Question

Determine the magnitude of the force F1F1 component acting along the uu axis. Express your answer to three significant figures and include the appropriate units. View Available Hint(s) Hint 1. How to approach the problemopened hint Since the uu and vv axes are not perpendicular, the force component magnitudes cannot be determined just using one proper trigonometric function. So we need to establish a triangle, a part of a parallelogram corresponding to the parallelogram law. Force F1F1 and its components will be the sides of that triangle. Then, finding the angles of the triangle and using the sine law should help to determine the force component magnitudes.

Answer 1

The first image below shows force F1 and the axes.

Answer: $(F_{1})_{u}=$ 3.62 kN

Explanation: The second figure below express the parallelogram method to calculate the u component of force F1.

The Parallelogram Method is a method to determine resultant force and is applied as described in the question above.

With the three components, $F_{1},(F_{1})_{u}$ and $(F_{1})_{v}$ and angles, it can be used the Law of Sines, which states:

$\frac{a}{sin\alpha} =\frac{b}{sin\beta} =\frac{c}{sin\theta}$

i.e., there is a relation of proportionality between an angle and its opposite side.

For the triangle below:

$\frac{u}{sin30} =\frac{F_{1}}{sin105}$

$u=F_{1}\frac{sin(30)}{sin(105)}$

$u=7\frac{0.5}{0.966}$

u = 3.62

The magnitude of the component acting along the u-axis is 3.62kN.