Ball attached to string attached to wall, find force against wall

[melizabeth]

Homework Statement

A solid uniform 50kg ball of diameter 30cm is supported against a vertical frictionless wall using a thin 35cm wire of negligible mass (the wire is attached to the wall, the ball is attached to the wire and rests against the wall). Make a free body diagram for the ball and use it to find the tension in the wire. How hard does the ball push against the wall?

Homework Equations

∑Fx = max
∑Fy = may
(no given equations - these are ones i would fine useful)

The Attempt at a Solution

i have no idea how to set up this problem. i know free body diagrams, but i don't know how to orient my coordinate system for this problem. Please don't help me solve the problem, but pleasepleaseplease help me with how to set it up.

 

[jackarms]

Hello! So I think the setup for this will look like the ball right up against the wall, with the wire going up to where it's anchored on the wall at the pivot. You can find the angle with right triangles. So for forces you'll have the tension going up along this angle, the weight force going straight down, and the normal force from the wall onto the ball that's horizontal. For coordinate systems it really doesn't matter. The natural system would be to have the y-axis up and down along the wall, and the x-axis perpendicular to that.

I'll give you a hint though -- if you have the y-axis going along the wire, and the x-axis corresponding to that, you can solve it more efficiently.

 

[melizabeth]

thanks jackarms! I actually figured how to set it up right after i did this post. But now I'm stuck on this other part. Here's what i got.

so

sinθ = 15/50
(i got this by taking the radius of the circle as opposite and taking the length of the wire plus the radius)
θ = 17.46

∑Fx = Tsinθ - N = ?

∑Fy = Tcosθ - w = 0
solved T to be (513.7)

I don't know how to solve for ∑Fx because I won't know what N is

 

[jackarms]

Well, you know that $\Sigma F_{x} = ma_{x}$, so do you know what $a_{x}$ is?

 

[melizabeth]

This part makes me confused. I think the acceleration would be zero because it's not moving, but that would make the sum of the forces equal to zero in both x and y, but there is a uncounted force against the wall, which I'm trying to solve for. hmmmm

Am I adding in my equation the force which I'm trying to solve for?

Like,

∑Fx = Tsinθ - N + F(the force I'm trying to solve for) = 0

 

[melizabeth]

I wouldn't know what to call that force though... cause I feel it's a resultant force of the tension in the string. i wouldn't know what would cause the force other than from the result of other forces at work.