Question

A 0.141kg glider is moving to the right on a frictionless, horizontal air track with a speed of 0.900m/s . It has a head-on collision with a 0.302kg glider that is moving to the left with a speed of 2.25m/s . Suppose the collision is elastic

Find the magnitude of the final velocity of the 0.302kg glider

Answer 1

Let

M₁=mass of 0.141 kg glider

M₂=mass of 0.302 Kg glider

V_1i=Initial Velocity of glider of 0.141 kg ==0.9 m/s

V_2i=Iniitial Velocity of glider 0.302 Kg=-2.2 m/s

By conservation of momentum

m₁V_1i+m₂V_2i=m₁V_1f+m₂V_2f

0.141*0.9-0.302*2.25=0.141V_1f+0.302V_2f

0.141V_1f+0.302V_2f=-0.5526

V_1f=(1/0.141)[-0.5526-0.302V_2f]----------------------1

By Conservation of energy

(1/2)[m₁V_1i²+m₂V_2i²]=(1/2)[m₁V_1f²+m₂V_2f²]

[0.141*0.9²+0.302*(-2.25)²]=0.141V_1f²+0.302V_2f²

1.643=0.141*(1/0.141)²[-0.5526-0.302V_2f]²+0.302V_2f²

1.643=(1/0.141)(0.3054+0.3338V_2f+0.0912V_2f²)+0.302V_2f²

1.643=2.1657+2.367V_2f+0.6468V_2f²+0.302V_2f²

0.9488V_2f²+2.367V_2f+0.5227=0

V_2f=-0.245 m/s