Finding Radial Force from Free Body Diagram

[Slipjoints]

Homework Statement

Finf the radial force caused by the horizontal component of the normal force

Relevant Equations

Balance equation

I have a question regarding a homework exercise. My professor asked me to find the radial force in the free body diagram in the image included. There is a weight Fz from above and it is assumed that it is countered by the vertical component of both the Ff (friction force) and the Fn (normal force). The radial force (Fr) is supposed to be equal to the horizontal component of Fn. The other thing I know for sure is that the friction coefficient (Greek letter mu) should be in the final expression for Fr. However he also says there should not be any squared trigonometric functions in the final expression and I can't seem to make that work. So basically I have to find an expression for fr from the vertical forces balance equation that includes the coefficient of friction and without squared trigonometric functions, anyone that can help?

 

[Lnewqban]

Should it be force of friction rather than radial force?

Welcome!

 

[Slipjoints]

Yeah that's what I thought too initially, but he specifically said I should use the balance equation of vertical forces and substitute the horizontal component of the normal force into it in order to get the radial force expression.

 

[Slipjoints]

Should it be force of friction rather than radial force?

Welcome!

By accident replied to the thread instead of to your comment, but my reply to you is reply #3

 

[Slipjoints]

Should it be force of friction rather than radial force?

Welcome!

Just found out the right answer, thanks for the help anyway. I added an image in case youre curious. last line is because it is actually a cone.