A hiker, of mass 80 kg walks up a mountain, 700 m above sea level, to spend the night at the top in the first overnight hut. The second day she walks to the second overnight hut, 400 m above sea level. The third day she returns to her starting point, 200 m above sea level.
What is the potential energy of the hiker at the first hut (relative to sea level)?
How much potential energy has the hiker lost in the second day?
To determine the potential energy of the hiker at the first hut (relative to sea level), we need to calculate the gravitational potential energy at that height.
Gravitational potential energy (PE) is given by the formula:
PE = mgh
Where:
m = mass of the object (hiker) = 80 kg
g = acceleration due to gravity = 9.8 m/s^2 (approximately)
h = height above the reference point (sea level)
In this case, the height of the first hut above sea level is 700 m. Plugging these values into the formula, we get:
PE = (80 kg)(9.8 m/s^2)(700 m)
PE = 549,600 J
So, the potential energy of the hiker at the first hut is 549,600 Joules (J) relative to sea level.
To find out how much potential energy the hiker has lost on the second day, we need to calculate the difference in potential energy between the second hut and the first hut.
Since the second day involves descending from the second hut to the first hut, the change in height is 400 m (from 400 m above sea level to 700 m above sea level).
The change in potential energy (PE_lost) can be calculated using the same formula as before:
PE_lost = mgh_lost
Where:
m = mass of the object (hiker) = 80 kg
g = acceleration due to gravity = 9.8 m/s^2 (approximately)
h_lost = change in height = 700 m - 400 m = 300 m
Plugging these values into the formula, we get:
PE_lost = (80 kg)(9.8 m/s^2)(300 m)
PE_lost = 235,200 J
Therefore, the hiker has lost 235,200 Joules (J) of potential energy during the second day.
PE1 = Mgh1 = 80*9.8*700 = ___ Joules.
PE2 = Mgh2 = 80*9.8*400 =
PE1-PE2 =