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Four bricks of length L, identical and uniform, are stacked on top of one another in such a way that part of each extends beyond the one beneath. Find, in terms of L, the maximum values of the following, such that the stack is in equilibrium, on the verge of falling.

Respuesta :

  1. (a1)_ max = L/2
  2. (a2)_max =L/4
  3. (a3)_max = - L/6
  4. (a4)_max = -L/8
  5. h=25 L / 24

Explanation:

The system is in equilibrium and length of each brick = L

a)

for brick 1,

as the center of gravity lies to the right of L/2,

The value of (a1)_ max = L/2

b)

for brick 2,

as the center of gravity lies to the right of L/2,

The value of (a2)_max =1/2 (a1)-max

The value of (a2)_max =L/4

c)

for brick 3,

taking the moment of force

the value of (a3)_max =  [(-m L/2) + 2 m(0)] / 2 m +m

the value of (a3)_max = - L/6

d)

for the brick 4,

taking the moment of force

the value of (a4)_max = (3(0) m + m (-L/2)) / 3 m +m

the value of (a4)_max = -L/8

e)

the value of h = |a1| + |a2| +|a3| + |a4|

= L/2 + L/4 +L/6 +L/8

=((12+6+4+3)/24) L

h=25 L / 24

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