Calculating Speed and Rotation for Training Devices

[needhelp83]

A curve of radius 60 m is banked for a design speed of 90 km/h. If the coefficient of static friction is 0.30 (wet pavement), at what range of speeds can a car safely make the curve?

A device for training astronauts and jet fighter pilots is designed to rotate the trainee in a horizontal circle of radius 10.0 m . If the force felt by the trainee is 7.75 times her own weight, how fast is she rotating? Express your answer in both m/s and rev/s.

I am not sure where to even start. Any help would be appreciated.

 

[berkeman]

What equations relate the angular velocity of an object to the force required to keep that object rotating around in a circle? And in -1-, what equation relates the sideways frictional force F on an object to its mass (or weight) and the coefficient of friction mu?

 

[needhelp83]

For the second question:

F=ma
mv^2/r=7.75(m)(g)
mv^2=7.75(m)(9.8 m/s^2)(10)
v^2=759.5
v=27.56 m/s^2

Is this setup correctly?

Now for problem 2
F=mv^2/r=(0.30)(9.8)m
8100 km/h=.06(.30)(9.8)
8100=.1764

Definitely not doing this right? Any suggestions

 

[berkeman]

I think that on both of these you will need to draw a diagram to help you understand what forces to calculate.

-1- Draw the banked curve with a mass m on it. Show the forces from gravitational acceleration g and from the friction force mu*N and from the centripital acceleration.

-2- Draw the trainer chair at the end of the 10m arm. If the problem is stated correctly, it will show that the pilot's chair swivels as the g-forces get higher. When the chair is stationary, it hangs straight down. When the centrifuge is going super-fast, the chair would swing out almost to the horizontal. The swivelling chair is used to always keep the net force on the pilot aimed down through their body, just like in an aircraft pulling g's. If the chair did not swivel, the pilot would be smashed into the outer wall of the centrifuge module, which is not what the trainer is supposed to do. So draw the chair tilted out at some angle -- what determines this angle? And at that angle, what are the various forces acting on the pilot?

 

[needhelp83]

I understand that this is the formula for a banked curve...
R=v^2tan(theta)/g, but now how do I add in the friction

and for the second question I messed up on my units..
F=ma
mv^2/r=7.75(m)(g)
mv^2=7.75(m)(9.8 m/s^2)(10)
v^2=759.5
v=27.56 m/s

How do I convert from 27.56 m/s to rev/s

 

[needhelp83]

Any more help?