Question

A body of mass 5 kg falls from a height of 10 m to 4m. Calculate:

(i) the loss in potential energy of the body, and (ii) the total energy possessed by the body at any instant? (Take g=10 m $s^{-2}$).

Answer 1

Step 1: Given that:

Mass(m) of the body = $5kg$

maximum height(H) = $10m$

Attained height(h) after falling from top = $4m$

g= $10m{s}^{-2}$

Step 2: i) Calculation of loss in potential energy of the body:

The potential energy of a body of mass m kept at height h is given by;

$PE=mgh$

The potential energy at the top = $mgH$

Thus,

$P{E}_H=5kg\times 10m{s}^{-2}\times 10m$

$P{E}_H=500J$

The potential energy at height of 4m;

$P{E}_h=5kg\times 10m{s}^{-2}\times 4m$

$P{E}_h=50\times 4$

$P{E}_h=200J$

Now,

The loss in potential energy

$\Delta PE=P{E}_H-P{E}_h$

$\Delta PE=500J-200J$

$\Delta PE=300J$

Step 3: ii) Calculation of the total energy of the body at any instant:

The total energy of the body at any instant = Potential energy of the bpdy at top

= $P{E}_H$

= $500J$

Thus,

i) Loss in potential energy = $300J$

ii) Total energy at any instant = $500J$