# Extra credit test question

1. Oct 29, 2007

### ilkjester

1. The problem statement, all variables and given/known data
A 32-N force acting at 25 degrees and a 36-N force acting at 75 degrees act concurrently on point p. What is the magnitude and direction of a third force that produces equilibrium at point P?

The teacher said that we had to know higher math then algebra 1 for this question. But could do it with the law of cosines. Just wondering if you guys could help me figure out how to do it.
2. Relevant equations
r^2=a^2+b^2-2abcos R

3. The attempt at a solution

2. Oct 30, 2007

### Shooting Star

You have to formulate your question more precisely. 25 deg to what?

I'll give you the formula: r^2 = a^2 + b^2 + 2ab cox x, where x is the angle betwen the forces.

Now let's see you solve it.

3. Oct 30, 2007

### tyco05

I agree the question needs to be formulated more precisely. A diagram is your best friend.

Plus, I don't know about all of this formula hoo-haa.

Resolve the forces into their horizontal and vertical components.

Then solve.

All you need for this question is basic year 9 trigonometry and an understanding of vector addition.

4. Oct 30, 2007

### saket

The equation you have quoted is slightly erroneous, if symbols have their usual meaning.

The relevant equation should be r^2 = a^2 + b^2 + 2*a*b*cos R. Use it (and forget what your teacher said) to get the magnitude of the third force. Note, (i) 'R' is the angle between the two forces. (ii) and magnitude of a force is always positive.

As far as direction goes, rightly quoted by "tyco05", knowledge of basic trigonometry would do.
Direction of the resultant,Φ, with one of the forces (say A), is given by (Let other force be B and angle between A and B be "R".):
tanΦ = (B*SinR)/(A + B*CosR).

Therefore, the third force, which will produce equilibrium at point P, would be in the opposite direction to this resultant force.

I hope, now you can manage to get that 'extra credit'. Cheers!

Last edited: Oct 30, 2007