Collision

Elasticity

---

For example, there is a drastic contrast of elasticity between a small rubber ball and a handful of dough. One is highly elastic and the other is highly inelastic. So when describing collisions, one can qualitatively state that the collision is either elastic, or inelastic.

Now, to quantitatively explain elasticity, there is the coefficient of restitution for two objects in a head-on, direct collision:

e = -(v_1f - v_2f)/(v_1i - v_2i)

Using the equation, If e=1 (perfectly elastic collisions), the relative velocity before impact equals in magnitude the relative velocity after impact. And if e=0 (perfectly inelastic collisions) the two bodies adhere after impact. Steel against steel has a high value for e whereas fabric is almost inelastic. In real life, the values of e for all things fall somewhere in the interval of 0 < e < 1.

Impulse

A cue at rest struck by the player achieves a velocity in a relatively short span of time. When the collision or impact occurs the ball is deformed and large internal stresses are created. These stresses tend to restore the ball to its original shape and it is the combined effect of these stresses which cause the ball to jerk forward.
Mathematically speaking, an impulse is equivalent to:


From the above equation, we see that impulse is the total force from t=0 to t=t, or the change in the linear momentum.
Home/Next