# Forces involved in a 'tug of war'

1. Sep 2, 2014

### bobie

Can someone give a detailed phusical description description of the forces involved in this game?
Let consider only the first player on the right:

0) does it make any difference if he is pulling aagainst an opposing varying force or he is pulling a truck?
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1) does friction play any role here? if his heels are dug in a hole or lean on a reversed starting block, does it make any difference?
2) his legs are fully stretched. Can he exert a force directly on the ground?
3) can he exert a greater force either on the rope or on the ground
4) if yes, how
5) if no, is it due to Newton third law? suppose his legs are stretched and the ground is just a point of support: when he pulls the rope is half force discharged on the ground?
6) if he wants the rope to accelerate in his direction is it necessary that the two forces be unequa? Is it true that if they are equal the total force on the player will vanish?

6) in conclusion, after all your evaluations which force is more important for victory, the one on the rope or the one ond the ground

Thanks in advance, it would be great to have a sketch of the forces in play showing how forces are discharged to the ground.

Last edited: Sep 2, 2014
2. Sep 2, 2014

### A.T.

What are your own thoughts on the questions?

3. Sep 2, 2014

### bobie

I think
- the friction plays no role if foot is dug in. I am posting because I read that even if it is in a hole or on a staring block it is relevant.
- with stretched legs you cannot push directly on the ground. If you push the force can never be greater then the pull on the rope.
- wherevere you exert a force, as you must prop up on the opposite side, you discharge half of the force on the other side by 3rd law. But also in this regard I read that if the force on the ground and the rope are equal there can be no acceleration, motion of the rope toward you

4. Sep 2, 2014

### A.T.

What if the hole is shallow, so the effective surface you push against is not perpendicular to gravity + rope force?

But the question was if he "exerts a force on the ground". If he didn't what would be the horizontal net force on him and thus his acceleration?

Are you talking about total magnitudes, or just the horizontal components? Can you win the game if the horizontal components are always equal.

Where does 3rd law talk about "half of the force"?

5. Sep 2, 2014

### bobie

What has gravity got to do here? why has the hole to be deep or perpendicular , ( what matter is if it blocks your foot)? how do you exert directly a force on the ground if you do not stretch your legs (the force on the ground is exerted mainly by the opponent)? and what about 2nd law here? how do you get an acceleration if not pulling on the rope? if you do not answer the 0 question I do not have a clear picture.

Last edited: Sep 2, 2014
6. Sep 2, 2014

### A.T.

Why don’t you sketch all the forces acting on the man?

Who said it has to be perpendicular? The question was when friction becomes necessary. To see this draw a diagram with all the forces and the ground contact surface.

When you just stand around with already stretched out legs, do you exert a force on the ground?

Can the rope accelerate if it has equal but opposite force on both ends?

7. Sep 2, 2014

### bobie

I am not able to draw and post a sketch, that is why I asked for it in OP.

You are confusing me even more. Force on the ground must be exerted horizontally to win the game, what is the use of g?
I begged you twice, start with the truck, which is simple: to pull a truck you pull horizontally on the rope and prop up your feet to an obstacle in/on the ground. Do you exert a force directly on the obstacle or just as a consequence of the pull on the rope? suppose you use 100 N, how much of this is discharged on the obstacle, if not 50%? what determines this percentage?
If you discharge 50% of the force , 50 N, on the ground you have two equal forces, but no work is done on the ground so you can have an acceleration on the rope, what is the problem?

8. Sep 2, 2014

### A.T.

Can the force on the ground be purely horizontal under gravity?

It's not that simple to beat a truck that uses it's engine. With engine off the truck can at best get a tie.

9. Sep 2, 2014

### bobie

I mentioned no engine. But I suppose you can't tell more on the subject.

10. Sep 2, 2014

### A.T.

Then it depends on how deep the truck will sink into the mud. On asphalt even a single human can pull a truck, with decoupled wheels and brakes off.

