The Center of Gravity — Question 5

Question 5

Scale readings reveal a hidden load location

A horizontal board of weight $100\,\mathrm N$ has its own center at $x=1.0\,\mathrm m$. Supports at $x=0$ and $x=2.0\,\mathrm m$ read $90$ and $110\,\mathrm N$ respectively. One unknown point load rests on the board.

1. Find the total center of gravity and the added load weight.

2. Locate the added load.

Question 5 - Solution

Scale readings reveal a hidden load location

(a) Derivation and calculation

Force balance fixes the total weight: $$W_{\mathrm{tot}}=90+110=200\ \mathrm N.$$ Taking moments about the left support, $$200x_G=110(2)\quad\Longrightarrow\quad\boxed{x_G=1.10\ \mathrm m}.$$

(b) Result and interpretation

The added object weighs $$W_o=200-100=100\ \mathrm N.$$ Subtracting the board moment, $$100(1)+100x_o=220\quad\Longrightarrow\quad\boxed{x_o=1.20\ \mathrm m}.$$

Physical check

The combined center lies midway between the board and object centers because their weights are equal.