Chapter 9, Problem 60GP

To determine

To Find: The minimum mass that that will cause the table to overturn.

Answer to Problem 60GP

  $25\mathrm{kg}$

Explanation of Solution

Given:

The mass of the table. $M=25\mathrm{kg}$

Formula used:

Let the minimum mass that can be placed to overturn the table is $m\mathrm{kg}$ .

  

The mass is placed symmetrically between the two legs.

Taking the torque about the axis that passes through the two legs.

  $\begin{array}{l}{\tau }_{axis}=0\\ Mg\times OA=mg\times AB\mathrm{................................}(1)\end{array}$

Calculation:

Putting the values in equation (1):

  $25\cdot OA\cdot \sin 90=mg\cdot AB\cdot \sin 90$ As per symmetry :

The A is the midpoint of OB.

  $\begin{array}{l}OA=AB\\ 25\mathrm{g}=m\mathrm{g}\\ m=25\mathrm{kg}\end{array}$

Conclusion:

The minimum mass that can be placed to overturn the table is $25\mathrm{kg}$ .