Question

5. [1pt] Five identical books of mass 890 g and width a = 217 mm are stepped equally and so as to maximize the overhang, d. Calculate d.

Please help me solve this question and shows the processes of the solutions, thank you :)

Answer 1

We take the book is uniform and the COM is located at a/2 from the left edge taken as origin.

each book is offset by a distance x from the lower one

the COM of the second one is located at a/2 +x, third at a/2 +2x , fourth at a/2 +3x and the fifth at a/2 +4x

COM of the stack

x_cm = m(a/2 + (a/2+x) +(a/2+2x) +(a/2+3x) +(a/2+4x) ) /5m - m mass of each book

= a/2+ 2x.

Weight of the stack acts vertically down from COM, for stability the vertical line from COm must be within the contact boundary

x_cm <a

x <a/4

over hang d = 4x <a.

The over hang can be a , max i.e 217 mm