Question

Ball 1, with a mass of 110 g and traveling at 15 m/s , collides head on with ball 2, which has a mass of 340 g and is initially at rest.

What is the final velocity of the ball 1 if the collision is perfectly elastic?

What is the final velocity of the ball 2 if the collision is perfectly elastic?

What is the final velocity of the ball 1 if the collision is perfectly inelastic?

What is the final velocity of the ball 2 if the collision is perfectly inelastic?

Answer 1

m1 = 110 kg                   m2 = 340 kg

speeds before collision

u1 = 15 m/s                   u2 = 0 m/s

speeds after collision

v1 = ?                         v2 = ?

initial momentum before collision

Pi = m1*u1 + m2*u2

after collision final momentum

Pf = m1*v1 + m2*v2

from moentum conservation

total momentum is conserved

Pf = Pi

m1*u1 + m2*u2 = m1*v1 + m2*v2 .....(1)

from energy conservation

total kinetic energy before collision = total kinetic energy after collision

KEi = 0.5*m1*u1^2 + 0.5*m2*u2^2

KEf =   0.5*m1*v1^2 + 0.5*m2*v2^2

KEi = KEf

0.5*m1*u1^2 + 0.5*m2*u2^2 = 0.5*m1*v1^2 + 0.5*m2*v2^2 .....(2)

solving 1&2

we get

v1 = [ ((m1-m2)*u1) + (2*m2*u2) ] /(m1+m2)

v2 = [ ((m2-m1)*u2) + (2*m1*u1) ] /(m1+m2)

v1 = [ ((110-340)*15) + (2*340*0) ] /(110+340)

v1 = -7.67 m/s

v2 = [ ((340-110)*0) + (2*110*15) ] /(110+340)

v2 = 7.33 m/s

++++++++++++++

for perfect inelastic

V1 = V2 = V

Pf = (m1+m2)*V

Pf = Pi

(110+340)*V = (110*15)

V = 3.67 m/s

v1 = 3.67 m/s

v2 = 3.67 m/s