a 12g object moving at 31 cm/s hits a 23g object moving in the same direction at 13 cm/s,whats its final veloc

Question

using conservation of momentum and energy what is the velocity of the slower object after the collision and what is the velocity of the faster object after the collision?

Answer 1

This is an elastic head-on collision problem. Equations are derived from the ref.
Notation is: V = velocity, M = mass, CR = coefficient of restitution (1 in elastic collision) (=1 when elastic), KE = kinetic energy; 1, 2, CM, Rel = body 1, body 2, system, relative (body 1 relative to body 2); (i), (f) = initial, final.
The answers you ask for are V2(f) initially slower, now faster, and V1(f) initially faster, now slower.
M1,M2 = .012 .023
V1(i),V2(i) = .31 .13
VCM = (M1V1(i)+M2V2(i))/(M1+M2) = .191714285714286
VRel(i) = V1(i)-V2(i) = .18
VRel(f) = -CR*VRel(i) =-.18
V1(f) = VCM+VRel(f)*M2/(M1+M2) = 7.34285714285715D-02
V2(f) = VCM-VRel(f)*M1/(M1+M2) = .253428571428571
KE1(f) = M1*V1(f)^2/2 = 3.23505306122449D-05
KE2(f) = M2*V2(f)^2/2 = 7.38599469387755D-04

Answer 2

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