Question

A cart of mass m1 = 5.69 kg and initial speed = 3.17 m/s collides head-on with a second cart of mass m2 = 3.76 kg, initially at rest. Assuming that the collision is perfectly elastic, find the speed of cart m2 after the collision.

Answer 1

ELASTIC COLLISION

m1 = 5.69                                     m2 = 3.76 kg

speeds before collision

v1i = 3.17m/s                                 v2i = 0

speeds after collision

v1f = ?                                        v2f = ?

initial momentum before collision

Pi = m1*v1i + m2*v2i

after collision final momentum

Pf = m1*v1f + m2*v2f

from momentum conservation

total momentum is conserved

Pf = Pi

m1*v1i + m2*v2i = m1*v1f + m2*v2f .....(1)

from energy conservation

total kinetic energy before collision = total kinetic energy after collision

KEi = 0.5*m1*v1i^2 + 0.5*m2*v2i^2

KEf =   0.5*m1*v1f^2 + 0.5*m2*v2f^2

KEi = KEf

0.5*m1*v1i^2 + 0.5*m2*v2i^2 = 0.5*m1*v1f^2 + 0.5*m2*v2f^2 .....(2)

solving 1&2

we get

v1f = ((m1-m2)*v1i + (2*m2*v2i))/(m1+m2)

v1f = ( ( 5.69 - 3.76)*3.17 + 0 )/(5.69 + 3.76) = 0.65 m/s

v2f = ((m2-m1)*v2i + (2*m1*v1i))/(m1+m2)

v2f = ( (3.76 - 5.69)*0 + 2*5.69*3.17)/(5.69+3.76) = 3.82 m/s