Chapter 9, Problem 14P

To determine

The position where a person can sit on table without tipping it over.

Answer to Problem 14P

Solution:

0.2818 m from the edge of the table.

Explanation of Solution

Given:

The table is 2.2m long and there are two legs placed 0.5 m from each end of the table. with 1.2 meters between the two legs. the top of the table is 0.80 m tall.

Mass of table =24 kg

Mass of person = 66 kg

Formula Used:

For rotational equilibrium:

  ${\displaystyle \sum \tau ={\displaystyle \sum F\times r=}0}$

Calculation:

The moment produced by the weight of the table is

  $24\times 9.8\times 0.6=141.12\text{N}\cdot \text{m}$

The moment produced by person, where x = distance from edge

  $66\times 9.8(0.5-x)=323.34-646.8x$

Set those equal to each other (where the moment from the person equals the moment from the table weight. If the person had any more moment produced it would exceed the table moment and start to rotate).

  $\begin{array}{l}141.12=323.34-646.8x\\ 646.8x=182.6\\ x=0.2818\text{m}\end{array}$

Conclusion:

Hence, 0.2818 m from the edge of the table.