How much momentum will a dumb-bell of mass 10 kg transfer to the floor if it fails from a height of 0.8 m ? Take its downward acceleration to be `10m//s^2`?

Explanation

Mass of dumb bell, m= 10 kg
Height, h = 0.8 metre
Acceleration, `a=g=10m//s^2`
Initial velocity of the dumb bell, u = 0
Let velocity of the dumb-bell just before hitting the ground = v
Using `v^2-u^2=2aS`, we have
`v^2-(0)^2=2xx10xx0.8=16`
or `v=sqrt(16)=4m//s`
`therefore` Momentum of the dumbbell just before hitting the floor
=mass `xx` velocity = `10xx4`
= 40 kg m/s
Velocity of the dumb-bell after hitting the floor = 0
`therefore` Momentum of the dumb-bell after hitting the floor
= mass `xx` velocity = 10 = 0
`therefore` Momentum transferred to the floor by the dumbbell change in momentum of the dumb-bell = 40 - 0
= 40 kg