Question

The lowest point in Death Valley is 85m below sea level. The summit of nearby Mt. Whitney has an elevation of 4420m.

a) what is the change in potential energy of an energetic 95.3kg hiker who makes it from the floor of death valley to the top of mt. whitney?

b) if a frictionless track was constructed from the top of mt. whitney to the bottom if death valley such that a roller coaster car was allowed to run on the track without air resistance, how fast would the car be moving when it reached the bottom?

Answer 1

GIVEN VALUES:

Initial height / lowest point (y_i) = - 85 m (-ve as sea level is considered as origin)

Highest height (y_f) = 4420 m

Mass of hiker = 95.3 kg

SOLUTION:

a) Change in gravitational potential energy = ∆ U_g = ∆ U_gf - ∆ U_gi

∆ U_g = mgy_f - mgy_i

∆ U_g = mg (y_f - y_i)

∆ U_g = 95.3 x 9.8 (4420 - (- 85))

∆ U_g = 95.3 x 9.8 (4420 + 85))

∆ U_g = 4,207,399.7 J or 4.2 MJ

b) As the car would drive down, the gravitational potential energy would be converted into kinetic energy.

So, ∆ U_g = KE

4,207,399.7 = 1/2 (95.3) v²

v = 297.14 m / s