Question

A 0.180-kilogram cart traveling at 0.80 meter per second to the right collides with a 0.100-kilogram cart initially at rest. The carts lock together upon collision. Calculate the final velocity of the carts.

Answer 1

According to the saving of the momentum law, the total momentum before collision equals to the total momentum after collision

After collection, the 2 carts lock together, one body with a mass $m=m_{1}+m_{2}$ and velocity $v$

$(P_{1}+P_{2})_{before}=P_{after}$

from the definition of the momentum $P=mv$

$P_{1,before}=m_{1}v_{1,before}=0.180*0.80=0.144kg.m/s$

$P_{2,before}=m_{2}v_{1,after}=0.100*0=0kg.m/s$

thus

$P_{after}=(0.144+0)_{before}=0.144 kg.m/s$

we calculate the velocity

$v=\frac{P}{m}=\frac{0.144}{0.180+0.100}= 0.514m/s$