# Trouble Understanding Newton's Third Law

• revo8778

#### revo8778

I apologize in advance if this belongs in the Homework section, but my question is not all about one problem and doesn't fit the template.

I have some trouble understanding Newton's Third Law. I tried understanding it myself (my teacher is an imbecile who accomplishes almost nothing in every lesson), and my failure to grasp the concept cost me dearly on a test. I need some outside help.

Here's what I understand about forces so far. Call me out on it if something's wrong.

So far, I can understand that "equilibrium" of an object is when there is no net force on an object, meaning that it is either at rest or moving at a constant speed, and that the net force acting upon it is zero.

I also understand that the net force is the difference of all of the forces acting on an object. For example when a 10 N eastbound force and a 30 N westbound force act on an object, the difference is 20 N and the object will be accelerated west.

Here's my problem:

For Newton's third law, my textbook describes two demonstrative scenarios: two ice skaters pushing against each other, and a ball on a table on Earth. In scenario 1, I can understand that there are two systems interacting upon each other. What I don't understand is where the points of the Third Law "all forces come in pairs" and "two forces in a pair act on two different object and are equal in magnitude but opposite in direction" are applied here. The second scenario (ball on a table on Earth) I can't understand at all. For the third law to work, there would have to be two exclusive system here, right? What are they? My book points out that the "upward force from the table to the ball" and the "downward force of gravity on the ball" are NOT an interaction pair. Why? It seems like that that would be a perfect example of the Third law.

Thanks in advance for any help.

My book points out that the "upward force from the table to the ball" and the "downward force of gravity on the ball" are NOT an interaction pair.
At the contact point between ball and table, the ball exerts a downwards force onto the table, coexistant with the table exerting an upwards force on the ball.

Gravity is an attractive force between the ball and earth, exerting a downwards force onto the ball and an equal and opposing upwards force onto the earth.

My book points out that the "upward force from the table to the ball" and the "downward force of gravity on the ball" are NOT an interaction pair. Why? It seems like that that would be a perfect example of the Third law.
There are multiple forces here, not just two. The third law counterpart to the downward force of gravity on the ball is an equal but opposite upward force of gravity on the Earth. The third law counterpart to the upward normal force exerted by the table on the ball is an equal but opposite downward normal force exerted by the ball on the table.

One final clue that the downward force of gravity and the upward force from the table are not a third law pair: The net force on the ball is not zero. The Earth is rotating about its axis. Unless the table is right at the north or south pole, the ball is undergoing uniform circular motion about the Earth's rotation axis with an angular velocity of one revolution per day. There must exist some non-zero net force on the ball that point toward the Earth's rotation axis.

And for the ice skaters, say they each extend a hand and push off against one another. The force of hand A on hand B, pushing skater B backward, the has the same magnitude and the opposite direction as the force of hand B on hand A, pushing skater A backward. So if the skaters have the same mass, they'll shoot off in opposite directions at the same speed.

You might imagine it would be possible for two skaters of the same mass, initially at rest on the ice, to push off each other in such a way that one shoots off faster than the other, or perhaps they could shoot off at an angle to each other instead of in completely opposite directions. The third law tells you that this is not in fact possible, unless the skaters do something tricky with their skates, like digging into the ice or steering, introducing new forces into the problem.

@The_Duck: So in the most simple form of the scenario, two skaters with equal strength and equal mass, the Third Law holds true? And is the law suddenly no longer valid even if one skater weighs only a gram more?

@D H: So, from what I gather, the force of the ball on the table and the table on the ball IS an interaction pair, because the net force is zero and the table would HAVE to produce enough upward force to cancel out the ball's 9.8N downward (assuming the ball weighs only 1Kg)? Would that mean that the force of gravity on the ball and the force of the ball's very minor pull on Earth are also an interaction pair? It doesn't seem like they could be.

And one final question: So far I gather that an interaction pair requires opposing, equal forces from two different system. Skater A and Skater B are those two systems. But what are the systems in the ball on table scenario?

Would that mean that the force of gravity on the ball and the force of the ball's very minor pull on Earth are also an interaction pair? It doesn't seem like they could be.
They are. That is precisely what Newton's law gravitation says: The gravitational force exerted by the ball on the Earth is exactly equal but opposite to the gravitational force exerted by the Earth on the ball. Note that a 9.81 Newton force will make an object with a mass of one kilogram accelerate at 9.81 meters/second2 but it will make an object with a mass of 5.974×1024 kilograms accelerate at a paltry 1.64×10-24 meters/second2. Just because the forces are equal but opposite does not mean the accelerations are.

I apologize in advance if this belongs in the Homework section, but my question is not all about one problem and doesn't fit the template.

I have some trouble understanding Newton's Third Law. I tried understanding it myself (my teacher is an imbecile who accomplishes almost nothing in every lesson), and my failure to grasp the concept cost me dearly on a test. I need some outside help.

Here's what I understand about forces so far. Call me out on it if something's wrong.

So far, I can understand that "equilibrium" of an object is when there is no net force on an object, meaning that it is either at rest or moving at a constant speed, and that the net force acting upon it is zero.

I also understand that the net force is the difference of all of the forces acting on an object. For example when a 10 N eastbound force and a 30 N westbound force act on an object, the difference is 20 N and the object will be accelerated west.

