Question

A 28.0-g object moving to the right at 20.5 cm/s overtakes and collides elastically with a 11.0-g object moving in the same direction at 15.0 cm/s. Find the velocity of each object after the collision. (Take the positive direction to be to the right. Indicate the direction with the sign of your answer.)

Answer 1

Explanation:

It is given that,

Mass of object 1, $m_1=28\ g=0.028\ kg$

Initial speed of object 1, $u_1=20.5\ cm/s=0.205\ m/s$

Mass of object 2, $m_2=11\ g=0.011\ kg$

Initial speed of object 2, $u_2=15\ cm/s=0.15\ m/s$

The momentum of an object in case of elastic collision remains conserved. It is given by :

$m_1u_1+m_2u_2=m_1v_1+m_2v_2$

$0.028\times 0.205+0.11\times 0.15=0.028v_1+0.011v_2$

$0.028v_1+0.011v_2=0.02224$.............(1)

For elastic collision, the coefficient of restitution is equal to 1. It is given by :

$\dfrac{v_2-v_1}{u_1-u_2}=1$

$\dfrac{v_2-v_1}{0.205-0.15}=1$

${v_2-v_1}=0.055$...............(2)

On solving equation (1) and (2) we get :

$v_1=0.555\ m/s=55.5\ cm/s$

$v_2=0.61\ m/s=61\ cm/s$

Hence, this is the required solution.