PS7 - This problem has two parts. I will list the questions for both parts and additional info below in "Description".

Question

A hiker of mass 69 kg is going to climb to the top of Mount Tam, which has an elevation of 2,574 ft.

Part a) If the hiker starts climbing at an elevation of 530 ft, what will their change in gravitational potential energy be, in joules, once they reach the top? Assume the zero of gravitational potential energy is at sea level.

Part b) Repeat the above calculation for the change in gravitational potential energy, but assume the gravitational potential is zero at the top of the mountain.

Answer 1

Gravitational Potential Energy (E_GP) can be calculated from:

E_GP = mgh where "m" is the object's mass, "g" is the acceleration due to gravity (9.81 m/s²) and "h" is the object's height from some reference point.

Note: "g" is not always a constant because it does vary with altitude HOWEVER, the change between sea level and 2574 feet is so small to make no difference in our result using 2 (or even 3) significant figures.

When comparing E_GP at 2 heights we can use:

ΔE_GP = mg(h₂ - h₁) where "h₂" and "h₁" are the two heights

So, between h₁ = 530 ft (or 161.5 meters) and h₂ = 2,574 ft (or 784.6 meters):

ΔE_GP = (69)(9.81)(784.6 - 161.5) = 42000 joules (rounded to 2 sig figs)

If we consider the top as zero, then the 530 ft elevation would be -2044 ft or -623 meters

So with h₂ = 0 and h₁ = -623 then:

ΔE_GP = (69)(9.81)(0 - -623) = 42000 joules (rounded to 2 sig figs)