Question

A mass of 10 kg is dropped from a height of 50 cm. Find its:
(a) kinetic energy, and (b) velocity
Just as it reaches the ground, does the velocity depend on the mass of the particles? Explain.

Answer 1

Step 1: Given data

Mass is, $m=10kg$

Height is, $h=50cm=0.5m$

Step 2: (a) Calculating kinetic energy

The kinetic energy of a mass which is dropped from a height will be equal to the loss in its potential energy. Therefore, kinetic energy will be given as,

$KE=PE=mgh$

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

Assume $g=10m/s^2$

Substituting the known values in the equation for kinetic energy, we get,

$$\begin{gathered} KE=10kg\times 10m/s^2\times 0.5m \\ KE=50J \end{gathered}$$

Therefore, kinetic energy is $50J$.

Step 3: (b) Calculating velocity

Kinetic energy is given as,

$KE=\frac{1}{2}m{v}^2$

where, $m$ is mass and $v$ is velocity

For the given situation, we know that,

$KE=PE$

Therefore,

$$\begin{gathered} \frac{1}{2}m{v}^2=mgh \\ {v}^2=\frac{2mgh}{m} \\ v=\sqrt{2gh} \end{gathered}$$

Substituting the known values in the equation for velocity, we get,

$$\begin{gathered} v=\sqrt{2\times 10m/s^2\times 0.5m} \\ v=\sqrt{10} \\ v=3.16m/s \end{gathered}$$

Therefore, velocity is $3.16m/s$.

Step 4: Explaining if velocity depends on mass

Velocity is given as,

$v=\sqrt{2gh}$

It can be said that velocity depends on acceleration due to gravity and height.

Therefore, velocity does not depend on the mass of the particle.