Four bricks, each of length , are put on the top of one another (fig) in such a way that part of each extends beyond the one beneath. For the largest equilibrium extensions,
a) |
The top brick overhanging the one below by |
b) |
The second brick from top overhanging the one below by |
c) |
The third brick from top overhanging the bottom one by |
d) |
The total overhanging length on the edge of the bottom brick is |
Four bricks, each of length , are put on the top of one another (fig) in such a way that part of each extends beyond the one beneath. For the largest equilibrium extensions,
a) |
The top brick overhanging the one below by |
b) |
The second brick from top overhanging the one below by |
c) |
The third brick from top overhanging the bottom one by |
d) |
The total overhanging length on the edge of the bottom brick is |
(a,b,c,d)
Let the weight of each brick be and length As bricks are homogeneous, the centre of gravity of each brick must be at the midpoint. Therefore, the topmost brick will be in equilibrium if its centre of gravity lies at the edge of brick below it, i.e., II brick. Thus the topmost brick can have maximum equilibrium extension of
is the centre of mass of the top two bricks which lies on the edge of the third brick
is the centre of mass of the top three bricks which lies on the edge of the fourth brick
Thus, the maximum overhanging length to top from the edge of bottom brick is