Here's my problem:

For Newton's third law, my textbook describes two demonstrative scenarios: two ice skaters pushing against each other, and a ball on a table on Earth. In scenario 1, I can understand that there are two systems interacting upon each other. What I don't understand is where the points of the Third Law "all forces come in pairs" and "two forces in a pair act on two different object and are equal in magnitude but opposite in direction" are applied here. The second scenario (ball on a table on Earth) I can't understand at all. For the third law to work, there would have to be two exclusive system here, right? What are they? My book points out that the "upward force from the table to the ball" and the "downward force of gravity on the ball" are NOT an interaction pair. Why? It seems like that that would be a perfect example of the Third law.

Thanks in advance for any help.

Hey, I used to have similar problems you did in the first scenario. One big thing that helped me understand was Newton's second law 'Everything has an equal and opposite reaction.'
So let's say for one force to push right (let's use + in this case) and another force to the left (-) with the same amount of force (5N) the two forces will equal zero.
($$\Sigma$$F=m1a-m2a=5+(-5)=0N)
So in this case, your two forces would be applied equally, such as your pushing against a wall, or a ball sitting on a table with no movement, or your pushing a ball at a constant acceleration across the ground.

So if you a system of two forces applied one way (+5N to the right each), and three forces applied in the negative direction(-5N to the left, each), you would add similarly to the first scenario.
($$\Sigma$$F=[m1a+m2a]-[m3a+m4a+m5a]=[5+5]-[5+5+5]=-5N).
In this scenario the object would have a net force of 5 Newtons applied to it to move in the - direction (left).

Hopefully this helps a little bit with the third law!

@The_Duck: So in the most simple form of the scenario, two skaters with equal strength and equal mass, the Third Law holds true? And is the law suddenly no longer valid even if one skater weighs only a gram more?

No, sorry, that's not what I meant to imply. The third law applies no matter what the skaters' masses are. But if you apply equal forces to equal masses, you get equal accelerations (a = F/m). So if the skaters weigh the same amount, they'll go off at the same speed. If, say, one of them weighs twice as much as the other, he'll go off at half the speed of the other. Both experience forces of equal magnitude, but the one that's twice as heavy experiences only half the acceleration and so ends up with half the final speed as the other.

I think I'm getting this now. I think my problem was a failure to understand the fact that equal acceleration is not needed for the forces to be equal.

Just to double-check that I have everything understood, here's one of the questions that I originally got wrong on my physics test:

"A horse pulls a cart on a flat road. Consider the four forces present in this situation:

1. The hore pulling on the cart
2. The cart pulling on the horse.
3. The horse pushing on the road.
4. The road pushing on the horse. "

Then there are two questions based on this scenario:

1. "Suppose that the horse and cart have started from rest; and as time goes on, their speed increases in the same direction. Which of the following conclusions is correct concerning the magnitudes of the forces mentioned above:

A. F1 exceeds F2
B. F2 is less than F3
C. F2 exceeds F4
D. F3 exceeds F4
E. F1 and F2 cannot have equal magnitudes.

2. "Which two forces form an "action-reaction" pair that obeys Newton's third law?

A. F1 and F4.
B. F1 and F3.
C. F2 and F4.
D. F3 and F4.
E. F2 and F3.

The correct answers are B for 1 and D for 2. Based on what I've learned here, I come to answer D for 2, so that I understand well now. I still do not know how to answer question 1. How do the two system relate?

I still do not know how to answer question 1. How do the two system relate?
Hint: Consider the net force on the horse.

(Also: You should be able to eliminate any answer that violates Newton's Third Law.)

Well, if the horse is accelerating, then there would have to be a net force acting on the entire systm, in the direction of is accel. Assuming that the direction is to the right, there has to be some force creating a net force pulling to the right. C wouldn't make any sense because then the horse and cart would be moving backwards. D and E wouldn't work because they are action and reaction pairs, gathering from what I've learned here.

A and B are left. Based on my elimination of E, choice A would automatically be invalid, as F1 and F2 have to be action/reaction. Chice B WOULD work because the hiorse's efforts on the road would move the cart forward.

I think I'm getting this now.

Looks good. You've got it.

Newton's laws are the necessary consequences of conservation of momentum.

The first law says that momentum is conserved.
The second law says that one can define a thing called 'force' as the rate of change of momentum.
And the third law just says that however two bodies interact, momentum is neither created nor destroyed, but may pass from one body to another body.

Understanding when and where to use the First Law and the Third Law...

It's easy to decide which law applies based on some key decision points.. but it's easy to go wrong also!

The First Law (object at rest etc..) tells us that the total of all forces acting equals zero. It says nothing about how many forces act. That is a different question.

The Third Law (action and reaction etc..) applies to one physical interaction between two objects. We must identify what the physical interaction is if we are to use this law correctly.

Combining both laws we can often deduce that two forces are equal and opposite, even though neither law alone would require that to be true.

Example: Apple resting on a table.

By gravitational interaction the apple pulls upwards on the Earth and the Earth pulls downwards on the apple. Two objects - one physical process. So we can apply the third law. Those two forces are equal and opposite.

By molecular repulsion processes at point of contact the apple pushes down on the table and the table pushes up on the apple. Again, two objects and one physical process. So we can apply the third law again. Those two forces are equal and opposite.

The apple is at rest. OK... So the first law tells us the total of all forces acting on the apple is zero.

Now the tricky bit: Are we absolutely certain we have considered all the forces acting on the apple. Yes? Then since A) we believe there are only two forces acting on the apple and B) the total force is zero, we can deduce C) that those two forces are equal and opposite.