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.
Rotational Equilibrium And Rotational Dynamics
In physics, the state of balance between the forces and the dynamics of motion is called the equilibrium state. The balance between various forces acting on a system in a rotational motion is called rotational equilibrium or rotational dynamics.
Equilibrium of Forces
The tension created on one body during push or pull is known as force.
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.
Solution
Just before slipping, we say that the block is still at rest, so the net force on the x-axis is:
ΣFx=mg-f=
Evaluating, we get:
f = mg
But the frictional force is expressed as the product of coefficient and the normal force so.
μs = mg
For an inclined plane. The normal force is
n=mg
Then,
μs=mg/cos(θ)
so:
μs=tan(θ)
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