Question

How much momentum will a dumb-bell of mass 10 kg transfer to the floor if it falls from a height of 80 cm? Take its downward acceleration to be 10 m$s^{-2}$.

Answer 1

Given,

Mass of dumb-bell = $m=10kg$

Dispalcement of the dumb-bell = $s=80cm=0.8m$

Downward acceleration of the dumb-bell = $10m/s^2$ (Downward direction is positive).

From the 3rd equation of motion we have,

$v^2=u^2+2as$

$\Rightarrow v^2=2+2\left(10\right)0.8$

$\therefore v=4m/s$

Momentum with which the dumbbell hits the floor,

$p=mv=10\times 4=40kgm/s$.

Thus the dumb-bell transfers $40kgm/s$ of momentum to the floor.