# Elastic Collision Formula

Elastic Collision Formula

An elastic collision is a collision where both kinetic energy, KE, and momentum, p, are conserved. This means that KE0 = KEf and po = pf. Recalling that KE = 1/2 mv2, we write 1/2 m1(v1i)2 + 1/2 m2(vi)2 = 1/2 m1(v1f)2 + 1/2 m2 (v2f)2, the final total KE of the two bodies is the same as the initial total KE of the two bodies. And, since p = linear momentum = mv, then we write m1v1i + m2v2i = m1v1f + m2v2f.

[A] m1v1i + m2v2i = m1v1f + m2v2f

[B] 1/2 m1(v1i)2 + 1/2 m2(vi)2 = 1/2 m1(v1f)2 + 1/2 m2 (v2f)2

KE = kinetic energy

p = momentum

m = mass, kg

mi = mass of 1st object

m2= mass of 2nd object

v = velocity, m/s

v1 = velocity of 1st object

v2 = velocity of 2nd object

vi = initial velocity

vf = final velocity

Elastic Collision Formula Questions:

1) A red ball of mass 0.2 kg hits a blue ball of mass 0.25 kg, in an elastic collision, and the red ball comes to a stop. The red ball has a velocity of 5 m/s, and the blue ball was at rest. What is the final velocity of the blue ball?

Answer: The mass of the 1st ball, m1 = 0.2 kg; the mass of the 2nd ball, m2 = 0.20kg. The initial velocity of the 1st ball, v1i = 5 m/s; the initial velocity of the 2nd ball, v2i = 0; the final velocity of the 1st ball, (v1f) = 0.

m1v1i + m2v2i = m1v1f + m2v2f

(0.2 kg)(5 m/s) + (0.20 kg)(0 m/s) = (0.2 kg)(0) + (0.20 kg)(v2f)

1.0 kg.m/s + 0 = 0 + (0.20 kg)(v2f)

1.0 kg.m/s = (0.20 kg)(v2f)

(1.0 kg.m/s) / 0.2 kg = (v2f)

5 m/s = (v2f)

2) Use the equation for conservation of kinetic energy in an elastic collision to determine the final velocity for the blue ball.

Answer: The mass of the 1st ball, m1 = 0.2 kg; the mass of the 2nd ball, m2 = 0.20kg. The initial velocity of the 1st ball, v1i = 5 m/s; the initial velocity of the 2nd ball, v2i = 0; the final velocity of the 1st ball, (v1f) = 0.

1/2 m1(v1i)2 + 1/2 m2(vi)2 = 1/2 m1(v1f)2 + 1/2 m2 (v2f)2

1/2 (0.2 kg)(5m/s)2 + 1/2 (0.2 kg)(0) = 1/2 (0.2 kg)(0) + 1/2 (0.2 kg)(v2f)2

1/2 (0.2 kg)(5m/s)2 = 1/2 (0.2 kg)(v2f)2

(5m/s)2 = (v2f)2

25 m2/s2 = (v2f)2

v2f = √25 m2/s2

v2f = 5 m/s