Chapter 3, Problem 3.1P

through 3.3 Determine the magnitude, direction, and sense of the resultant for the coplanar concurrent force systems shown Use the parallelogram law. Also sketch the force triangle.

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To determine

Determine the magnitude,direction and resultant coplanar concurrent force.

Explanation of Solution

Given:

Concept Used:

Parallelogram law of forces. Constructing a parallelogram of OABC with AB is parallel to side OC and represents of $45lb$ and OA is parallel to OC represents the force $25lb$ .

Calculation:

  $\angle AOC={60}^{\circ }-{10}^{\circ }={50}^{\circ }$

Angle AOC and Angle OAB are supplementary

  $\begin{array}{l}\angle OAB={180}^{\circ }-\angle AOC\\ \angle OAB={180}^{\circ }-50\\ \angle OAB={130}^{\circ }\end{array}$

By applying the law of cosine rule R can be determined

  $\begin{array}{l}{R}^2=P{1}^2+P{2}^2-2P1P2\cos A\\ R^2={25}^2+{45}^2-2\left(25\right)\left(45\right)\cos {130}^{\circ }\\ R=64LB\end{array}$

By taking the law of sine rule

  $\begin{array}{l}R/sinO=AB/sinO\\ sinO=AB\sin A/R\\ O={\sin }^{-1}\left(45\sin {130}^{\circ }/64\right)\\ O={32.6}^{\circ }\end{array}$

  $\begin{array}{l}\theta ={60}^{\circ }-\angle AOB\\ \theta ={60}^{\circ }-{32.6}^{\circ }\\ \theta ={27.4}^{\circ }\end{array}$

Conclusion:

Therefore, the magnitude and resultant coplanar as follows

  $\begin{array}{l}\theta ={27.4}^{\circ }\\ R=64lb\end{array}$