The magnitude of the resultant force acting on the bracket is to be 400 N. Determine the magnitude of F1 if Φ = 30°
Let us first draw out the vector components as follows:
We drew this image quite large, because it’s really important to see the x and y components of each of the force vectors. We also set Φ to 30° as stated in the question.
Now, we can write the components of each force, F_1, F_2, F_3, using our diagram.
To find the resultant, we will sum the x and y forces. We simply add the x components together, and we add the y components together, and in this case, we chose up and to the right as the positive side.
The question states that the magnitude of the resultant, F_R is 400 N. Therefore, we can write the following using the Pythagorean theorem.
Solving for F_1 gives us:
Notice that we got a negative value as well. This simply means the direction we chose for F_1 is opposite to that of what we chose.