Two spheres of equal radius with masses m1=5 kg and m2=20 kg are moving towards

Question

Two spheres of equal radius with masses m1=5 kg and m2=20 kg are moving towards each other along the same straight line along a friction less, horizontal surface. V1i=+10m/s V2i=-5m/s and during the collision 25% of the total initial kinetic energy is lost

A-what are the initial and final kinetic energies in the center of mass frame?

B-What are the final velocities of the two objects in the center of mass reference frame?

C-What are the final velocities of the two objects in the lab reference frame?

Explanation / Answer

BY THE conservationof momentum

initial mometum = final momentum

5*10 + 20*(-5) = 5v1 + 20v2

v1 + 4v2 = -12.5 ------(1)

velocity of approach = velocity of recess

v2 -v1 = u1 - u2

v2 - v1 = 10 - (-5) = 15 ------(1)

adding both equation we have

5v2 = 2.5

v2 = 0.5 m/s

v1 = v2 -15 =0.5-15 = -14.5 m/s

final velocity of the object in lab reference frame = -14.5 , 0 .5

A) Velocity of COM = m1u1 + m2u2/m1+m2 = 5*10 + 20(-5) / 5+20 = -2 m/s

initial KE = 0.5(M+m)Vc^2 = 0.5*(5+20)*2^2 = 50 J

25% of inital KE is lost in collision

so final KE = 0.75*50 = 37.5 J

B) final velocity of the objects in centre of mass reference frame = -2m/s

C)final velocity of the masses in lab reference frame

mass 5 kg = -14.5 m/s

mass 20 kg =0.5 m/s

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