Fairground ride, main driver & pin, forces, stress & angular velocity help

[bobmarly12345]

Homework Statement

A fair ground ride comprises of a car, connected to an arm, secured to the main driver by a pin. It rotates about a vertical axis.

when operational:
a) what type of stress is experienced by the pin?, and what type of stress is experienced by the arm?
b) if the max allowable stress in the pin is 15MN/m²; the pin is 25mm diameter, determine the max force F that the car should exert on the pin.
c)if the loaded mass of the car is 200Kg and the radius from the axis of rotation to the centre of mass of the car is 8m determine the angular velocity of the car about the axis of rotation which will give rise to a stress of 12MN/m² in the pin.

I know its a lot to ask but I've really been tearing my hair out over this question as i don't have an example to work from so any help on this would be great .. an example for me to work off would be even better. Thanks

Homework Equations

Centrifugal force ... F=(m)(r)(w²)

The Attempt at a Solution

Homework Statement

Homework Equations

The Attempt at a Solution

 

[LawrenceC]

"I know its a lot to ask but I've really been tearing my hair out over this question..."

Are you referring to question c or are you referring to the entire problem?

Hint: There are tensile-compressive stresses and there are shear stresses.

 

[bobmarly12345]

the entire question, a b & c .
tensile on the arm & shear on the pin?

 

[LawrenceC]

You must make an attempt before we can help - forum rules.

 

[bobmarly12345]

my apologies,

for question b) i believe that to find the force i must use the formula stress=Force/Area and re-arrange it to be Stress X Area = force.

for c) if stress = F/A and using the centrifugal force F=mass x r x angular velocity² do i substitute the centrifual force formula into the stress =f/a formula. then rearrange it all so i can work out the angular velocity which the question is asking for?

so Stress = (m.r.w²)/area of circle
rearranged to: stress x (area of circle)/(mass x radius) =w²
then square root the answer to get angular velocity?

i might be completely wrong but that's what i assume would be the way of getting the right answer

 

[LawrenceC]

"for question b) i believe that to find the force i must use the formula stress=Force/Area and re-arrange it to be Stress X Area = force. "

Correct

"for c) if stress = F/A and using the centrifugal force F=mass x r x angular velocity² do i substitute the centrifual force formula into the stress =f/a formula. then rearrange it all so i can work out the angular velocity which the question is asking for?"

Yes, that's it.

 

[bobmarly12345]

that's brilliant! thank you! :)