Question

A space station with a radius of 120 m rotates once every 70 s to create artificial gravity. If the astronaut has an earth weight of 160 lbs, then what is its artificial weight?

Answer 1

Answer:

Artificial weight = 70.27 N = 15.80 lbs

Explanation:

The earth weight of the astronaut = 160 lbs = 711.72 N

The weight on earth = m × g(earth)

g(earth) = 9.8 m/s²

711.72 = m × 9.8

m = (711.72/9.8)

m = 72.62 kg

But at the space station, the space station rotates once every 70 s to create an artificial radial acceleration that creates a radial gravity pulling the objects on the space station towards the centre of that space station.

radial acceleration = α = (v²/r)

v = rw,

α = (rw)²/r

α = rw²

r = radius of rotation = 120 m

w = angular velocity = (2π/70) (it completes 1 rotation, 2π radians, in 70 s)

w = 0.0898 rad/s

α = 120 × (0.0898²)

α = 0.968 m/s²

Artificial weight = (mass of astronaut) × (Radial acceleration) = 72.62 × 0.968

Artificial weight = 70.27 N = 15.80 lbs

Hope this Helps!!!