Centripetal Acceleration and period of rotation

[Heat]

Homework Statement

In a test of a “g -suit,” a volunteer is rotated in a horizontal circle of radius 7.7m.

What must the period of rotation be so that the centripetal acceleration has a magnitude of 3.7g ?

What must the period of rotation be so that the centripetal acceleration has a magnitude of 10g?

Homework Equations

F=ma
w=ma
4pi^2r/T

The Attempt at a Solution

Ok I started by converting 3.7g, by doing this 9.8*3.7 = 36.26

4pi^2(7.7)/ 36.26

but it is wrong, how would I solve this?

 

[hage567]

4pi^2r/T

This isn't right, check the units. It's supposed to be acceleration, right? Did you derive it yourself?

 

[Heat]

I've been told it has something to do with the equation, although I don't think I am using properly.

what would you do in the following situation?

 

[hage567]

Well, start with the equation for centripetal acceleration, a = v^2/r. You need to relate it to the period. You can do that by the velocity term. What's a way to express the velocity of an object moving in a circle?

 

[Heat]

velocity would be distance/time.

Circumference = 2*pi*Radius

v=2pir/t ?

 

[hage567]

That's right. Now put that together with the a=v^2/r and you should come up with the equation you need.

 

[Heat]

a = 4pi^2r / t^2

?

 

[hage567]

Yes. So solve that for t and use it to find the period.

 

[Heat]

ok got it. thank you