Question

Derive an expression for P.E. of a stone thrown up on the roof of a house.

Answer 1

Step 1: Assumptions

Let the mass of the stone be $m$

Let the height acquired by the stone be $h$

Let acceleration due be gravity be $g$

Step 2: Deriving an expression for potential energy

When the stone is thrown up the roof, work done by the stone is given as,

$W=FS$

where, $F$ is force and $S$ is the displacement

Now the displacement of the stone is equal to the height acquired by it, therefore,

$W=Fh$

We know that force is given as,

$F=ma$

where, $m$ is mass and $a$ is acceleration.

When the body is thrown up, the force of gravity acts on the body, therefore,

$F=mg$

Substituting this equation for force in the equation for work done, we get,

$$\begin{gathered} W=Fh \\ W=mgh \end{gathered}$$

Now, the work done to throw the stone up the roof is equal to the potential energy gained by the body, therefore,

$PE=mgh$

Hence, the expression for P.E. of a stone thrown up on the roof of a house is given as,

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