The coefficient of restitution is the relative speed of separation divided by the relative speed of approach along the line of impact, with 0<=e<=1 for ordinary passive impacts.
Why this shows up in the exam
Ball-floor rebounds · Repeated wall impacts · Oblique impacts with smooth surfaces
Learn the idea
Restitution compares separation speed with approach speed along impact. A bounce remembers the normal relative-speed ratio through e; tangential motion needs a separate smoothness or friction condition.
🧠 Memory hook: Approach becomes separation, scaled by e.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- e = (v₂-v₁)/(u₁-u₂) — one-dimensional signed restitution
- h_rebound = e² h_drop — vertical bounce under uniform gravity
- v_n,after = -e v_n,before — impact with a fixed smooth surface
How to approach it
- 1Mark the line of impact
- 2Write signed approach and separation velocities
- 3Combine restitution with momentum or flight energy
Common slip-ups that cost marks
- •Using speed magnitudes without direction
- •Applying e to tangential velocity
- •Assuming e equals retained energy fraction
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A 2 kg body speeds up from 3 m/s to 7 m/s. What net work is done on it?
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