Question

A 98 N person is standing on a board, 1 m from the end. The board is balanced on a point that is 2m from the same end. The board is 49 N. How long is the board overall?

Answer 1

ANSWER:

8 m

STEP-BY-STEP EXPLANATION:

To calculate the length is the board overall we must apply the center of mass formula, which is as follows:

$x_{cm}=\frac{m_{\text{board}}\cdot x_{\text{noard}}+m_p\cdot x_p}{m_{\text{board}}+m_p}$

The mass of the person and that of the board, we calculate it as follows:

$\begin{gathered} F_{\text{p}}=m_{\text{p}}\cdot g_{} \\ m_{\text{p}}=\frac{F_{\text{p}}}{g}=\frac{98}{9.8}=10kg \\ F_{\text{board}}=m_{\text{board}}\cdot g_{} \\ m_{\text{board}}=\frac{F_{\text{board}}}{g}=\frac{49}{9.8}=5kg \end{gathered}$

Replacing:

$\begin{gathered} -2=\frac{5\cdot x_{\text{board}}+10\cdot(-1)}{5+10} \\ (-2)(15)+10=5\cdot x_{\text{board}} \\ x_{\text{board}}=\frac{-20}{5} \\ x_{\text{board}}=-4\text{ m} \end{gathered}$

Since the CM of the board is only 4 m from the edge of the board, and the MC of the board is at its center, the board is 8 m long.