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

m1 = 5kg , m2 = 20 kg

v1i = 10 m/s , v2i = -5m/s

(A) Ki -Kf = 0.25Ki

0.75 Ki = Kf

Ki = (1/2)m1v1i^2 +(1/2)m2v2i^2

Ki = (0.5*5*10*10) +(0.5*20*-5*-5)

Ki = 500 J

Kf = 0.75*500 = 375 J

(B) From conservation of momentum

m1v1i+m2v2i =m1v1f+m2v2f

(5*10)+(20*-5) = (5*v1f) +(20*v2f)

-50 = 5v1f+20v2f ... (1)

Kf = (1/2)m1v1f^2 +(1/2)m2v2f^2

375 = (0.5*5*v1f^2) +(0.5*20*v2f^2) ..(2)

By solving (1) and (2) we get

v1f = 8.19 m/s, v2f = -4.15 m/s

(C) v1f = -12.9 m/s , v2f =0.54 m/s

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