Explain why it is easier to climb a mountain on a zigzag path rather than one straight up the side. Is your increase in gravitational potential energy the same in both cases? Is your energy consumption the same in both?

Power: Power is a scaler quantity defined as the rate at which energy is consumed.

Gravitational potential energy: The gravitational potential energy stored in the body equals the work done in raising a body to some height against the gravitational force of attraction.

The gravitational potential energy is given as,

$\text{PE}=mgh$

Here, m is the mass of the body, g is the acceleration due to gravity and h is the height from which the surface object is raised.

The height of the mountain (displacement of the climber) is the same in both cases whether the climber takes a zigzag path or a straight path. Hence, the gravitational potential energy is the same in both cases.

The power is given as,

$\text{Power}=\frac{\text{Energy}}{\text{Time}}$

The zigzag path is longer than the straight path because it takes longer to work while climbing a mountain.

From the expression of power, we can conclude that it takes less power to climb a mountain via a zigzag path rather than a straight path. This makes the climb easier on a zigzag path as it is easier to generate a small amount of power for long periods of time in a zigzag path rather than to generate a large power for a short period of time.

So, the energy consumption per unit of time is smaller in the zigzag rather than the straight path while climbing up a mountain.