another ramp question

[F.B]

I am really stuck on this question i just got part a of it and now b is left.

 

Mu= Weird friction symbol

 

A box of a mass m=22 kg is at rest on a ramp inclined at 45 degrees to the horizontal. The coefficient of friction between the box and the ramp are "Mu s" = 0.78 and "Mu k" = 0.65.

b) Determine the magnitude of the smallest force that can be applied onto the top of the box, perpendicular to the ramp, if the box is to remain at rest.

 

Im having trouble drawing the Fapp arrow, so its messing with my equations.

I'll post what i did so far.

 

Fn= Fgy - Fapp

Fnet=0

Fnet= Fgx - Ffs

 

i'm pretty sure my Fnet equation is right. But i dont know about my Fn. So can anyone please tell me if those are the right equations.

[swansont]

Can't tell yet. You should be able to put the forces in terms of mg, the inclination angle and the relevant coefficient of friction.

[LazerFazer]

Well, do you have an answer that i can compare to? From my calculations, I got Fapp=43.1N as the smallest force to keep the box stationary. If you wish, i can email you a scan of how I went about doing it, along with possible explanations.

 

cheers,

LazerFazer

[swansont]

here is a problem with a link to the solution.

 

another

 

and another

 

Note: I have not checked the problems for correctness, but they all seem to be physics-course-related, so you have to figure at least one semester's worth of students have had a chance to find errors and complain.