Angles between the forces Problem

[krypt0nite]

Two forces-- 50N and 60N are applied to the same point on a cart. Determine the resultant force on that cart when the angle bewteen the two forces is:
a) 60 degrees

Ok, I'm getting weird answers. I draw a diagram of that. Then I use cosine law and plug everything in and I end up getting 56N. But the answer for the question is 95N. What am i doing wrong?

 

[cepheid]

*Vectors add tip to tail*

The question says that the two vectors are acting at the same point. That means that when both arrowheads are touching, the angle between the arrows is 60^o. But remember that vectors add tip to tail. Make sure you understand the reason for this. Slide one of the vectors until its tail touches the tip of the other, and you will see the angle between them is actually 120^o. Use the cosine law as you originally thought to compute the magnitude of the resultant force vector.


EDIT: Cool, a fellow Vancouverite

 

[Hypercase]

Hi Kryptonite.
Here the drawing a free body diagram we get two vectors joined at the tail.
By using cosine rule what you have found out is the difference of the two vectors.
To find the sum(resultant) first rearrange them so that they are head to tail.
Then try using cosine rule.

 

[CinderBlockFist]

well, if you draw the 2 vectors, using the parallelogram rule /=/ (i can't draw the pic), with the 50N force being the horizontal (along the bottom), and the 60N force going to the upper right. Since the angle given is 60*, the angle in the bottom right corner of the parallelogram will be 120*. So, using the Cosine Rule you plug in these values and you get :

(60)^2 + (50)^2 - 2(60)(50)cos120* and you should get the answer 95 N.


Hopefully you can see what I mean without me drawing the diagram. Good luck.