Question involving Newton's laws

[mlb2358]

Homework Statement

A horizontal wire holds a solid uniform ball of mass m in place on a tilted ramp that rises 35.0° above the horizontal. The surface of this ramp is perfectly smooth, and the wire is directed away from the center of the ball.(a) How hard does the surface of the ramp push
on the ball? (b) What is the tension in the wire?

Homework Equations

The Attempt at a Solution

I drew a picture and made a triangle with the normal force as one side, the ramp as one side, and the weight as the hypotenuse. I believe the angle between the ramp and the hypotenuse is 55 degrees. That would mean sin(55) = N/mg and that N = mg*sin(55). This is equivalent to approximately 0.82mg. However, the answer I have for this problem is 1.22mg and 1/sin(55) equals 1.22. I am trying to figure out what I am doing wrong here. Any help would be appreciated!

 

[danielu13]

I am confused as to what you are looking for. You found an answer where you listed your attempt, but you didn't provide a mass to use. Otherwise:

F_N = mgsinθ

However, without the knowing the mass, it would be hard to find out where you went wrong.

 

[mlb2358]

Thanks for the reply.
I didn't list a mass because the question didn't provide one. The answer is expected to be in terms of mg. The answer is supposed to be 1.22mg, but I am getting an answer of .82mg.

 

[danielu13]

Strangely enough, I had a problem like this in my physics course a few weeks ago that took me a while to actually understand. I'm not sure if I can explain it, but the way that I understand it is that when on a plane, F_N is represented by a leg of the triangle, and gravity by the hypotenuse. In order to solve this triangle, you must divide by the sine.

 

[Nickie]

Your approach is correct, but you made a small error in your calculation. The angle between the ramp and the hypotenuse is not 55 degrees, but rather 35 degrees (as stated in the problem). Therefore, the correct equation would be sin(35) = N/mg, which results in N = mg*sin(35). This is equivalent to approximately 0.57mg, which is closer to the given answer of 1.22mg. Always make sure to double check the given information and units when solving a physics problem. Keep up the good work!