Question

A cart A of mass $50kg$ moving at a speed of $20km/h$ hits a lighter cart $B$ of mass $20kg$ moving towards it at a speed of $10km/h$.The two carts cling to each other. Find the change of momentum of cart A.

Answer 1

Momentum of cart A before collision is $p_A=50kg\times 20km/h=1000kgkm/h$

And that of B was $p_B=20kg\times (-10km/h)=-200kgkm/h$

After clinging the net mass of the system will be $50+20=70kg$

and if the common velocity be $v$ then the new momentum of the system will be $70v$

this new momentum should be eqaul to the $net$ momentum before collision so $70v=p_A+p_B=1000-200=800kgkm/h$ so $v=\frac{80}{7}km/h$

So the new momentum of A will be $p_A^{\prime }=m_A\times v=50\times \frac{80}{7}$

Accordingly the change is is $p_A-p_A^{\prime }=1000-571.4=428.6kgkm/h$