Rotation period of a space station

[ross moldvoer]

Homework Statement

To simulate the extreme accelerations during launch, astronauts train in a large centrifuge. If the centrifuge diameter is 13.5m , what should be its rotation period to produce a centripetal acceleration of
If the centrifuge diameter is 13.5m , what should be its rotation period to produce a centripetal acceleration of 2 g? of 5g?

Homework Equations

T=2*pi*r/v

The Attempt at a Solution

i tried solving for v using a=v^2/r and then plugging it in but i got the wrong answer

 

[haruspex]

Homework Statement

To simulate the extreme accelerations during launch, astronauts train in a large centrifuge. If the centrifuge diameter is 13.5m , what should be its rotation period to produce a centripetal acceleration of
If the centrifuge diameter is 13.5m , what should be its rotation period to produce a centripetal acceleration of 2 g? of 5g?

Homework Equations

T=2*pi*r/v

The Attempt at a Solution

i tried solving for v using a=v^2/r and then plugging it in but i got the wrong answer

Please post your working, or we can't tell if or where you went wrong.
(Are you sure it asks for a centripetal acceleration of that magnitude, not a net g-force corresponding to it?)

 

[ross moldvoer]

i did 9.8=v^2/6.75, v^2=(9.8)(6.75)=66.15 v=8.13
then i plugged v into the equation i gave above

 

[haruspex]

i did 9.8=v^2/6.75, v^2=(9.8)(6.75)=66.15 v=8.13
then i plugged v into the equation i gave above

It says 2g and 5g, not 1g.

 

[dean barry]

You need to introduce T into the root equation.
You have a = v ² / r
But v = ( 2 * π * r ) / T

 

[ross moldvoer]

then what equation should i use to solve for v since i don't know T?

 

[haruspex]

then what equation should i use to solve for v since i don't know T?

I think dean barry is suggesting you eliminate v between the two equations so that you can go straight to finding T without having to calculate v. That's good advice generally, since it serves to reduce accumulation of rounding errors, but I don't think it matters here.
Do you have a response to my post #4?

 

[ross moldvoer]

i did accidently forget to do 2g instead of just 9.8.

 

[haruspex]

i did accidently forget to do 2g instead of just 9.8.

So does that resolve your issue, or do you still have the wrong answer?

 

[ross moldvoer]

that fixed it. thanks a ton

 

[ross moldvoer]

so after solving for omega i plug it into T=2*pi*r/v? i get 407 when i do this and this seeems a little high

 

[haruspex]

so after solving for omega i plug it into T=2*pi*r/v? i get 407 when i do this and this seeems a little high

Yes, that's way too high. Please post all your steps.

 

[dean barry]

Take: a = v ² / r
You know:
v = ( 2 * π * r ) / T
( which introduces T into the game )
You get: a = ( ( 2 * π * r ) / T ) ² ) / r
Transpose for T