Is mgsinθ=static frictional force on an inclined plane?

[dkhan2]

According to Newton's 3rd law, for every force there's an equal opposing force. Since a block is sitting on an inclined plane, wouldn't that mean the static friction is acting like the opposing force for mgsinθ thus, mgsinθ=static frictional force? Please respond

 

[Orodruin]

No, you have a very common misconception about Newton's third law. Newton's third law is a statement about forces between two different objects, not about forces on the same object. For example, it states that if the frictional force on the block from the plane is $F_s$ directed upwards along the plane, then the frictional force from the block on the plane is $-F_s$ directed upwards along the plane (or, equivalently, $F_s$ downwards along the plane). The third law does not state anything about the different forces acting on the same object.

From the second law, we can infer that the force sum on an object which is not being accelerated is zero, since $\sum_i \vec F_i = m\vec a$.

 

[sophiecentaur]

N3 describes situations where Conservation of Momentum is important. N1 is about Equilibrium situations where the sum of all forces is zero.

 

[Chandra Prayaga]

According to Newton's 3rd law, for every force there's an equal opposing force. Since a block is sitting on an inclined plane, wouldn't that mean the static friction is acting like the opposing force for mgsinθ thus, mgsinθ=static frictional force? Please respond

(1) The first thing to do is, give up all the very vague statements of Newton's third law, or any law for that matter. State it fully: If object A exerts a force on object B, then object B exerts an equal force in the opposite direction on A. These two are called action and reaction. It does not matter which one you call the action and which the reaction.
(2) For some time, until it becomes natural to you, when you state that there is a force, also state which object is exerting that force on which object. For example, never say "static friction force" like you did. Rather, follow the example of Orodruin in his response and say "frictional force on the block from the plane". Then you will realize that, automatically, the reaction to the frictional force MUST be "on the plane by the block". Your mgsinθ is not by the block, so it is not a reaction, so it need not be equal to the static friction force. In some cases, it may turn out to be equal, but that is because of that particular situation, but not because of Newton's third.