Determine the magnitude of the resultant force F_{R} = F_{1} + F_{2} and its direction, measured clockwise from the positive u axis.

#### Solution:

Let us draw the vector components. When doing this question, it is highly recommended to draw a very large diagram, otherwise, the v-axis can cause confusion as it might appear to be the resultant force.

Now, we will use the law of cosines to figure out F_R. (Forgot the Law of Cosines?)

(F_{R})^2=300^2+500^2-2(300)(500)\cos95^0

F_R=\sqrt{300^2+500^2-2(300)(500)\cos95^0}

F_R=605.1N

F_R=\sqrt{300^2+500^2-2(300)(500)\cos95^0}

F_R=605.1N

To figure out \theta we will use the law of sines. (Forgot the Law of Sines?)

\dfrac{605.1}{\sin95^0}=\dfrac{500}{\sin \theta}

\theta = 55.40^0

\theta = 55.40^0

As the question asks us for the direction measured from the positive u-axis, we need to add 30^0 to our \theta value. Remember that \theta only represents the angle between force F_1 and F_R.

\phi=55.40^0+30^0

\phi=85.4^0

\phi=85.4^0

how do you get that 95 deg angle?

Looking at force F1 and F2, notice how it creates an angle of 45°+40°=85° angle (between the two). Now, notice the dashed line coming from the end point of force F1 heading towards the end point of force FR. That dashed line, and force F2 creates an interior angle (please refer to: https://goo.gl/vBHDxy), where it must equal 180°. Thus, the inside angle must then be 180°-85°=95°. Hope that helps you out! 🙂

Why tetha + 30 degree ?

The reason we add 30° is because the question asks us to find the direction

measured clockwise from the positive u axis. Therefore, the resultant force is θ+ 30°, where 30° is the angle between the positive u-axis and the force F1. Remember that θ represents the angle between force F1 and FR, not the total angle measured from the positive u-axis. Hope that helps! 🙂How did we know to use 95 as the resultant angle?

Please kindly check the previous reply to another comment asking the same question, thanks 🙂

Resolve the force F1 and F2 into components acting along the u and v axes.

Please see: https://www.youtube.com/watch?v=Ixv1QYUAMWk