Find the magnitude and the direction of the resultant of each of the following systems of forces using geometric vectors.

a) Forces of 3 N and 8 N acting at an angle of 60 degrees to each other.

Please help me with this question. I don't understand the wording, so I don't know how to graph this correctly. If you could please include a diagram, it'll be appreciated!

The answer: 9.8 N, 15 degress to 8 N

3 answers

You first need to define a set of coordinate axis to do the problem.

Let the 8 N vector be the x axis. Then the vectors that you add have the following components:
8 + 3 cos 60 = 9.5 along the x axis and
3 sin 60 = 2.598 along the y axis
The magnitude of the resultant is
sqrt [(9.5)^2 + (2.598)^2]= 9.85 N
angle = arctan 2.598/9.5 = 15.3 degrees to relative to the 8 N vector (the x axis, in this case)
This is the way your teacher probably wants you to do it:

draw two lines from the same point so they form a 60º angle to each other, make one line 8 units long and the other 3.

This is half of a parallelogram,so finish the parallelogram by having opposite sides 8 and 3 respectively and the opposite angle as 60º.

Draw the diagonal between the two 60º vertices.
This line is your resultant, let's call its length x units

now by the Cosine Law
x^2 = 3^2 + 8^2 - 2(3)(8)cos 120º
I get x = 9.85

Now let the angle between the 8 unit line and the resultant be α

then sinα/3 = sin 120/9.85

for that I got α = 15.3º
LOL
This proves conclusively that physicists think in vector components and mathematicians think in triangles and parallelograms.