Chapter 9, Problem 74GP

To determine

To Find: The normal force applied by the road on the rear tires at point A and the vertical force applied to the trailer by support B.

Answer to Problem 74GP

The vertical force applied to the trailer by support B is $\text{6738 N}$ .

The normal force applied by the road on the rear tires at point A is $\text{14822 N}$ .

Explanation of Solution

Given:

Mass of trailer, $\text{m = 2200 kg}$

Distance from point A to C.G of trailer, ${\text{d}}_{AG}\text{= 2}\text{.5 m}$

Distance from C.G of trailer to point B, ${\text{d}}_{GB}\text{= 5}\text{.5 m}$

Formula used:

Taking a torque of all forces about the rear tire that is at point A,

  ${\text{(R}}_{\text{B}}\times {\text{ d}}_{\text{AB}}\text{) - (mg }\times {\text{ d}}_{\text{AG}}\text{) = 0}$

Here, ${\text{d}}_{\text{AG}}$ is the distance from A to Centre of gravity of trailer.

Here, ${\text{d}}_{\text{AB}}$ is the distance from A to B.

Applying the equilibrium condition for the vertical direction,

  ${\text{R}}_{\text{A}}{\text{ + R}}_{\text{B}}\text{ - (m}\times {\text{g) = 0}}_{}$ -(2)

Calculation:

Substitute the given values in equation1,

  $\begin{array}{l}{\text{(R}}_{\text{B}}\times \text{8) - (2200}\times \text{9}\text{.8}\times \text{2}\text{.5) = 0}\\ {\text{(R}}_{\text{B}}\times \text{ 8) = 53900}\\ {\text{R}}_{\text{B}}\text{ = }\frac{\text{53900}}{\text{8}}\text{ = 6738 N}\end{array}$

Substitute the given values in equation 2,

  $\begin{array}{l}{\text{R}}_{\text{A}}{\text{ + R}}_{\text{B}}\text{ = m}\times \text{g}\\ {\text{R}}_{\text{A}}\text{ + 6738 = 2200}\times \text{9}\text{.8}\\ {\text{R}}_{\text{A}}\text{ = 21560 - 6738}\\ {\text{R}}_{\text{A}}\text{ = 14822 N}\end{array}$

Conclusion:

The vertical force applied to the trailer by support B is $\text{6738 N}$ .