# Newton's Laws of Motion

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The fig. shows a uniformly dense rectangular brick of length a, height b resting on a rough inclined plane of angle theta.

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 theta, obtain an expression for the angle at which the brick will first start sliding down the plane.

b) Assuming theta 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)

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##### Solution Summary

The step-by-step solution compares slipping vs. tipping on an inclined plane

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Please refer to the attachment.

N a

b

F

f

mgsinθ

h mg mgcosθ

θ

The fig. above shows a uniformly dense rectangular brick of length a, height b. The interface between surface and brick has associated coefficients of friction μs, μk. 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 ≤ μsN)

Solution: a) Forces acting on the brick are shown in the fig.. Weight mg is resolved into ...

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