Chapter 8.3, Problem 38PP

To determine

The forces exerted by the two sawhorses.

Answer to Problem 38PP

The force exerted by the sawhorse A is $79.8\text{N}$ and the force exerted by the sawhorse B is $31.92\text{N}$ .

Explanation of Solution

Given Data:

Mass of the ladder, $m=11.4\text{kg}$

Distance of the sawhorse A from the centre of gravity of the ladder, $r_g=0.30\text{m}$

Distance of the sawhorse B from the sawhorse A, $r_B=1.5\text{m}$

Formula Used:

The force exerted by the sawhorse A is,

  $F_A=mg\left(1-\frac{r_g}{r_b}\right)$ ….. (1)

The force exerted by the sawhorse B is,

  $F_B=\frac{mg{r}_g}{r_b}$ …… (2)

Calculation:

Substitute values in the expression (1).

  $\begin{array}{c}{F}_A=\left(11.4\text{kg}\right)\left(9.8\text{m}/{\text{s}}^2\right)\left(1-\frac{0.30\text{m}}{1.05\text{m}}\right)\\ =79.8\text{N}\end{array}$

Substitute values in the expression (2).

  $\begin{array}{c}{F}_B=\left(11.4\text{kg}\right)\left(9.8\text{m}/{\text{s}}^2\right)\left(\frac{0.30\text{m}}{1.05\text{m}}\right)\\ =31.92\text{N}\end{array}$

Thus, the force exerted by the sawhorse A is $79.8\text{N}$ and the force exerted by the sawhorse B is $31.92\text{N}$ .