Question

An object of mass $1\mathrm{kg}$ travelling in a straight line with a velocity of $10\mathrm{m}/\mathrm{s}$ collides with, and sticks to, a stationary wooden block of mass $5\mathrm{kg}$. 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.

Answer 1

Step 1: Given data

Mass of objects, $m=1\mathrm{kg}$

Velocity, $u_1=10\mathrm{m}/\mathrm{s}$

Mass of wooden blocks, $M=5\mathrm{kg}$

Step 2: Formula used

${\mathrm{mu}}_1+{\mathrm{Mu}}_2=(\mathrm{m}+\mathrm{M})\mathrm{v}$

Step 3: Calculation of velocity of the combined object

From the perspective of momentum conservation,

$Initialmomentum=Finalmomentum$

${\mathrm{mu}}_1+{\mathrm{Mu}}_2=(\mathrm{m}+\mathrm{M})\mathrm{v}$

By substituting the values, we get

$1\times 10+5\times 0=(1+5)v$

$10=6\mathrm{v}$

$\mathrm{v}=\frac{5}{3}m{s}^{-1}$

Hence, the velocity of both is $\mathrm{v}=\frac{5}{3}m{s}^{-1}$. The total momentum just before and after the collision is 10 Kgm/s.