Question

Four bricks of length l, identical and uniform, are stacked on top of one another (the figure) in such a way that part of each extends beyond the one beneath. Find, in terms of l, the maximum values of (a) a1, (b) a2, (c) a3, (d) a4, and (e) h, such that the stack is in equilibrium

Answer 1

The maximum values of a₁, a₂, a₃, a₄ and h to make the stack in equilibrium are; a₁_max = L/2; a₂_max = L/4; a₃_max = - L/6; a₄_max = -L/8; h = 25L/24

What is the maximum width?

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

a) For brick 1;

Due to the fact that the center of gravity lies to the right of L/2,

Then we can say that the maximum value of a₁ = L/2

b) For brick 2;

Since the center of gravity lies to the right of L/2, then we can say that;

The maximum value of a₂ = ¹/₂a₁_max

Thus, the maximum value of a₂ = L/4

c) For brick 3;

Taking the moment of force, the maximum value of a₃ is;

a₃_max =  [(-¹/₂mL) + 2m(0)]/(2m +m)

a₃_max = - L/6

d) For the brick 4;

Taking the moment of force, the maximum value of a₄ is;

a₄ = [3(0) m + m(-L/2)]/(3m + m)

a₄_max = -L/8

e) The value of h = |a1| + |a2| +|a3| + |a4|

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

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

h = 25L/24

Read more about center of mass at; brainly.com/question/16835885