In the film Mission to Mars (released in 2000), the spacecraft (see the figure b

Question

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?

Compare the centripetal acceleration of

a 2.0-m-tall astronaut at his feet to

that at his head.

Compare these accelerations to g.

C)afeet g =

D) ahead g =

Explanation / Answer

a)

Diameter D = 10 m

Radius R = D/2 = 10/2 = 5 m

Time period T = 30 s

Angular velocity w = 2*pi/T = 2*3.14/30 = 0.2093 rad/s

a)

Centripetal acceleration at feet a_feet = R*w^2 = 5*0.2093^2 = 0.219 m/s^2

Radius at head R_head = R - 2 = 5-2 = 3 m

Centripetal acceleration at head a_head = R_head*w^2 = 3*0.2093^2 = 0.1314 m/s^2

b)

In terms of g = 9.81 m/s^2 we'll have

a_feet = 0.219 / 9.81 = 0.0223

a_head = 0.1314/ 9.81 = 0.0134

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