Newton's Third Law and a ball

1. Mar 29, 2010

FeDeX_LaTeX

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.

2. Mar 29, 2010

Rajini

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

3. Mar 29, 2010

mathman

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

4. Mar 29, 2010

dacruick

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.

5. Mar 29, 2010

Staff: Mentor

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!

6. Mar 29, 2010

FeDeX_LaTeX

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?

7. Mar 29, 2010

Staff: Mentor

Because the other 100 N acts on the road, not the car.

8. Mar 29, 2010

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?

9. Mar 29, 2010

Rajini

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

10. Mar 29, 2010

Staff: Mentor

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.

11. Mar 29, 2010

Staff: 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."

12. Mar 30, 2010

sganesh88

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

13. Mar 30, 2010

dacruick

haha agreed

14. Mar 30, 2010

collinsmark

Hello FeDeX_LaTeX,

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. ]

Last edited: Mar 30, 2010
15. Mar 31, 2010

bp_psy

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.

16. Mar 31, 2010

Staff: Mentor

Bingo!

17. Jul 2, 2010

malu

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)

18. Jul 2, 2010

Staff: Mentor

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.

19. Jul 2, 2010

sameerpaisari

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..

20. Jul 3, 2010

malu

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.