# How are objects able to move even after newton's third law of motion [duplicate]

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I can't understand at all why objects move even though after newton's third law.I also have a doubt in following example If we apply a force on an object the object applies a backward push on us according to newton's third law of motion.let us now put the force vector applied by the object to its back. Now we can cut off Its forces then how is the object able to move.

## marked as duplicate by JMac, Gert, Dvij Mankad, ZeroTheHero, David HammenMay 22 at 17:10

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• The two forces are applied to two different objects, not the same object. – David White May 22 at 13:50

## 2 Answers

I think the problem you are having is thinking that Newton's third law means that the equal and opposite forces cancel each other in terms of the effect one has on the other. Sometimes that's true, sometimes not.

Let's say you push against a fixed wall and neither of you move. The wall does not move because the ground exerts a force on the wall equal and opposite to the force you exert on the wall. Therefore there is no net force on the wall. You don't move because the ground exerts a force (friction) on your feet equal and opposite to the force the wall exerts on you. So there is no net force on you.

If you are driving a car at constant velocity and an insect hits your windshield, the insect exerts an force on your windshield equal and opposite to the force your windshield exerts on it. The effect on each is dramatically different. The deceleration of the car due to the force applied by the insect is minuscule compared to the acceleration of the insect due to the same force applied by the car. This is because you need to couple Newton's third law with Newton's second law, $$F=ma$$.

The force the insect exerts on the windshield is

$$F=-Ma$$

The force the windshield exerts on the insect is

$$F=mA$$

Where $$M$$ is the mass of the car, $$m$$ is the mass of the insect, $$a$$ is the acceleration of the car, $$A$$ is the acceleration of the insect. Comparison of the magnitudes is

$$M>>>m$$ $$a<<

So while the sum of the forces equals zero, there is a net force on each due to the other causing a different acceleration of each.

Hope this helps.

If you take a steel tube & put a propellant charge in the middle with a lead ball on either side of it,then set off the charge,the two balls will exit the tube at the same velocity in opposite directions. Seal one end of the tube,put the propellant in,then the ball. Ignite the charge & the ball will go one way & the steel tube the other way with equal energy. Put a wooden stock on the sealed end & a marksman to hold & aim it,& the ball will exit with the same energy while the tube recoils with the same energy,but because the tube has to push against a much larger mass,it won't move very much,& the energy will be absorbed by the body of the marksman,but nevertheless Newton's 3rd Law of Motion holds true: for every action there is an equal & opposite reaction.

• Where you said two objects move with equal energy, I suspect you meant to say with equal momentum. – The Photon May 22 at 16:00