Why is There Acceleration Despite Newton's Third Law of Motion?

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Newton's Third Law states that for every action, there is an equal and opposite reaction, which can create confusion regarding acceleration. The key point is that the forces described by this law act on different bodies, meaning they do not cancel each other out when considering the motion of a single object. For example, when one person pushes another with a force of 100N, the acceleration of the person being pushed depends on the net forces acting on them, not on the force they exert back. To determine whether an object accelerates, one must apply Newton's Second Law, which focuses on the net forces acting on that specific mass. Understanding this distinction clarifies how acceleration can occur despite the equal and opposite forces described by Newton's Third Law.
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Homework Statement


The law states that "Whenever one body exerts a force on another, the second exerts an equal and opposite force on first." But then, why is there acceleration?


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The Attempt at a Solution


If there will be force responding to the first one with equal magnitude, then there won't be any net force.Then why is there acceleration?
 
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One must keep in mind that the two forces mentioned in Newton's 3rd law act on two different bodies.
 
but, for example. When I push a wall, I will exert a force on the wall, and the wall will exert a force on me.
In another case, when I am pushing a person with 100N, and that person also pushes me with 100N, in opposite direction, then none of us will move. How do you explain that?
 
Consider a person being pushed by me by 100N.
To find whether he will accelerate or not one has to see if there are other forces acting thus contributing to increase or decrease the effect of the !00N that I am applying.
That is to find HIS acceleration one is interested in the forces acting ON HIM and not on me.
 
Oh, so what you are saying is that it's other forces which make the person accelerate, right?
 
What I said was that to find the acceleration on a certain mass, one has to find the forces acting on THAT mass. That is what Newton's 2nd law says.
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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