# Problem Potential Energy at Different Heights

**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:

Leaning Tower of Pisa, \(57 \, \mathrm{m}\).

Eiffel Tower, \(300 \, \mathrm{m}\).

Burj Khalifa, \(828 \, \mathrm{m}\).

## Solution tips

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

## Exercise solutions

## Solution for (a)

**Formel: Gravitative potentielle Energie**

Formula anchor $$ \begin{align} W_{\text{pot}} = m \, g \, h \end{align} $$

**Beispiel 1: Potentielle Energie berechnen**

Formula anchor $$ \begin{align} W_{\text{pot}} ~&=~ 70\,\mathrm{kg} \cdot 9.8\,\frac{\mathrm m}{\mathrm{s}^2} \cdot 57\,\mathrm{m} \\\\

~&=~ 39 102 \, \mathrm{J} \end{align} $$

~&=~ 39 102 \, \mathrm{J} \end{align} $$

## Solution for (b)

**Beispiel 2: Potentielle Energie berechnen**

Formula anchor $$ \begin{align} W_{\text{pot}} ~&=~ 70\,\mathrm{kg} \cdot 9.8\,\frac{\mathrm m}{\mathrm{s}^2} \cdot 300\,\mathrm{m} \\\\

~&=~ 205 800 \, \mathrm{J} \end{align} $$

~&=~ 205 800 \, \mathrm{J} \end{align} $$

## Solution for (c)

**Beispiel 3: Potentielle Energie berechnen**

Formula anchor $$ \begin{align} W_{\text{pot}} ~&=~ 70\,\mathrm{kg} \cdot 9.8\,\frac{\mathrm m}{\mathrm{s}^2} \cdot 828\,\mathrm{m} \\\\

~&=~ 568 008 \, \mathrm{J} \end{align} $$

~&=~ 568 008 \, \mathrm{J} \end{align} $$