Finding Minimum Magnitude of Force Fr

[skateza]

Homework Statement

Determine the magnitude of force F so that the resultant Fr of the three forces is as small as possible. What is the minimum magnitude of Fr?

Homework Equations

Their is a 5N force heading horizontally to the right,
a 4 N force heading vertically downwards,
Force F is directed upwards and to the left, at an angle of 30 degrees south east of vertical (30 degrees from the 4N force)

The Attempt at a Solution

My prof said to leave it as a variable and solve it as normal, but i don't see how i can solve it. Do i find the resultant of the two known forces and use F as a variable from then on, seperating both into their separate components to find the final resultant force?

 

[mda]

Yes. Once you have the expression for the resultant force, minimize in the usual way by differentiation.

 

[blochwave]

Well I think you'll have an expression for the magnitude of Fr in terms of, say, Fx and Fy, but Fx and Fy are related through trig since you were given an angle, so you can find them both and then the magnitude of F for the minimum Fr