Chapter 9, Problem 21P

To determine

The normal force exerted by the road on the rear tires at A, andthe vertical force exerted on the trailer by the support B.

Answer to Problem 21P

Solution:

Normal force at A $F_A=\text{1}\text{.7}\times {\text{10}}^4\text{N}$

Vertical force at $F_B=\text{7}\text{.7}\times {\text{10}}^3\text{N}$

Explanation of Solution

Given:

Mass of the truck, $M=2500\text{kg}$

Formula used:

Equilibrium condition: the net force and torque would be zero.

  $\begin{array}{l}{\displaystyle \sum F=0}\\ {\displaystyle \sum \tau =0}\end{array}$

Calculation:

The free body diagram is shown below

  

Figure.2

  $\begin{array}{l}{\displaystyle \sum F=0}\\ F_n+F_v-Mg=0\\ F_n+F_v-2500(9.8)=0\\ F_n+F_v=24500\end{array}$  ........ (1)

Taking sum of all the torques about A

  $\begin{array}{l}{\displaystyle \sum \tau =0}\\ F_v(8)-Mg(2.5)=0\\ F_v(8)-(2500)(9.8)(2.5)=0\\ F_v=7656.25\text{N}\\ F_v=\text{7}\text{.7}\times {\text{10}}^3\text{N}\end{array}$

Plugging the value of $F_V$ in the (1)

  $\begin{array}{l}{F}_n+F_v=24500\\ F_n+7656.25=24500\\ F_n=16843.75\text{N}\\ F_n=\text{1}\text{.7}\times {\text{10}}^4\text{N}\end{array}$

Conclusion:

Normal force at A $F_A=\text{1}\text{.7}\times {\text{10}}^4\text{N}$ .

Vertical force at B, $F_B=\text{7}\text{.7}\times {\text{10}}^3\text{N}$ .