I know in order for a team to win tug-of-war, the frictional force has

[Bashyboy]

I know in order for a team to win tug-of-war, the frictional force has to be greater than the force with which the opposing team pulls with; but which friction is it, static or kinetic?

 

[K^2]

Maximum static friction is always greater than kinetic. If you are sliding, and therefore using kinetic friction, you are already losing. So you only need to compare maximum static friction forces. The actual force of static friction on both sides will be about the same.

Of course, friction isn't the only possible limiting factor. You still need to be able to pull hard enough for that to become important, and that will depend on your footing.

 

[Bashyboy]

So, in the situation where there is only two people involved in tug-of-war, the person that is more massive will win, provided that they are both wearing the same style shoe and on the same surface containing friction?

 

[K^2]

Everything else being equal, and provided that they can pull with strength in excess of their weight (on dry surface friction coefficient will be around 1), yes, heavier person wins. Heavier person will, of course, always have an advantage, but there is more to Tug-of-War, than that. For example, the other person could be pulling slightly up, increasing own normal force, and reducing that of the opponent. One could also make a sudden pull, or release a bit, to try to force opponent to lose balance.

But if both persons know what they are doing, it does usually become just a difference of weight, which is why one-on-one Tug-of-War competitions aren't common. They just aren't interesting, as you can guess outcome in advance. With teams, it's far more interesting. A lot more teamwork becomes involved, and weight variations play a lesser role.

 

[danmay]

(1) Weight matters in terms of increasing the normal force between your feet and the ground, which may (or may not) increase the friction force holding you in place. For that to transfer to the rope and the opponent, however, you must hold fast onto the rope. In other words, your body (e.g. hands and any part experiencing the force) must be strong enough to bear that much force. As force increases, the side that can no longer bear the force will start "giving" somewhere, at the hands (which would lower the force), feet (which would make their bodies slide), or their posture will have to deform (up to a limit before it can no longer help). These scenarios would likely make you lose.

(2) When both sides are sliding, mass resists acceleration. The more massive side will move less in the same amount of time compared to the lighter side; therefore the latter will lose "earlier".

 

[K^2]

(2) When both sides are sliding, mass resists acceleration. The more massive side will move less in the same amount of time compared to the lighter side; therefore the latter will lose "earlier".

Both sides accelerate at the same rate, because there is a tight rope constraint between them.

 

[danmay]

Both sides accelerate at the same rate, because there is a tight rope constraint between them.

The length of rope between them is not necessarily fixed. You can let it slip, grab on to it and pull more in or let more out.

 

[Ken G]

But you never have both sides losing, with one side losing "earlier". That just doesn't happen.

Also, I think that in addition to weight, we have to consider strength. If you had a team of five year olds all wearing 200 pound backpacks, that is not going to be a very successful tug-of-war team. K^2 already mentioned that you would have to assume they can pull with a force in excess of their own weight, but that's a rather strong assumption! Most people could not suspend their weight for very long by hanging from a rope with just their hands, their muscles would fatigue quickly. So it might also matter more how long a person can sustain their own weight in a force from their hands on a rope, if the contest isn't deciding immediately by one team being much heavier.

 

[danmay]

But you never have both sides losing, with one side losing "earlier". That just doesn't happen.

I wrote both sides sliding, not both sides losing; and obviously one side losing "earlier" is just another way of saying that the other side has outlasted/won. Can we say it never happens that both sides are sliding? I'm not 100% certain. It could be a case similar to momentum exchange.

Also, I think that in addition to weight, we have to consider strength. If you had a team of five year olds all wearing 200 pound backpacks, that is not going to be a very successful tug-of-war team. K^2 already mentioned that you would have to assume they can pull with a force in excess of their own weight, but that's a rather strong assumption! Most people could not suspend their weight for very long by hanging from a rope with just their hands, their muscles would fatigue quickly. So it might also matter more how long a person can sustain their own weight in a force from their hands on a rope, if the contest isn't deciding immediately by one team being much heavier.

Something like post #5? Escalating/increasing force in order to maximize what you may have as an advantage from weight-->normal force-->foot friction is important. It's also important to be able to withstand that force in any link through your body from the ground to the rope.

 

[Ken G]

Can we say it never happens that both sides are sliding?

Not if we wish to gain any understanding of how tug-of-wars actually work.

Something like post #5? Escalating/increasing force in order to maximize what you may have as an advantage from weight-->normal force-->foot friction is important. It's also important to be able to withstand that force in any link through your body from the ground to the rope.

The many issues that would come up if someone was really trying to devise the best tug-of-war strategy are probably quite complex. Maybe there's a website on it somewhere, there usually is!

 

[Bashyboy]

I believe danmay is right in saying that someone could lose sooner than the other. For instance, if you had two people with equal masses on a frictionless surface, with some midpoint between them, and they began pulling each other, they would both accelerate towards each other at the same rate and meet at the midpoint at the same time. But suppose one person was more massive than the other, that person would have more inertia and therefore resist any accelerate more than the less massive person; this would cause him to move towards the midpoint more slowly than the other person.

 

[Ken G]

Have you ever seen a tug of war?

 

[Bashyboy]

 

[Ken G]

Yeah, my point exactly-- nothing about that video resembles an actual tug-of-war in the least way! If you want to talk about what is going on in that video, that's a very different issue from a tug-of-war competition, if you've ever seen one. Maybe MIT students haven't seen one either, but I think it is just a joke.

 

[danmay]

Yeah, my point exactly-- nothing about that video resembles an actual tug-of-war in the least way! If you want to talk about what is going on in that video, that's a very different issue from a tug-of-war competition, if you've ever seen one. Maybe MIT students haven't seen one either, but I think it is just a joke.

Don't make fun of my school! :D