Finding the Resultant of Two Forces: A Vector Addition Problem

[MrMechanic]

Homework Statement

The resultant of the two forces has a magnitude of 650 lb. Determine the
direction of the resultant and the magnitude of P.
[See Attachment for Figure]

Homework Equations

Well, I only know is R^2=Fx^2+Fy^2
im still confused by this problem

The Attempt at a Solution

I tried using cosine law but it doesn't work well since the answer in the back is
(a) 71.8 degrees and (b) 235lb
Can someone help me?
Very Much appreciated.

 

[Simon Bridge]

You have to show your working ... start by sketching the vectors out head-to-tail.
The cosine rule will work if you have the correct angle and the correct relationships between the sides.
i.e. you have to understand what you are doing instead of just putting numbers into equations.

 

[MrMechanic]

I see. Okay I've tried this
Summation of Px = pcos30
summation of Py = -Psin30
summation of Ny (which is the 500lb force) = -500
R = 650lb
Rx = 650cos@?
Ry = 650sin@?
I'm not really sure on what equations should I use.
Thanks for the reply.

 

[Curious3141]

In this case, I would suggest that the magnitude of P is easier to work out first.

You've already resolved P into horizontal and vertical components. There is an additional 500lb force acting vertically downward.

What is the total horizontal force? What is the total vertical force? All in terms of P.

Now what is the magnitude of the resultant force in terms of P. Use Pythagoras' theorem.

Equate that to 650. Can you solve that equation for P?

Remember that sin 30 deg and cos 30 deg are "nice" results - apply this.

 

[MrMechanic]

What do you mean by "Now what is the magnitude of the resultant force in terms of P. Use Pythagoras' theorem."
It got me confused.
I now know the horizontal and vertical force in terms of P but they are all equations.. I've build up 2 equations.

 

[Curious3141]

What do you mean by "Now what is the magnitude of the resultant force in terms of P. Use Pythagoras' theorem."
It got me confused.
I now know the horizontal and vertical force in terms of P but they are all equations.. I've build up 2 equations.

How do you work out the resultant of two forces at right angles to each other?

Think about a right angled triangle.

 

[Chestermiller]

You have two forces, 500 lb down and the force P at an angle of 60 degrees to the vertical. You want to find the vector sum of these two forces. In terms of P and the angle, what is the equation for the vertical component of the sum of the two forces (which is the same as the sum of their vertical components)? In terms of P and the angle, what is the equation for the horizontal component of the sum of the two forces? In terms of P, what is the resultant of these combined horizontal and vertical components?

 

[Simon Bridge]

You have determined already: F=-500j, and P=Pcos(30)i - Psin(30)j, and you know the resultant Q=|Q|=640 (all forces in lbs and "down" is negative).

You also know that Q=F+P
Do you know how to add vectors?
Do you know how to find the magnitude of a vector?