11. Sep 2, 2014

### sophiecentaur

@bobie
I agree with AT. You need to draw a very simplified model - two guys and a rope - and draw in the forces. In the equilibrium situation, clearly, both guys must be pulling with the same force (= tension in rope). If one guy is stronger or the other guy has less traction, there will be no longer be equilibrium.
As OP, it is really up to you to draw the diagram and present it, otherwise we do not know what we are supposed to be discussing. There are dozens os drawing utilities available and, if you 'Go Advanced', you can find how to upload a file - there is a big choice of formats that are accepted.

12. Sep 2, 2014

### bobie

Thanks sophiecentaur, my main concern is not the equilibrium of forces, that is why I insisted on the truch, which does not pull.
My question cannot be answered by a drawing, but only by one expert physicist like you. I want to know how much of the force I exert goes really to the truck and how much is lost, doing no work on the ground, and if this percentage can be altered and why.
Is it clear now?

I'll appreciate even a brief reply with just the percentages. My assumption 50-50% has been rejected.

13. Sep 2, 2014

### sophiecentaur

There a some basics that you must accept first. You can only find an answer if you examine what forces are operating. I could not hope to start on such a problem without drawing a diagram. Unless you do, you risk missing out something relevant.
A force is not "lost". No work is done on anything unless there is movement involved. Man pulls truck truck provides exactly the same amount of force on rope. There's no "50%/50% involved (as a diagram would show, aamof). The forces around the man are a bit more complex because he is leaning backwards. There is his weight, friction and the rope tension. (Diagram again) all acting at different places and establishing equilibrium (unless he moves the truck).
You just can't do this one by waving arms around (any more than the guy with the rope. )

14. Sep 2, 2014

### bobie

Thanks for your help, probably this is to complicated for me.

15. Sep 2, 2014

### PhanthomJay

Assuming no hand slippage, the tension in the rope is the same pulling on each team. Although there are complexities involved, friction/traction of feet on ground is key. If one team is on ice and the other on soil, I bet you know who wins.

16. Sep 2, 2014

### sophiecentaur

The diagram I had in mind is below (jeez, I'm good to you, aren't I?)This is the essence of the one man pulling a rope attached to 'something' and I am assuming that things are in equilibrium, for a start. It assumes the man is strong enough to provide the tension and the leg thrust and that the friction with the ground is enough to hold him. To work out the tension, you need to consider the Moments about a point (choose his contact point with the ground). The moment of the tension will be equal and opposite to the moment of his weight. He will need to be at the correct angle to the ground for this. The calculation involves some Trig - but I have left it out, initially.
There are just two horizontal forces here, so T will equal R.

If he is 'winning' then T will be enough to drag the truck and he will need to be walking backwards, so he does T times x work, where x is the distance moved. I assume the truck is moving very slowly and not accelerating appreciably. All the work done is against friction. If he is actually managing to produce significant acceleration then you would need to include the kinetic energy situation too.

If T increases then he needs to lean back more and the friction needs to be high enough or he will fall on his backside or start 'surfing' through the mud (if he can control it).

PS Powerpoint is easy to use to produce this simple diagram -once you get used to it.

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17. Sep 2, 2014

### A.T.

There are also many free online sketching tools, where you draw in the browser and get a link to your drawing for posting here on the forum.

Last edited: Sep 2, 2014
18. Sep 2, 2014

### A.T.

How can those forces be in equilibrium, if the ground reaction acts only horizontally?

19. Sep 2, 2014

### Staff: Mentor

Forces do not work this way. You are thinking of something which is conserved and so you can say that 50% goes here and 50% goes there. Forces are not conserved. For example, on a simple lever you may exert a force of 10 N and get out a force of 100 N. Talking about "lost" or "percentage" of force just doesn't have any physical meaning. That is probably why you are not getting good answers to that part of your question.

20. Sep 2, 2014

### sophiecentaur

The reaction R against the Tension is horizontal. Of course there is another vertical force to balance weight etc.
I could put more arrows in - plus angles and distances etc. But this is a very stock 'Forces' situation. Other well known ones are ladders leaning against walls and men pushing wheelbarrows. Once you've seen and done one, you've seen 'em all.