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Problem Potential Energy at Different Heights

Potential energy of a body near the planet surface
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)
Potential energy of a body near the planet surface
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Potential energy of a mass near the planet surface.

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 \( 568\,\mathrm{kJ} \).

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