# Newton's Third Law and a ball

Gold Member
Hello;

I am a little confused here. A friend asked me that, due to Newton's Third Law of Motion, for every force there is an equal and opposite force. Therefore, why is it, for example, that when we throw a ball up into the air, it moves upwards at all, if the force exerted on the ball upwards is the same downwards (plus gravity)? Same thing for a rocket - if the rocket applies, say, a 10000N force upwards, and if there is a 10000N force downwards acting on the rocket, why does it still move? I just need to get this cleared up as I know I am missing something important here.

Thanks.

moving of rocket (including mass) = downwards force acting on rocket!!..
if force on left side is more then it would move to compensate

mathman
The initial impetus gives the ball and the rocket an initial velocity. The forces act to change velocity.

I think a tenth of my posts are regarding newton's third law so you aren't the only one who misses this subtle yet crucial circumstance of the law. When Newton says that there is an equal and opposite force, that does not mean that the forces act on the same object. Everytime you do a pushup, you apply maybe 100 newtons of force. That force pushes you up off the ground. But every time you do that push up, you also apply 100 newtons of force downwards against the earth. But, since the earth weighs so much, it doesn't move at all. Also, everytime you punch a wall. You exert a certain amount of force against that wall, but your hand hurts because that wall exerts that exact same force back to you.

Now think about punching through paper. Maybe you punch paper with 100 newtons of force in your fist. Paper takes about 1 Newton of force to break. So upon punching paper, you lose 1 Newton out of your 100 Newtons of force. Now because your fist carries through the paper, your arm much apply 99 Newtons in the opposite direction to stop your hand. So you can see there is a conservation of force here.

If you have any questions feel free to ask.

Dale
Mentor
2020 Award
In Newton's 3rd law the equal and opposite forces act on different objects. So, for the rocket, the 10000 N upwards force on the rocket is equal and opposite to the 10000 N downwards force on the exhaust, which is why the exhaust accelerates down so quickly and the rocked accelerates up. When you throw a ball up it pushes you down, equal and opposite forces acting on different objects.

Oh, looks like dacruick was faster!

Gold Member
Thanks guys! I understand the law a lot better now. But... if I were to take a car travelling with a force of 100N to the right, why must the force to slow the car be more than 100N? Why does it being 100N exactly have no effect?

Dale
Mentor
2020 Award
Because the other 100 N acts on the road, not the car.

Gold Member
Okay, what if it was a projectile in the air? Surely the opposing 100N force would cause it to slow? Where else could it be acting on?

that is the reason why projective doesn't continue forever.

Dale
Mentor
2020 Award
Okay, what if it was a projectile in the air? Surely the opposing 100N force would cause it to slow? Where else could it be acting on?
The air would push backward on the projectile and the projectile would push forward on the air. Equal and opposite forces on different bodies, always.

jtbell
Mentor
The long-winded version of Newton's Third Law: "The force that object 1 exerts on object 2 is equal in magnitude and opposite in direction to the force that object 2 exerts on object 1."

@Jtbell
The force that object 1 exerts on object 2 is equal in magnitude and opposite in direction to the force that object 2 exerts on object 1.

If Newton had postulated the third law in this way,we'd have had half the number of posts in PF. :D

@Jtbell

If Newton had postulated the third law in this way,we'd have had half the number of posts in PF. :D

haha agreed

collinsmark
Homework Helper
Gold Member
Hello FeDeX_LaTeX,

Okay, what if it was a projectile in the air? Surely the opposing 100N force would cause it to slow? Where else could it be acting on?

You don't need friction to figure this one out.

At the time you throw a 100 N ball (projectile) into the air, you must exert an extra force on the projectile/ball (above and beyond the ball's weight). At the same time your feet exert the same extra force on the Earth (above and beyond your own weight and the ball's weight), but in the opposite direction.

After you throw the ball in the air, The Earth continues to exert a 100 N force on the ball. So where is the so-called equal and opposite force? The ball exerts a 100 N force on the Earth! The ball is (in part) actually the one bringing the Earth closer to it!

Every time you throw an object into the sky, you are also pushing the earth away from the object at the same time. The distances that each moves is different though. Because the Earth is so much more massive than most objects, it hardly budges. But the Earth does move away from the object just a tad.

You can calculate the acceleration that the earth experiences after you throw an object up by using (assuming you don't throw it very far up, and assuming the object is small compared to the Earth):

$$F = mg = Ma$$

where M is the mass of the earth, and a is the acceleration of the Earth caused by the ball.

$$a = \frac{mg}{M}$$

So immediately after throwing up a 100 N object into the air, the object experiences an acceleration of 9.8 m/s2 in the down direction, but the Earth experiences a
(100 N)/(5.97 × 1024 kg) = 16.75 × 10-24 m/s2 in the up direction.

The accelerations of the Earth and the ball are obviously different (the acceleration of the Earth is so small, it's not even measurable). But the forces that one causes on the other are identical, except in opposite direction.

So the next time you're tempted to say, "I fell down and hit my head on the ground," you can always rephrase it instead as "The ground came up and hit me on the head." Both have about the same validity. But to be truly accurate, they both happen at the same time. Newton's third law. [Edit: The same is true with apples. ]

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@Jtbell

If Newton had postulated the third law in this way,we'd have had half the number of posts in PF. :D

Actually Newton's explanation of the third law in Principia is very clear and complete.He stresses the fact that the forces are on different bodies. The problem is due to newer textbooks that are not clear or much more often due to the reader not reading the whole paragraph.

jtbell
Mentor
much more often due to the reader not reading the whole paragraph.

