1. The problem statement, all variables and given/known data It's Problem 3 of this page: http://www.problemsphysics.com/forces/inclined_planes_problems.html "A box of mass M = 10 Kg rests on a 35° inclined plane with the horizontal. A string is used to keep the box in equilibrium. The string makes an angle of 25 ° with the inclined plane. The coefficient of friction between the box and the inclined plane is 0.3." 2. Relevant equations See link. 3. The attempt at a solution I don't have a problem understanding most of it, but there is one thing that left me thinking: how do we know, in advance (if we can know it), where the direction of the Friction force points? The thing is, the solved problem has Friction force (Fs) pointing downwards (left), but as far as I can tell we could have just as rightfully assumed that it pointed upwards (right). In other words, on the X axis we could have two possible situations: 1. Like they did: Wx and Fs pointing left; Tx pointing right. So at the equilibrium it becomes (chosen +left, -right): Wx + Fs - Tx = 0 2. Like I tried doing before checking their solution: Wx pointing left, Tx and Fs pointing right. Then we have (chosen +left, -right): Wx - Fs - Tx = 0 I tried to think about it, but only managed to come up with two things. First, if we knew how much Wx and Tx are, then we can certainly know that, to keep the equilibrium, Fs must "assist" the "weaker" one of them, and therefore must be on the "weaker one's side". In other words, if Wx was +3, and Tx was -5, then Fs must be +2 (pointing left, like Wx); viceversa, if Wx was +5, and Tx was -3, then Fs must be -2 (pointing right). But then I realized that we don't know Tx when this decision should be made (when setting the equations). So how do we make the decision? The best I could come up with was this: do both methods, and then double-check if there are any contradictions in either one. If there are, discard that one. So I went on and did my thing. Here's what I got by assuming that Fs pointed up. Equilibrium on X (+left, -right): +Wx - Fs - Tx = 0 Equilibrium on Y (+down, -up): +Wy - N - Ty = 0 => N = Wy - Ty => N = mg cos (35°) - T*sin (25°) => N = 80.36 - T*0.42 Back to the first equation: +Wx - Fs - Tx = 0 => Wx = Fs + Tx => mg sin (35°) = N*μ + T*cos (25°) => 56.27 = (80.36 - T*0.42) * 0.3 + T*0.91 => (...) => T = 41 N So Tx = 37.2 N Now Fs: +Wx - Fs - Tx = 0 => Fs = Wx - Tx => Fs = +19 N Alternatively: N = Wy - Ty => N = 63 Newtons So Fs = N*μ => Fs = +19 N again So to recap the set of data I got: W = 98.1 Wx = 56.3 Wy = 80.4 T = 41 Tx = 37.2 Ty = 17.3 Fs = 19 N = 63 X axis: Wx - Fs - Tx =? 0 => 56.3-19-37.2 = 0.1 => seems good (aside from approximations) Y axis: Wy - N - Ty =? 0 => 80.4-63-17.3 = 0.1 => close enough again Is there a contradiction somewhere that I'm missing, or are there actually two possible ways to solve this problem?