A 55 kg hiker starts at an elevation of 1600 m and climbs to the top of a 3400 m peak.
(a) What is the hiker's change in potential energy?
ΔPE=mgΔh=55•9.8•(3400-1600) =...
To calculate the hiker's change in potential energy, we need to use the following equation:
ΔPE = mgh
Where:
ΔPE = change in potential energy
m = mass of the hiker
g = acceleration due to gravity (approximately 9.8 m/s²)
h = change in height (elevation)
Given:
m = 55 kg
h = 3400 m - 1600 m = 1800 m
Plugging in the values, we can calculate:
ΔPE = 55 kg * 9.8 m/s² * 1800 m
Calculating further:
ΔPE = 970200 Joules
Therefore, the hiker's change in potential energy is 970200 Joules.
To calculate the change in potential energy, we need to know the gravitational potential energy formula. The formula for gravitational potential energy is:
ΔPE = mgh
Where:
ΔPE is the change in potential energy
m is the mass of the object (in this case, the hiker)
g is the acceleration due to gravity (approximately 9.8 m/s² on Earth)
h is the change in height (elevation)
Given:
m = 55 kg (mass of the hiker)
g = 9.8 m/s² (acceleration due to gravity)
h = 3400 m - 1600 m = 1800 m (change in height)
Using the formula, we can calculate the change in potential energy:
ΔPE = (55 kg) * (9.8 m/s²) * (1800 m)
ΔPE = 96,060 J (Joules)
Therefore, the hiker's change in potential energy is 96,060 Joules.