Question

A body of mass 10 kg is dropped from a height of 20 m. Find (i) its potential energy before it is dropped, (ii) its kinetic energy when it is 8 m above the ground and (iii) its kinetic energy when it hits the ground.
Take g = 10 ms.

Answer 1

Given data:

Mass is, $m=10kg$

Height is, $h=20m$

Acceleration due to gravity is, $g=10m/s^2$

(i) Calculating potential energy:

Potential energy is given as,

$PE=mgh$

where $m$ is mass, $g$ is the acceleration due to gravity and $h$ is height.

Substituting the known values, we get,

$$\begin{gathered} PE=10kg\times 10m/s^2\times 20m \\ PE=2000J \end{gathered}$$

The potential energy of the body before it is dropped is $2000J$.

(ii) Calculating kinetic energy when $h=8m$:

1. When the body falls from a height, there is a loss in potential energy and a gain in kinetic energy.
2. According to the law of conservation of energy, loss in potential energy will be equal to the gain in kinetic energy.
3. The kinetic energy at $8m$ will be equal to the change in potential energy of the body from the initial height to the height of $8m$. Therefore,

$$\begin{gathered} KE=PE=mgh \\ KE=10kg\times 10m/s^2\times (20-8)m \\ KE=10\times 10\times 12 \\ KE=1200J \end{gathered}$$

The kinetic energy of the body at $8m$ above the ground is $1200J$.

(iii) Calculating kinetic energy when the body hits the ground:

1. When a body is at its highest point, it possesses only potential energy and no kinetic energy.
2. As the body falls from the height, potential energy is converted to kinetic energy.
3. As the body hits the ground, it possesses only kinetic energy and no potential energy as all the potential energy is converted to kinetic energy.
4. The transformation of energy takes place due to the law of conservation of energy, which states that energy is neither created nor destroyed, but is transformed from one form to another.
5. The kinetic energy of the body when it hits the ground will be equal to the potential energy of the body at the top, that is $2000J$.

The kinetic energy of the body when it hits the ground is $2000J$.