# How are unbalanced forces even possible, given Newton's 3rd law? [duplicate]

The notion of an unbalanced force seems to contradict Newton's third law, entirely.

For instance, apparently, if you push a rock, then an unequal force is being applied in the opposite direction with respects to friction, in your pushing of the rock. To me, this makes complete sense, though then I was taught Newton's third law, which made no sense until I got deeper into the intuition behind that. For instance, the reason why it's hard to push, in particular a heavy rock, is because of this equal and opposite force, otherwise you could push it effortlessly, literally. So, I've gone from my initial intuition being shattered, to internalizing Newton's ideas, and now nothing makes sense anymore, because my initial intuition and my newfound insight is just battling out.

• "the reason why it's hard to push, in particular a heavy rock, is because of this equal and opposite force". That is not correct. The force that the rock exerts on you has nothing to do with how hard it is to get the rock to accelerate, because the force that the rock exerts on you affects your motion, not the rock's. There's no problem with there being unbalanced forces on one object, because Newton's 3rd Law doesn't apply to the situation where you are considering just the forces acting on one object (the 3rd-Law forces are there, just not relevant). – march Dec 20 '15 at 3:29
• What Newton's law does is to simply formalize that pushing something with large mass results in a small acceleration while pushing something with a small mass with equal force results in a much larger one. That's a simple observation. Why does it not make sense to you? Mass is really just a measure for inertia, while force is a measure for the product of acceleration and mass. These definitions depend on each other and the naive observation that there is a real difference between objects of different masses. – CuriousOne Dec 21 '15 at 2:41