kramtus51
2021-12-19
Answered

One problem for humans living in outer space is that they are apparently weightless. One way around this problem is to design a space station that spins about its center at a constant rate. This creates “artificial gravity” at the outside rim of the station. (a) If the diameter of the space station is 800 m, how many revolutions per minute are needed for the “artificial gravity” acceleration to be $9.80\frac{m}{{s}^{2}}$ ? (b) If the space station is a waiting area for travelers going to Mars, it might be desirable to simulate the acceleration due to gravity on the Martian surface $\left(3.70\frac{m}{{s}^{2}}\right)$ . How many revolutions per minute are needed in this case?

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Jacob Homer

Answered 2021-12-20
Author has **41** answers

Step 1

Given:

Step 2

We know that the centripetal acceleration is given by

and we also know that the linear velocity for a rotation object is given by

Hence,

And this is a general formula for both cases in this problem.

Step 3

a) We need to make the centripetal acceleration equals the free-fall acceleration of Earth, so, from (1);

solving for

Plug the given;

We need to find it in rev/min, so we will use some converting factors.

Noting that

and

Step 4

Multiply (2) by the two converting factors (A) and (B).

rad ans s are cancelled.

Step 5

b)Using the same approach above but changing the free-fall acceleration of Earth

Hence, from (1)

solving for

Plug the given;

Multiply (3) by the two converting factors (A) and (B).

porschomcl

Answered 2021-12-21
Author has **28** answers

A) The circumference can be used to obtain the radius of the space station

The acceleration a for a rotational motion in terms of angular velocity

The number of revolution required is the frequency of

B) We adopt the same procedure as we did for Part A except that the acceleration in now

nick1337

Answered 2021-12-27
Author has **575** answers

Explanation:

In space station artificial gravity is created by rotational motion of space station

Centifugal acceleration creates artificial gravity

NSK

no of turns per min

For Mars

Same theory will apply

per min

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