Momentum Animation

Click, drag, release!

images/momentum.js

Try this: Drag the balls and let them collide. Then change the elasticity setting. What happens when it is 0? What about 1?

Explanation

Collisions can be on a scale of 0 (Inelastic) to 1 (Elastic).

A ball of dough splatting flat on a floor (inelastic) next to a rubber ball bouncing high (elastic).

Inelastic collisions are mushy (like dough balls)
Elastic collisions are bouncy (like rubber balls)

In the Gravity Animation, the collisions are either inelastic (two objects smashing into each other) or elastic (the objects swing around each other and head off again).

Formula

The formulas used in this animation are:

new v_a = elast × m_b(v_b − v_a) + m_av_a + m_bv_bm_a + m_b

new v_b = elast × m_a(v_a − v_b) + m_av_a + m_bv_bm_a + m_b

Where:

elast = "Coefficient of Restitution", 0=inelastic, 1=elastic
v_a and m_a are the velocity and mass of object a
v_b and m_b are the velocity and mass of object b

Let's see how these formulas work:

Example: Collision! 2 kg at 3 m/s hits 1kg at rest

Ball A: mass (m_a) = 2 kg, moving at velocity (v_a) = 3 m/s
Ball B: mass (m_b) = 1 kg, at rest (v_b) = 0 m/s
Elasticity (elast) = 1 (perfectly bouncy)

Let's calculate the new velocity of Ball A:

new v_a = 1 × 1 × (0 − 3) + 2 × 3 + 1 × 02 + 1

new v_a = −3 + 6 + 03 = 33 = 1 m/s

Now let's calculate the new velocity of Ball B:

new v_b = 1 × 2 × (3 − 0) + 2 × 3 + 1 × 02 + 1

new v_b = 6 + 6 + 03 = 123 = 4 m/s

After the collision, Ball A slows down to 1 m/s, and Ball B shoots forward at 4 m/s!