Getting a Feeling for Energy

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Have you heard of GravityLight?

It is a gravity-powered lamp designed as an alternative for off-grid families who would otherwise use kerosene lamps. It is basically only a 12kg weight, lifted and put on the gravity light. When the weight goes down again it pulls a cord. This cord drives an electric motor which generates electricity for LEDs. If you lift the weight 1.83m, the light lasts for about 20 minutes.

I wondered how much weight I would need to lift (assuming 100% efficiency) to power my computer for 8 hours.

According to the power supply unit, my laptop can consume up to 65 Watt. That is astonishingly low. I think my big one is at about 600-800 Watt.

\begin{align} 65 W \cdot 8 h &= \frac{65 kg \cdot m^2 \cdot 8h \cdot 60 \frac{min}{h} \cdot 60 \frac{s}{min}}{s^3}\\ &= 1872 \cdot 10^3 \frac{kg \cdot m^2}{s^2} \end{align}

You might also remember from your physics courses that potential energy is \(E_{pot} = m \cdot g \cdot h\) where \(m\) is the mass (in kg), \(g = 9.80 \frac{m}{s^2}\) is the gravitational acceleration and \(h\) is the height in meters.

\begin{align} m \cdot h &= \frac{E_{pot}}{g}\\ &= \frac{1.872 \cdot 10^6 \frac{kg \cdot m^2}{s^2}}{9.80 \frac{m}{s^2}}\\ &= 191.0 \cdot 10^3 kg \cdot m \end{align}

This means I would have to lift 191 000 one-liter packages of milk to a height of 1 meter. Every day. Just to let my small laptop run.

Or let's view it from another angle. I think lifting about 5 packages of milk to a height of about 1.8m each hour would not be too exhausting. This would generate about \(E_{pot} = 5kg \cdot 1.80m \cdot 9.80 \frac{m}{s^2} / (1h \cdot 60 \frac{min}{h} \cdot 60 \frac{s}{min}) = 0.0245 \frac{kg \cdot m^2}{s^3} = 0.0245 W\). Let's think about what you can power with 0.0245 Watt...

It is amazing how much energy we have today.