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 thecritical angle e where slipping occurs.mySolutionJust before slipping, we say that the block is still at rest, so the net force on the x-axis is:EFx=mg-fEvaluating, we get:= mgBut the frictional force is expressed as the product of coefficient and the normal force so.= mgFor an inclined plane. The normal force isn=mgThen,Hs=mgcos(e)so:tan(0)

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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 Hs by measuring the critical angle e where slipping occurs. Ar

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 Hs by measuring the critical angle e where slipping occurs. Ar

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter6: Applications Of Newton's Laws

Section: Chapter Questions

Problem 56P: If an object is to rest o an incline without slipping, then friction must equal the component of the...

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Question

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 e where slipping occurs.
my
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
Then,
Hs=mg
cos(e)
so:
tan(0)

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