A wooden block is placed on a horizontal plate which is at rest. The
coefficient of static friction, mu, is given. What force, applied to the
block will initiate sliding? We know the answer, F=mu*m*g. And now a
different question. What is the minimum acceleration, a, of the supporting
plate which will result in sliding (of the block with respect to the plate)?
Everybody knows that the block will slide backward when the acceleration of
the plate is too large. How do we explain this? We say that the net force
acting on the non-sliding block must be m*a and that for very large a this
exceeds the static frictional force mu*m*g. Thus the answer is a=mu*g.
I am not sure this is correct, even in elementary mechanics.
In a fixed frame of reference I recognize two objects, an accelerating
plate and a block above it. A free body diagram for the block shows three
forces acting on it: (1) Weight, mg, pointing down, (2) the reaction force
from the plate and (3) horizontal force due to "static friction". I am not
sure that the reaction force (plate acting on the block) is vertical when
the plate is accelerating. The answer a=mu*g is correct only when the
first two forces cancel each other.
Ludwik Kowalski