Question

A 0.5 kg croquet ball makes an elastic head-on collision with a second ball initially at rest. Ball 2 moves off with one third the initial speed of the first ball.
a) What is the final speed of ball 1 v1¹ in terms of the initial speed of ball 1 v1.

b) What is the mass of the second ball?

Show all work and equations and remember the units.

Answer 1

u1= initial speed of ball 1, final speed of ball 1 = v1, final speed of ball 2= u1/3

let's conserve the momentum and KE

0.5 ( u1) + m2 (0) = 0.5 ( v1) + m ( u1/3)-------------conserving momentum

0,5 u1 = 0.5 ( v1)+ m ( u1/3)----------eq(1)

u1 ( 0.5 - m/3) = 0.5 v1

v1 ( final speed of ball 1) = 2u1 (0.5 - m/3)

conserving kE

0.5 (u1)^2 = m ( u1^2/ 9) + 0.5 ( v1^2)---------------conserving KE

0.5 ( u1-v1) ( u1+ v1) = m ( u1^2/9)

m = 4.5 ( u1-v1) ( u1+ v1) u1^2

finall speed of ball 2= 2 ( 0.5) / ( 0.5 + m) initial speed of ball 1

1/3 = 1/ ( 0.5 + m)

m = 3-0.5 = 2.5 kg

0,5 u1 = 0.5 ( v1)+ 2.5 ( u1/3)

u1 ( 0.5- 2.5/3) = 0.5 v1

u1 ( -1/ 3) = 0.5 v1

u1= -1/5 v1