An object of mass `1kg` travelling in a straight line with a velocity of `10m//s` collides with, and sticks to, a stationary wooden block of mass `5kg`. Then, they both move off together in the same straight line. Calculate the total momentum just before the impact and just after the impact. Also, calculate the velocity of the combined object.

Explanation

Mass of object `m_1=1kg`
Velocity of object before collision
`u_1=10 ms^-1`
Mass of wooden block `m_2=5kg`
velocity of wooden block before collision `u_2=0`
(i) `therefore` Total momentum before the impact
`=m_1u_1+m_2u_2=1 times 10+5 times 0`
=`10 kg ms^-1`
According to the law of conservation of momentum
Total momentum after the impact= Total momentum before the impact `=10 kg ms^-1`
(ii) Mass of compound object, M=mass of object +mass of block `=1+5=6kg`
Let V=velocity of the combined object after collision
`therefore` Momentum of combined object =MV =`(6V) kg ms^-1`
Now momentum of combined object = Total momentum after the impact
i.e, 6V=10
or `V=10/6=1.67 ms^-1`