A block of mass m is placed on a rough surface inclined relative to the horizontal. The incline angle is increased until the block start to move. Show that you can obtain the coefficient of static friction μs by measuring the critical angle θ where slipping occurs.

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A block of mass m is placed on a rough surface inclined relative to the horizontal. The incline angle is increased until the block start to move. Show that you can obtain the coefficient of static friction μs by measuring the critical angle θ where slipping occurs.

 

A block of mass m is placed on a rough surface inclined relative to the horizontal. The incline angle is increased until the block start to move. Show that you can obtain the coefficient of static friction Us by measuring the critical angle 0 where
slipping occurs.
Problem
mg
mg cs
Solution
Just before slipping, we say that the block is still at rest, so the net force on the x-axis is:
EFx=mg
-f
Evaluating, we get:
= mg
But the frictional force is expressed as the product of coefficient and the normal force so.
= mg
For an inclined plane. The normal force is
n=mg
cos(e)
Then,
Us=mg
so:
tan(e)
Transcribed Image Text:A block of mass m is placed on a rough surface inclined relative to the horizontal. The incline angle is increased until the block start to move. Show that you can obtain the coefficient of static friction Us by measuring the critical angle 0 where slipping occurs. Problem mg mg cs Solution Just before slipping, we say that the block is still at rest, so the net force on the x-axis is: EFx=mg -f Evaluating, we get: = mg But the frictional force is expressed as the product of coefficient and the normal force so. = mg For an inclined plane. The normal force is n=mg cos(e) Then, Us=mg so: tan(e)
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