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Final Velocities : Elastic

Ball 1, with a mass of 100 g and traveling at 15 m/s, collides head on with ball 2, which has a mass of 350 g and is initially at rest.

What are the final velocities of each ball if the collision is perfectly elastic?

Known variables:

Mass(m1) of the first ball = 100 g or .100 kg

Initial velocity (v1) of the first ball= 15.0 m/s

Mass(m2) of the second ball = 340 g or .340 kg

Initial velocity(v2) of the second ball= 0 (initially at rest)

(V(fx)1 and (Vfx)2 are the velocities of the 2 after the collision

If elastic then the formulas would be the following:

V(fx)1= 2m2v2/m1+m2 + (m1-m2/m1+m2)v1

V(fx)2= 2m1v1/m1+m2 + (m1-m2/m1+m2)v2

V(fx)1:

2(.340 x 0)/.100 + .340       +        (.100 – .340/ .100 + .340) x (15)

0 + (-.240/.440) x 15

V(fx)1=  -8.3 m/s

V(fx)2:

2(.100 x 15)/.100 + .340        +            (.100 – .340/ .100 + .340) x (0)

2(1.5)/.440            +             0

V(fx)2= 6.7 m/s

3) What are the final velocities of each ball if the collision is perfectly inelastic?

Inelastic Collision:

If the collision is inelastic, the combined speed of both balls after the collision can be figured out through this equation.

v= m1v1+ m2v2/ m1 + m2

(.100 kg x 15 m/s) + 0 / (.100 + .340)

1.5 / .440

=3.3m/s

V(fx)1 & 2 = 3.3m/s

The final velocities of each ball would be the same.

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