Question

A metal ball of mass $2kg$ is allowed to fall freely from rest from a height of $5m$above the ground.

(i) Determine the potential energy possessed by the ball when initially at rest.

(ii) What is the kinetic energy of the ball just before hiring the ground?

(iii) What happen to the mechanical energy after the ball hits the ground and comes to rest?

Answer 1

Given data:

Mass $m=2kg$

$h=5m$

Assumption $\left(g=10m/s^2\right)$

(i) Calculation of $PE$ possessed by the ball:

We know the formula for potential energy,

$PE=mgh$, where $m$ is mass, $PE$ is potential energy, $g$ is acceleration due to gravity and $g$ is height.

$PE=mgh$

$=2\times 10\times 5$

$=100J$

(ii) Calculation of kinetic energy of the ball before hitting the ground:

Kinetic energy of the ball just before hitting the ground $=$ initial potential energy possessed by the ball

Initial potential energy possessed by the ball is given by,

$PE=mgh$

$=2\times 10\times 5$

$=100J$

(iii) Mechanical energy after the ball hits the ground:

The mechanical energy after the ball hits the ground and comes to rest is converted into heat and sound energy.

Hence, for a metal ball of mass $2kg$ is allowed to fall freely from rest from a height of $5m$above the ground,

(i) Potential energy possessed by the ball is $100J$ .

(ii) Kinetic energy of the ball before hitting the ground is$100J$.

(iii) Mechanical energy is converted to sound and heat energy.