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## Homework Statement

"A solid uniform 45-kg ball of diameter 32cm is supported against a verticle frictionless wall using a thin 30cm wire of negligible mass.

A)Make a free body diagram for the ball and use it to find the tension in the wire.

B)How hard does the ball push against the wall?[/B]

## Homework Equations

##\sum(Fx) = 0##

##\sum(Fy) = 0##

##a^2 + b^2 = c^2##

[/B]

## The Attempt at a Solution

There is a picture of the situation.

Here is another picture of my free body diagram.

Now, using the equilibrium equations, I got ##\sum(Fy) = -441.45 + TSinθ = 0##

So, ##Tsinθ = 441.45## (Newtons).

Now for the x components.

##\sum(Fx) = Tcosθ - N = 0##

So, ##Tcosθ = N##

Now I need to figure out what the angle is. The diameter of the sphere is 32cm, so the radius must be 16cm. The length of the wire is 30cm. I used the pythagorean theorem to find the height from the sphere to the wire.

##16^2 + b^2 = 30^2##

##256 + b^2 = 900##

##b^2 = 644##

##b = 25.38##

Now ##\arcsin(25.38/30) = 57.78 degrees##

This is where I start to have trouble. I figured I would find T by plugging that angle into ##Tsinθ = 441.45## and solving for T. This gave me an answer of 521.8 N. When I check the back of the book, the answer is actually 470 Newtons.

Any help?