# Power to the people

No, before you hit ‘close’, this isn’t anything to do with the election.

Last Saturday, I walked up Mt Te Aroha. For those not familiar with this part of the country, Mt Te Aroha is part of the Kaimai range, and rises majestically 950 metres above the Hauraki Plains, about 50 km North-West of Hamilton. Its bush-clad slopes are home to tui, kereru, parakeets, oodles of piwakawaka, and at least one feral goat, which I nearly tripped over. Anyway, I spent the following day wondering why I was so tired and hungry. Admittedly the tired bit had probably more to do with staying up to watch the election results, but the hungry bit is down to physics.

It doesn’t take too much physics understanding to estimate how much energy is needed to take myself to the top of Te Aroha. The gravitational potential energy gained, when something gains height, is given neatly by the mass of the object raised (me), times the height raised, times the acceleration due to gravity (which is how fast something gains speed when dropped, equal to 10 metres per second, every second). Now, I weight about 65 kg, the height of the mountain is 950 m (and starting from virtually sea-level, I climbed all of it), so multiplying those together gives me about 600 thousand joules, or 600 kJ of energy. That’s about 25 g of chocolate (and very nice it was too).

But this is a woefully inadequate calculation. For a start, our muscles are only around 25% efficient, so that’s a factor of 4 to multiply by. And those of you who know the path up Te Aroha, will appreciate its not simple going like walking up a flight of stairs (mud, tree roots, rocks…)  So probably I should double the value again. This then becomes more like 4800 kJ of energy (a bit over 1000 kcal in old money), or 200 g of chocolate.

Of course, this is only a very rough estimate, but it is enough to explain why I felt like such a large lunch the following day.