Pleaes answer In the film Mission to Mars (released in 2000), the spacecraft (se

Question

Pleaes answer

In the film Mission to Mars (released in 2000), the spacecraft (see the figure below) features a rotating section to provide artificial gravity for the long voyage. A physicist viewing a scene from the interior of the spacecraft notices that the diameter of the rotating portion of the ship is about five times the height of an astronaut walking in that section (or about 10 m). Later, in a scene showing the spacecraft from the exterior, she notices that the living quarters of the ship rotate with a period of about 30 s. Did the movie get the physics right? Yes No Compare the centripetal acceleration of a 1.8-m-tall astronaut at his feet to that at his head. afeet = m/s2 ahead = m/s2 Compare these accelerations to g. afeet/g = ahead/g =

Explanation / Answer

The movie got the physics wrong. Here's why. Centripetal acceleration at the radius r=d/2 is omega^2*r, so that

m*omega^2*r=m*a_feet

a_feet=omega^2*r=(2*pi/T)^2*r=(2*3.14/30)^2*(10/2)=0.22 m/s^2

This is your artificial gravitation constant g_art at the feet. But the real Earth gravitation constant which the ship allegedly tries to emulate is 9.81 m/s^2

a_feet/g=0.22/9.81=0.022

This is far from 1. Similarly, at the head position

a_head=omega^2*(r-h)

Here, h=1.8 meters, r=d/2=5 meters. So,

a_head=(2*pi/30)^2*(5-1.8)=0.14 m/s^2

a_head/g=0.14/9.81=0.014.

This is also far from 1. So, the movie got it wrong.

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