Question

Consider a perfectly elastic, one-dimensional collision in the following scenarios and find each masses final velocity.

a)

m=2kg with v0=55m/s

M=250kg with v0=0m/s

b)

m=12kg with v0=20m/s

M=1kg with v0=-10m/s

c)

m=24.5kg with v0=35.7m/s

M=24.5kg with v0=0m/s

Answer 1

AFTER COLLISION

a) for first body

V1f = (m1-m2)*Vo1/(m1+m2) +(2*m2*u2/(m1+m2))

V1f = (2-250)*55/(2+250) + 0

V1f = -54.12 m/s

for second body

V2f = (2*m1*Vo1)/(m1+m2)

V2f = (2*2*55)/(2+250) = 0.873 m/s

b)

for first body

V1f = (m1-m2)*Vo1/(m1+m2) +(2*m2*u2/(m1+m2))

V1f = (12-1)*20/(12+1) - (2*1*10)/(1+12)

V1f = 16.9 - 1.54

V1f = 15.36 m/s

For second body

V2f = (2*m1*u1)/(m1+m2) - (m2-m1)*Vo2/(m1+m2)

V2f = ((2*12*20)/(1+12))+((1-12)*10/(1+12))

V2f = 28.46 m/s

c) for first body

V1f = (m1-m2)*Vo1/(m1+m2) +(2*m2*Vo2/(m1+m2))

V1f = (24.5-24.5)*35.7/(24.5+2.45) + 0

V1f = 0 m/s

For second body

V2f = 2*m1*Vo1/(m1+m2)

V2f = (2*24.5*35.7)/(24.5+24.5) = 35.7 m/s