Chapter 9, Problem 28P

You are on a pirate ship and being forced to walk the plank (Fig. 9-68) You are standing at the point marked C. The plank is nailed onto the deck at point A, and rests on the support 0.75 m away from A The center of mass of the uniform plank is located at point B. Your mass is 65 kg and the mass of the plank is 45 kg. What is the minimum downward force the nails must exert on the plank to hold it in place?

Figure 9-68

To determine

The minimum downward force the nails must exert on the plank to hold it in place.

Answer to Problem 28P

Solution:The minimum downward force that the nails must exert to hold the plank in its place is $\text{2352}\text{N}$.

Explanation of Solution

Given:

Mass of the man, $M_1=65\text{ kg}$

Mass of the plank, $M_2=45\text{ kg}$

Formula used:

For rotational equilibrium

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

Calculation:

  $\text{Sum of all the torques about the support=0}$

  $\begin{array}{c}{\displaystyle \sum \tau }=0\\ F_n(0.75)-45(9.8)(0.75)-65(9.8)(3-0.75)=0\\ F_n(0.75)-330.75-1433.25=0\\ F_n(0.75)=1764\\ F_n=2352\text{N}\end{array}$

Conclusion:

Thus, the minimum downward force that the nails must exert to hold the plank in its place $\text{2352}\text{N}$ .