Net force equation on incline, tension at angle 
Here's the situation: a block is on an incline. A string is attached at a certain angle and applies tension to the block in the direction up the incline. What would the net force equation look like?
My instinct is that $F_\textrm{net} = T_y + T_x - Ff - F_{gx}$ (since $F_n$ and $F_{gy}$ balance out). But, the only force in the $y$ direction is $T_y,$ which seems to indicate the box will be lifted off the incline! Is there another force acting opposite of $T_y$? In real life, even if you pull something at an angle it doesn't necessarily lift off the ground. I feel like there's some part/explanation I'm missing out on.
Would the actual net equation be $F_\textrm{net} = T_x - F_f - F_{gx}$?
 A: Force is a vector quantity so you need to use vector addition.
The net force in the x-direction is $T_{\rm x }-F_{\rm f }-F_{\rm gx }$ and the net force in the y-direction it is $F_{\rm N }+T_{\rm y }-F_{\rm gy }$ which is presumably zero.
A: Here what you are facing problem is that the Fgx and Fn will not cancel out.I use the component method i.e. breaking fnet in x,y,z axis
The Fnet (in x direction) = Tx- Fgx -Ff(which i am assuming is frictional force)
The Fnet (in y direction) = Ty + Fn - Fgy
Here the normal force is not equal to Fgx as normal force is the force required to prevent penetrating of objects(though usually its value is Fgx).
If Ty is less than Fgy there will be a normal force acting to prevent penetration(whose value can change accordingly).
But is the Ty is greater than Fgy it will move up(if you pull a object with enough force it will move upwards). If equal it will just loose contact.
A: No rule says that $F_n$ and $F_{gy}$ must balance out.
They just often do in simple examples. But never remember this as a rule! Because it isn't. 
The normal force $F_n$ is a "holding up"-force. It can adjust. It is only as large as it needs to be.


*

*Put a book on a table, and a normal force appears to hold it up.

*Add another book, and the normal force grows to the double. 
In your case:


*

*Place a block on the incline, and the normal force appears to hold back the force that pushes against the surface. This is the y component of gravity. It balances it out completely. 

*Now pull a bit outwards in the box with a string. This pull balances a bit of the gravity, so there is now less left for the normal force to withstand. The normal force is thus smaller than without the extra pull. 
The total sum of these three forces is at all times zero. And that's the only rule.

(Except, of course, if the pull in the string is large enough to overcome gravity - then the object will fly off, and the normal force is zero and not needed since there is nothing to hold back against.) 
