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60. Problem 13.39P (HRW) Four identical bricks of length L are stacked on a table
as shown in the figure. We seek to maximise the overhang distance h in both
arrangements. We have to find the optimum distances
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and calculate h for the two arrangements.
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Solution: Click For PDF Version Arrangement 1 Key to maximising overhead distances is by ensuring that the normal force on the concerned brick lies at the edge of the brick/surface on which it is resting. Brick 3 is resting on brick 4, therefore, maximum value of
Using a similar argument as above the force that bricks 1 and 2 exert on the brick 4 is 2W and it acts on its left-hand edge. Therefore, the free-body diagram of the brick 4 is as shown.
We calculate the torque about the left-hand edge of brick 4 and require that for equilibrium the net torque on it has to be zero. This gives
And,
Arrangement 2 In this configuration by symmetry,
We will consider the free-body diagram of brick 3. Because of brick 1 there
will be a force W/2 on the left-hand edge of brick 3. From the symmetry
we note that a normal force of 3W/2 acts on brick 3 at the right-hand
edge of brick 4, which is at a distance
We calculate torque about the left-hand edge of brick 3 and as the brick is in equilibrium the net torque has to be zero. That is
And,
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is L/2 and the force that it exerts on brick 4 is W, the weight of
the brick and it acts at the right-hand edge of brick 4.
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from the
left-hand edge of brick 3. The free-body diagram of brick 3 is as shown.
