image below cc106-20 Consider a head-on elastic collision involving two particle

Question

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cc106-20 Consider a head-on elastic collision involving two particles. Before the collision, the smaller mass m1 is moving with velocity v = 1 m/s. toward the larger mass m2. After the collision, m2 moves with velocity V2, and m1 recoils, moving with negative velocity v1. Write the equations for momentum conservation and energy conservation. (The only energies here are the kinetic energies of the particles.) Solve the equations for v1 and v2. Suppose m1 = 0.54 m2. Evaluate v1 and v2.

Explanation / Answer

(A)

MOMENTUM CONSERVATION

m1 * v0 = m1 * (-v1) + m2 * v2

ENERGY CONSERVATION

(1/2)*m1 * (v0)^2 = [(1/2)*m1 * (v1)^2 ] + [ (1/2)*m2 * (v2)^2 ]

(B)

v1 = (v0*(m2 - m1))/(m1 + m2)

v2 = (2*m1*v0)/(m1 + m2)

(C)

v1 = 0.2987 v0

v2 = 0.013 v0

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