Bingo! I think a tenth of my posts are regarding newton's third law so you aren't the only one who misses this subtle yet crucial circumstance of the law. When Newton says that there is an equal and opposite force, that does not mean that the forces act on the same object. Everytime you do a pushup, you apply maybe 100 newtons of force. That force pushes you up off the ground. But every time you do that push up, you also apply 100 newtons of force downwards against the earth. But, since the earth weighs so much, it doesn't move at all. Also, everytime you punch a wall. You exert a certain amount of force against that wall, but your hand hurts because that wall exerts that exact same force back to you.

Now think about punching through paper. Maybe you punch paper with 100 newtons of force in your fist. Paper takes about 1 Newton of force to break. So upon punching paper, you lose 1 Newton out of your 100 Newtons of force. Now because your fist carries through the paper, your arm much apply 99 Newtons in the opposite direction to stop your hand. So you can see there is a conservation of force here.

If you have any questions feel free to ask.

hi
i just have simple question suppose if A pushes on B with 10 kn, then B pushes on A with 10 kn, (i am now not bothered about what happned to B) but why does A moves in oppsite direction although it was already carrying a force of 10 kn (that means a force of 10 kn was already on A in the direction of B) and B forced back 10 kn so A should stand still, but we say that it moves back, why ? (we all the time give example that when we push earth, it moves back although by small amount)

Doc Al
Mentor
hi
i just have simple question suppose if A pushes on B with 10 kn, then B pushes on A with 10 kn, (i am now not bothered about what happned to B) but why does A moves in oppsite direction although it was already carrying a force of 10 kn (that means a force of 10 kn was already on A in the direction of B) and B forced back 10 kn so A should stand still, but we say that it moves back, why ? (we all the time give example that when we push earth, it moves back although by small amount)
What do you mean by "it was already carrying a force of 10 kn"? Bodies don't 'carry' a force just by virtue of their motion.

If A was moving to right at a constant velocity (before colliding with B), then the net force on A is zero. When A collides with B, B exerts a force on A to the left--so A will accelerate to the left.

when a ball is thrown up, it goes up due to the force of us throwing it..but it doesn't stay up in the air..does it..?..it comes down as well..due to the gravity's force..

What do you mean by "it was already carrying a force of 10 kn"? Bodies don't 'carry' a force just by virtue of their motion.

If A was moving to right at a constant velocity (before colliding with B), then the net force on A is zero. When A collides with B, B exerts a force on A to the left--so A will accelerate to the left.

hi thanks a lot for that reply i understood that.

kindly also tell me when we say that when object A pushes on B and imparts acceleration on B then how long the acceleration will be there on B and after what time B will gain the constant velocity.

Doc Al
Mentor
kindly also tell me when we say that when object A pushes on B and imparts acceleration on B then how long the acceleration will be there on B and after what time B will gain the constant velocity.
As long as there is a net force on B, B will accelerate. When A stops pushing B, and the net force on B is zero, the acceleration of B will be zero and it will continue moving at constant velocity.

As long as there is a net force on B, B will accelerate. When A stops pushing B, and the net force on B is zero, the acceleration of B will be zero and it will continue moving at constant velocity.

Kindly see the attached picture and tell me what happens in three scenarios.
1. When a force of 20 N applied to a 5 kg block (ignore friction) what is the acceleration of 5kg block and what is the force on it.
2. If the 20 N force is continued on small block the block accelerates and hits the bigger block of 15 kg. what are the forces on smaller and bigger block at the moment of impact.
3. Even after hitting the bigger block the force of 20 N is continued now what is the force and accelerations of smaller and bigger blocks.

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Doc Al
Mentor
Kindly see the attached picture and tell me what happens in three scenarios.
1. When a force of 20 N applied to a 5 kg block (ignore friction) what is the acceleration of 5kg block and what is the force on it.
2. If the 20 N force is continued on small block the block accelerates and hits the bigger block of 15 kg. what are the forces on smaller and bigger block at the moment of impact.
3. Even after hitting the bigger block the force of 20 N is continued now what is the force and accelerations of smaller and bigger blocks.
The first and the third are straightforward applications of Newton's 2nd law. Why don't you give them a try?

The second is not straightforward. There's no simple way to predict the impact forces during the collision. It depends on the speed of collision, the time involved, the nature of the materials. But, no matter what, we know that at all times the two blocks exert equal and opposite forces on each other.

As long as there is a net force on B, B will accelerate. When A stops pushing B, and the net force on B is zero, the acceleration of B will be zero and it will continue moving at constant velocity.

The first and the third are straightforward applications of Newton's 2nd law. Why don't you give them a try?

The second is not straightforward. There's no simple way to predict the impact forces during the collision. It depends on the speed of collision, the time involved, the nature of the materials. But, no matter what, we know that at all times the two blocks exert equal and opposite forces on each other.

Kindly assume the time and material and even take an ideal scenario and please tell me what will happen in the second case. Moreover i have tried the 1st and the last case ii just want to check whether what i understood is right or not, if i can understand this than i am through with newtons laws. Please help me out to understand better

Doc Al
Mentor
Kindly assume the time and material and even take an ideal scenario and please tell me what will happen in the second case.
That can be quite complicated. What you can do, if you like, is make up some numbers like so: Assume that the first block is moving at some speed V when it collides with the second block. Assume further that the collision takes some very short time T, after which the blocks move together. Then you can calculate the average impact force during the collision by calculating the impulse delivered to each block.

Moreover i have tried the 1st and the last case ii just want to check whether what i understood is right or not, if i can understand this than i am through with newtons laws.
Excellent. Please describe what you found for the forces in those cases.