How do I work out the resultant of the following?? please see attachments hope someone can help. I know how to do them (kind of) but gone blank
Hello,
to #1:
1. I've added a sketch
2. use cosine rule: The resulting force divides the parallelogram of forces into 2 congruent triangles. 2 legs of the triangle are the known forces and the included angle is $\displaystyle \theta = 10^\circ$. Therefore the resulting force is:
$\displaystyle r = \sqrt{10^2+2.5^2-2 \cdot 10 \cdot 2.5 \cdot \cos(10^\circ) }\approx 7.55 \ kN$
3. to calculate the angle between the force of 10 kN and the resulting force $\displaystyle F_r$ use cosine rule again:
$\displaystyle \cos(\theta)=\frac{c^2-a^2-b^2}{-2 \cdot a \cdot b}$.......Plug in all values you know:
$\displaystyle \cos(\theta)=\frac{2.5^2-10^2-7.55^2}{-2 \cdot 10 \cdot 7.55} \approx 0.998361~\implies~\theta\approx 3.281^\circ$
In my drawing I've measured the angle between the x-axis and the resulting force.