# Newton's third law force homework

1. Dec 19, 2015

### Drizzy

1. The problem statement, all variables and given/known data

Emma and Caleb are playing a game. I don't know what the name is, but they put their fingers together like a hook and then pull. Caleb won. does that mean that Caleb pulls with greater force than Emma pulls him? Caleb wins. Does it mean that he pulls with greater force than Emma pulls him?

Excuse the awful picture lol
2. Relevant equations
Newtons thrid law

3. The attempt at a solution
how can he win when the opposite force is qual to his force?

2. Dec 19, 2015

### Incand

It's true that the forces between the hands are equal and opposite according to Newton's law. Are they affected by any other forces than the forces between them? Consider every force affecting a person and you should be able to resolve this

3. Dec 19, 2015

### Drizzy

Well their gravitational force is not the same. caleb is heavier so his force is greater.

4. Dec 19, 2015

### Incand

That's true, however that force is pointing towards the ground so not in the right direction (and is compensated by the normal force from the ground). Is there a force between him and what he's standing on?

5. Dec 19, 2015

### Drizzy

hmm the only forces are the gravity and the friction

6. Dec 19, 2015

### Incand

exactly! And this force is in fact related to the mass. Friction is proportional to mass. The heavier person experience a stronger force (in the opposite direction of the other forces pulling on him). Another possibility would be that they're holding in say a handle in the other hand.

So the person winning may not be the one that's able to pull with the greatest force, it's the one with the higher frictional force. Or with the stronger other hand if they're holding in something with the other hand.

7. Dec 19, 2015

### Drizzy

ohh but what if caleb and emma wiegh the same? then the forces and their friction is going to be equal

8. Dec 19, 2015

### Staff: Mentor

No, it means that Emma's grip is weaker. There are different forces at play here, doing different things. Her finger was unable to retain the "hook" position against the force applied by both of them pulling (equal opposite forces). Caleb had a stronger "hook" than Emma, but at no time were the normal forces at their join different (Newton's 3rd).

Friction plays no role here.

9. Dec 19, 2015

### Drizzy

why was she unable to retain the hook? is it because her mass is lower or because her hand muscles are weaker?

10. Dec 19, 2015

### Incand

Well perhaps one of them have shoes with a coefficient of friction. Or has there foot against something stopping them from moving.

Well that depends, I assumed a rather theoretical scenario where they hold that position with the fingers, just balancing the forces similarly to when pulling on a rope (from my experience this is what physics questions usually try to highlight).
So that's how I interpreted the question
Of course this is quite a theoretical scenario. In reality who usually lose may simply be the one that give up first by feeling more pain.

11. Dec 19, 2015

### Staff: Mentor

Hand muscles.

12. Dec 19, 2015

### Drizzy

I found this on a website that is written by the books author: (it is translated)

According to Newton's third law, Emma draws as hard in Caleb as Caleb pulls Emma. These forces are equal, but that does not mean that the fight ended in a draw. How Emma moves depends on the balance of forces on her. It is only when the force of Caleb becomes greater than the retarding forces at Emma that she begins to accelerate at Caleb's direction.

13. Dec 19, 2015

### Staff: Mentor

The problem mentions nothing about the acceleration or motion of either of their bodies as a whole, nor the surface they're standing on, nor any frictions. I think it is implied that the loser is the one whose "hook" fails to hold.

For all we know the pair of them may be seated with a table between them and they are strapped to chairs bolted to the floor.

14. Dec 19, 2015

### Mister T

Do you think Caleb would be able to win if Emma had her feet planted firmly on the ground and Caleb were standing on a skateboard?

Part of the problem statement is that the fingers are hooked, so one might argue that it's safe to assume the fingers are hooked. I agree that the problem is poorly worded. In particular it makes no mention of how one wins the game! One might argue that the reason Caleb wins is because the force he exerts on his finger is greater than the force that Emma exerts on her finger.

Most teachers, I think, when grading this would mark the student's answer at least partially correct provided it showed evidence of an understanding of the fact that the force exerted on Emma by Caleb is equal (but opposite) to the force exerted on Caleb by Emma. Students who claimed these forces are of different magnitude would get it marked wrong.

15. Dec 22, 2015

### Biker

On the marking point, From what I can see at the beginning each one of them was pulling the same amount of force to each other (opposite) but as I know if I want to make the hands or the hook to move from a point to another then someone should exert a greater force than the other person which will lead to making the hook moves to one side (Either Caleb or Emma). That is what I can conclude of this.

I am not sure about what you meant because I cant figure out a way better than this.

16. Dec 22, 2015

### osuboone

1st what are the two interacting objects in the system? Calebs finger and Emma's finger. Anything outside of these two things are not in the discussed system.
2nd at all points where they are in contact the force of Calebs finger on Emmas finger is equal (but in the opposite direction to) Emma's finger on Calebs finger.

Equal but opposite does not mean the same result for both interacting objects. Think bug and car windshield. When a bug hits the windshield the force of the bug on the windshield is equal in magnitude to the force of the windshield on the bug. The resulting effect on each object however is far from the same. Bug goes splat windshield is just fine.

17. Dec 23, 2015

### Drizzy

so momentum is the answer? Let's say the force is F and time is t so the impulse is Ft which is equal to mv Ft/m = v Emma will lose cuz her velocity is higher, right?

18. Dec 23, 2015

### Thewindyfan

So in this case where the system is just their interlocking hands, does that mean the person with less mass is more likely to accelerate/shift in position since acceleration = force/mass which in this case the third law reaction pair means the magnitude of their forces on each other are the same?
Don't we basically apply Newton's second law to this case as well? At least to get a better idea of thinking about what's going to happen if it's not completely obvious as to why that something is going to happen? Assuming the only force in this system is that third law pair between the two people.

19. Dec 23, 2015

### rcgldr

Hopefully this explanation will help. Assume Caleb is on the left. Consider each hand as an object. There is a Newton third law pair of equal in magnitude and opposing forces, Caleb's hand exerts a leftwards pulling force onto Emma's hand and Emma's hand exerts a rightwards pulling force onto Caleb's hand. Now consider the forces on each hand. Caleb's arm pulls leftwards on Caleb's hand, Emma's hand pulls rightwards on Caleb's hand. Likewise, Emma's arm pulls rightwards on Emma's hand, Calebl's hand pulls leftwards on Emma's hand. At the moment Caleb starts to win, the leftwards force exerted by Caleb's arm is greater than the rightwards force exerted by Emma's arm. This results in an imbalance in force of the hands, and the hands accelerate to the left. Although the magnitude of tension between hands may have changed, the tension between the hands remains a Newton third law pair of equal in magnitude but opposing forces. Part of the tension between hands is related to the mass times acceleration of Emma's hand. Part of the tension in Caleb's arm is related to the mass times acceleration of Caleb's hand, Emma's hand and Emma's arm.

20. Dec 23, 2015

### Thewindyfan

So basically the force with which Caleb's arm is pulling his hand is greater than the force Emma's arm is pulling her hand, causing her hand to shift towards Caleb due to the imbalance of the total net forces acting on each of their hands? Your explanation makes sense with considering that there's also the force of their arms pulling on their hands but it sort of sounded confusing at first.