Question

A(n) 43.1 g object moving to the right at 26.5 cm/s overtakes and collides elastically with a(n) 12.1 g object moving in the same direction at 18.9913 cm/s. Find the velocity of the first object immediately after the collision. Answer in units of cm/s.

Find the velocity of the second object immediately after the collision. Answer in units of cm/s.

Answer 1

Mass of first object,m1=43.1g

Mass of 2nd object,m2=12.1g

Initial velocity of 1st object,v1i=26.5 cm/s

Initial velocity of 2nd object,v2i=18.9913 cm/s

Let

Their final velocities are v1f and v2f.

According to principle of conservation of linear momentum.

linear momentum of system before collision =linear momentum of system after collision

m1v1i+m2v2i=m1v1f+m2v2f ..........................................(1)

According to principle of conservation of kinetic enenrgy

Kinetic energy of system before collision =Kinetic energy of system after collision

(1/2)m1v1i)2+(1/2)m2(v2i)2=(1/2)m1(v1f)2+(1/2)m2(v2f)2 ..........................................(2)

On solving (1) and(2)

v1f=[(m1-m2)/(m1+m2)]v1i+[(2m2)/(m1+m2)]v2i=[(43.1-12.1)/(43.1+12.1)]26.5+[(212.1)/((43.1+12.1))]18.9913=23.21 cm/s

v2f=[(2m1)/(m1+m2)]v1i-[(m1-m2)/(m1+m2)]v2i=[(243.1)/(43.1+12.1)]26.5-[(43.1-12.1)/(43.1+12.1)]18.9913=30.72 cm/s

So

velocity of the first object immediately after the collision.=23.21 cm/s

velocity of the 2ndobject immediately after the collision.=30.72 cm/s