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)
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
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
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.
This proves conclusively that physicists think in vector components and mathematicians think in triangles and parallelograms.