Question

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

Answer 1

Step 1: List the known values

Given,

Mass of the dumbbell $m=10kg$

Height of the dumbbell $h=80cm=0.8m$

Acceleration due to gravity $g=10m{s}^{-2}$

Initial velocity $u=0$

Step 2: Calculate the final velocity

According to Newton's equation of motion,

$v^2=u^2+2gh$

Upon substituting the values we get,

$v^2=0+2\times 10\times 0.8$

$=16$

$\therefore v=4m/s$

Step 3: Calculate the momentum

We know that the momentum of a body is given as,

$$\begin{gathered} ∆p=m∆v \\ ∆pisthechangeinmomentumand∆visthechangeinvelocity \end{gathered}$$

$$\begin{gathered} ∆v=v-u \\ ∆v=4-0 \\ ∆v=4m/s \end{gathered}$$

Upon substituting the values we get,

$p=10\times 4$

$=40kgm/s$

Hence, the dumbbell will transfer $40kgm/s$ momentum to the floor.