Question

Many mountain roads are built so that they spiral around the mountain rather than go straight up toward the peak. Discuss this design from the viewpoint of energy and power.

Answer 1

So, the mountain roads takes us from the base of the mountain to the top. Lets call this height h. We know that the potential energy will be:

$E_p \ = \ m \ g \ h$

and this equation its independent from the road we take. But, an spiral road will be longer than an direct road. This means that, if we wanna to cover at constant speed v, the time it will takes us will be longer.

As power its the rate of change of the energy over time, this means that we will need more power for the straight up road.

For any motor the amount of power we can obtain its limited, so its more convenient for our vehicles (and for ourselves) to build the roads on spiral, instead of going straight up.