Statics problem -- Hinged members and anchor points supporting a mass

[David Donald]

Homework Statement

Member BC exerts on Member AC a force P directed along line knowing that P must have a 325 N horizontal component, determine (a) the magnitude of the force P,

Homework Equations

Trig I suppose

The Attempt at a Solution

So I'm not sure if this correct

I found two angles using the lengths of 720 mm and 650 mm (90, 42.1 and 47.9)
I then used the equation Fx = F*Cos( ) to fin dthe magnitude of P

325 N = F Cos(47.9) ----> 484.76 N

 

[Jufro]

Looks good to me. Just for ease of clarity, when you list angles either name them as ACB, CAB, CBA, or mention in the order you are writing them down.

 

[haruspex]

There is no point in finding the angles from the lengths when all you are going to do with the angles is apply trig functions to them. Just use Pythagoras to find the hypotenuse, then use the ratios of the sides.

 

[Adrian-Mitchell]

What about the vertical component?

 

[Adrian-Mitchell]

For part b, I used the equation F_y=F*cos(∠B)=((484.76)*cos(42.1))N=359.68N.

What do you think?

 

[haruspex]

For part b, I used the equation F_y=F*cos(∠B)=((484.76)*cos(42.1))N=359.68N.

What do you think?

As I commented in post #3, there is no point in finding the angle. It just reduces precision.
$P=F\cos(ACB)$, vertical component is $F\sin(ACB)=P\tan(ACB)=325*\frac{720}{650}=360$.

 

[Adrian-Mitchell]

Ok, cool, I got the same answer! Thank you for the tips on improving my work too.