9. Luke is an astronaut that moves his position in the space shuttle by climbing a 3.0 m ladder in 5.0 seconds at Cape Kennedy (g = 9.8 m/s^2). After landing on the
moon (g = 1.6 m/s^2), Luke climbs a 3.0 m ladder in 5.0 seconds to begin the trip back to Earth. Is more power expended by the astronaut on Earth or on the moon, and by what factor?

It takes 6.125 times as much work on Earth as it does on the moon.

Explanation:

Formulas

The power formula is

P = Work / Time

Work = Force * distance

Givens

d = 3.0 meters

t = 5.0 seconds

g = 9.8 m/s^2 on earth

g = 1.8 m/s^2 on the moon

Solution

Earth

Work  = F * d

Work = m* a * 3.0 m

Work = m *9.8 * 3.0

Work = m * 29.4

Power = (Work * 29.4)/5

Power = 29.4/5 * m

Power = 5.88 watts.

Moon

You follow the same procedure except you use 1.6 for a.

Work = m * 1.6 * 3

Work = 4.8*m Joules

Power = 4.8 * m/ 5

Power = 0.96 * m Watts

P_earth/Power_moon = 5.88 * m / 0.96 * m = 6.125

Power =