An easy problem about friction force

[samet]

we have an inclined steel plain at angle 20 degree and have a 50 kg steel file the first question is finding the static friction force it's ok ı have found it by using Newton's 2nd law but the second question is at what angle will the cabinet begin to slide ? ı tried equations but ı wasn't able to do it
is it needed to know another thing ı thought when it begins to slide the acceleration will increase but couldn'T make it ı think it is easy but an unusual problem ı don't want to solve whole of the problem only give me a method or way to find it

 

[dextercioby]

I hope that for the first part u've gotten the static friction coefficient µ to be
$$\mu=\tan 20^{°}$$
For the second part,think about what will be the condition for the steel cabinet to slide down the incline...


Daniel.

PS.The answer still involves applying Newton's second law...

 

[samet]

ı thought that after the max static friction force cabinet will begin to slide
but ı can't set an equation if we say F=ma so when the cabinet begin to slide what will be it's acceleration? could you explain
thanks for your help

 

[dextercioby]

Well,let's see.I'll say that the condition for slipping is that the tangential component of gravity (the one that makes work) must be greater than the friction force and i'll state that through this equation:
$$mg\sin \alpha >\mu mg\cos \alpha$$(1)
,where u know that the friction coefficient is
$$\mu=\tan 20$$(2)
From the two equations,u find the angle "alpha" for which the steel begins to slide:
$$\tan \alpha>\tan 20$$(3)
,from where,using the fact that on the physically acceptable angle interval the tangent is uniform/surjective,u get
$$\alpha>20$$ (4)
,which is the condition the incline muxt fulfill in order for the steel to slide.

Daniel.

 

[samet]

ı can estimate this
so we can't say at what angle for instance 43.4 degree ,can we?
file cabinet and surfaces are made by steel
if we know steel's coefficient static force can it be found the right angle?

 

[dextercioby]

ı can estimate this
so we can't say at what angle for instance 43.4 degree ,can we?
file cabinet and surfaces are made by steel
if we know steel's coefficient static force can it be found the right angle?

Any angle bigger than 20° will do it.The steel will slide at any angle over 20°.That's that.U gave a justification,everything else is secondary...
So,yes,43.5° is a good angle,78° is a good angle...

Daniel.

 

[samet]

ok ı understood
thanks for your helps