The fig. shows a uniformly dense rectangular brick of length a, height b resting on a rough inclined plane of angle θ.
The interface between surface and brick has associated coefficients of friction us, uk. A force F is applied as indicated.
a) For F = 0, and varying θ, obtain an expression for the angle at which the brick will first start sliding down the plane.
b) Assuming θ is such that the brick does NOT slide down the inclined plane, obtain expressions for F that i) causes the brick to start sliding up the plane and ii) causes the brick to tip.
c) Plot a graph of f vs F as F is gradually increased from 0 to the value that causes sliding.
d) Obtain a constraint on h such that the brick will tip before it slides.
e) Suppose that instead of a brick of uniform density, we have a rectangular tank containing water. How will your answers to the above be affected?
(Note: static friction force has magnitude f≤usN)
