Chapter 7, Problem 51P

To determine

The center of gravity in the horizontal plane, so that the crane operator can pick up the load without tipping it.

Answer to Problem 51P

Center of gravity is $\left(1.2l ,0.9l\right)$ from the bottom left corner.

Explanation of Solution

Given:

Mass of each cube is $M$ , and the length of each cube is $l$

The given figure is shown below.

  

Formula used:

The center of mass is calculated as,

  $x_{cm}=\frac{{\displaystyle \sum M\times l}}{{\displaystyle \sum M}}$

Calculation:

Considering the figure shown below to calculate the location.

  

 &emsol$\begin{array}{c}{x}_{cm}=\frac{(5M)\left(\frac{l}{2}\right)+(3M)\left(\frac{3l}{2}\right)+(2M)\left(\frac{5l}{2}\right)}{10M}\\ =\text{1}\text{.2}l\end{array}$

  $\begin{array}{c}{y}_{cm}=\frac{(7M)\left(\frac{l}{2}\right)+(2M)\left(\frac{3l}{2}\right)+(M)\left(\frac{5l}{2}\right)}{10M}\\ =0.9l\end{array}$

Conclusion:

Hence, the center of mass from the back left corner of the pallet is $(1.2l,0.9l)$