0
$\begingroup$

I'm studying for my trig final and I know how to do all the math, but I don't always understand how to setup the story problems. Mostly I'm struggling with vector story problems. For example:

Forces of 4lbs and 12lbs act at an angle of 63 deg to each other. Find the magnitude of the resultant force.

Below is the picture I setup of how I think it should work, but I'm really not clear on what needs to be done after this. I think I need to add the two vectors together but I'm not certain. I got b using law of cosines, though I don't even know if that's relevant to this problem.

enter image description here

$\endgroup$
0
$\begingroup$

In this kind of problem it's helpful to think of the two forces as two adjacent sides of a parallelogram. Draw one force (magnitude and direction) and then draw the second force (magnitude and direction) starting at the "point" of the first force. Then, the resultant force will be the vector going straight from the tail of the first vector to the point of the second vector.

Or, an equivalent way to do it is to put the two vectors tails on top of each other, and then draw the diagonal of the parallelogram formed that has the common vertex as an endpoint. (The $b$ segment you have in your diagram is the other diagonal, not the one you need.)

In this case, you only need magnitude, so you don't really care about the direction of the force.

You can solve this by Law of Cosines but the angle you want is the complement of $63$ degrees, or $117$ degrees. You should see this if you draw it out, especially the first way above.

One other tip: You drew the two vectors above with pretty much equal length. One should be about three times as long as the other. Drawing things more to scale will help to give a visual check of your answer. You'll be able to see right off that the magnitude of the resultant force is bigger than those of either of the two individual forces.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.