Calculate the normal force and the tension in the string

[hadoken22]

Hello. I am starting tension in my physics class and am stuck on a problem. I was wondering if anyone could help me out. It seems really simple: an object of mass 50kg is being held by a string attached to the top of a frictionless inclined plane that is 60 degrees above the horizontal. I need to calculate the normal force and the tension in the string.
I am really not sure how to solve this problem. My thinking was that the normal force exerted by the inclined plane would be equal in magnitude to the force of gravity, but opposite in direction. Fg=50kg*9.81*sin(60)=-Fn But, I am not sure that this is really true. It could be that the force of gravity is equal to the sum of the tension and the normal force. I tried breaking the forces down to their components and summing them up, but I did not get very far. I feel that I am failing to grasp some fundamental concepts. Any help would be greatly appreciated. Also, the answer is supposed to be 508 Newtons.
Thank you!

 

[gnome]

I tried breaking the forces down to their components and summing them up, but I did not get very far

Well, that is the way to solve this problem, so why did you not get very far? How did you go about doing this?

Also, what answer is supposed to be 508 N? Are you sure about that? You said you are to calculate the tension and the normal force. Neither of those is going to be 508N, assuming the string is parallel to the surface of the inclined plane. Look, the weight of the object is only 490N, so if the string is parallel to the surface, the tension and the normal force must each be less than 490N. (And if the string is not parallel to the surface, we need more info -- such as the height of the object and the point of attachment of the string).

 

[hadoken22]

Thanks for your help. But, what you said about the answers being less than 508 is exactly what I was thinking. Unfortunately the answers in the back of my textbook lists that both values are 508 Newtons. I checked several times that these answers were indeed referring to the correct problem and chapter, and they are. In addition, the string is parallel to the inclined plane and no height is given for the object or the plane. Perhaps the answer in the back is wrong. I found the right answer for all of the other problems that I tried. I'll just have to ask my teacher about this one.

Thanks again.

 

[hadoken22]

My teacher announced today that the answers in the back of the book are indeed wrong. The answers that I was getting of 425N and 245N turned out to be correct.