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

$A$ hammer of mass $500 \,g$,moving at $50 \,m/s$,strikes a nail. The nail stops the hammer in a very short time of $0.01 \,s$. What is the force (in $N$) of the nail on the hammer?

$A$ stone of $1\, kg$ is thrown with a velocity of $20\, m\ s^{-1}$ across the frozen surface of a lake and comes to rest after travelling a distance of $50\, m$. What is the force of friction (in $N$) between the stone and the ice?

What is the momentum of an object of mass $m$, moving with a velocity $v$?

$A$ bullet of mass $10\, g$ travelling horizontally with a velocity of $150\, m/s$ strikes a stationary wooden block and comes to rest in $0.03\, s$. Calculate the distance of penetration of the bullet into the block. Also,calculate the magnitude of the force exerted by the wooden block on the bullet.

Explain why some of the leaves may get detached from a tree if we vigorously shake its branch.