# Problem Potential Energy at Different Heights

Level 1 (suitable for all)
Level 1 does not require any previous knowledge. Suitable for absolute beginners.

What potential energy does a person who has a weight of 70 kilograms have when he/she climbs the following building:

1. Leaning Tower of Pisa, $$57 \, \mathrm{m}$$.

2. Eiffel Tower, $$300 \, \mathrm{m}$$.

3. Burj Khalifa, $$828 \, \mathrm{m}$$.

Solution tips

Use Sauron's Eye to find the formula for potential energy.

## Exercise solutions

Solution for (a)

Use the formula for potential energy:

Formula: Gravitational potential energy
Formula anchor

Insert the mass $$m=70\,\mathrm{kg}$$, the gravitational acceleration $$9.8\,\frac{\mathrm m}{\mathrm{s}^2}$$, and the height of the Leaning Tower of Pisa $$h=57\,\mathrm{m}$$ to find the potential energy of the person at that height:

Example 1: How to calculate potential energy
Formula anchor

This is approximately $$39\,\mathrm{kJ}$$. Note that $$1\,\frac{\mathrm{kg} \, \mathrm{m}^2}{\mathrm{s}^2} = 1 \, \mathrm{J}$$.

Solution for (b)

As in exercise (a), insert the mass $$m=70\,\mathrm{kg}$$, the gravitational acceleration $$9.8\,\frac{\mathrm m}{\mathrm{s}^2}$$, and the height of the Eiffel Tower $$h=300\,\mathrm{m}$$ into the potential energy formula to find the potential energy at that height:

Example 2: How to calculate potential energy
Formula anchor

That is approximately $$206\,\mathrm{kJ}$$.

Solution for (c)

As in exercise (a), insert the mass $$m=70\,\mathrm{kg}$$, the gravitational acceleration $$9.8\,\frac{\mathrm m}{\mathrm{s}^2}$$, and the height of the Burj Khalifa $$h=828\,\mathrm{m}$$ into the potential energy formula to find the potential energy at that height:

Example 3: How to calculate potential energy
Formula anchor

That is approximately $$568\,\mathrm{kJ}$$.