Coefficient of Restitution
Drop a ball — each bounce loses energy; heights scale as h₀·e^(2n).
Key Notes
Coefficient of restitution e is the ratio of relative speed AFTER collision to relative speed BEFORE: e = |v_2 − v_1|/|u_1 − u_2|.
Range: 0 ≤ e ≤ 1. e = 1: perfectly elastic. e = 0: perfectly inelastic (objects stick together). 0 < e < 1: partially elastic.
Property of MATERIALS — not just objects. Different surface pairs have different e.
Typical values: glass-glass ~0.95, steel-steel ~0.7-0.9, basketball-floor ~0.75, clay-clay ~0.1-0.2.
Determines bounce height: h_n = e^(2n) × h₀ for n bounces.
Ratio of bounce heights: h_after/h_before = e². Direct experimental method.
In oblique collisions: e applies only to NORMAL component of velocity; tangential component (if smooth) is unchanged.
e depends slightly on relative speed and surface conditions — not a constant in all situations.
Formulas
Definition
Ratio of separation speed to approach speed.
Bounce height ratio
Useful experimentally (drop a ball, measure bounce).
Heights after n bounces
Geometric sequence — each bounce takes a fraction e² of previous height.
KE conservation in 1D collision
e < 1 ⇒ KE is lost.
Important Points
e ranges 0 to 1. NOT negative. e > 1 would mean colliding bodies gain energy — physically impossible without an external source.
e is a SURFACE-PAIR property, not just an object property. e(steel-steel) ≠ e(steel-rubber).
Dropped ball reaching ½ its initial height after one bounce ⇒ e² = ½ ⇒ e ≈ 0.707.
Repeated bounces: total distance traveled = h₀ × (1+e²)/(1−e²). Total time finite even though number of bounces is infinite (Zeno-like sum).
Tennis, basketball, golf — sport regulations set tight bounds on e of balls and surfaces.
Microscopic origin: how much elastic deformation energy is recovered vs lost to heat.
Coefficient of Restitution notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.