Question

An object with velocity 1.4 m/s i and mass 0.27 kg collides with an object whose velocity is -2.5 m/s i and whose mass is 0.12 kg. The motion takes place in one dimension. (a) What are the final velocities of the objects if the collision is elastic? b.) What is the total initial kinetic energy in the collision?

Answer 1

ELASTIC COLLISION ONE DIMENSIONAL

m1 = 0.27 kg                   m2 = 0.12 kg

speeds before collision

u1 = 1.4i                     u2 = -2.5i 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)

a)

v1 = ( ((0.27-0.12)*1.4) - (2*0.12*2.5) ) /(0.27+0.12)

v1 = -1 i m/s

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

v2 = ( 0-((0.12-0.27)*2.5) + (2*0.27*1.4) ) /(0.27+0.12)

v2 = 2.9 i m/s

b)

KE = 0.5*m1*u1^2 + 0.5*m2*u2^2 = (0.5*0.27*1.4^2) +(0.5*0.12*2.5^2) = 0.6396 J