In a tug-of-war match today, my summer camp students were very concerned about putting the biggest people at the back of the rope. Is there any advantage to this strategy?
[Physics] Does it matter how you order your tug-of-war participants
everyday-lifenewtonian-mechanics
Related Solutions
It is always best to draw a diagram to convince yourself of things in a case like this.
This is intended to represent a steady state situation: nobody is moving / winning. As you can see, there are two horizontal forces on A: the floor (pushing with 100N) and the rope (pulling with 100N). There will be two vertical forces (gravity pulling down on center of mass, and ground pulling up) to balance the torques - I did not show them because they are not relevant to the answer.
Now I drew a dotted line between A and B. Consider this a curtain. A cannot see whether the rope is attached to B (an opponent) or a wall. A can measure the tension in the rope by looking (for instance) at the speed at which a wave travels along the rope - or by including a spring gage.
Now ask yourself this question: if A feels a tension of 100N in the rope (this is the definition of the force on A), and can confirm (by looking at the gage) that the tension is 100 N, but he cannot see whether the rope is attached to a ring or to an opponent, then how can the tension be 200N? If I pull on a gage with a force of 100N, it will read 100N - it cannot read anything else (in a static situation, and where the gage is massless, ... )
I think I understand the source of your confusion based on the earlier q/a that you referenced - so let me draw another diagram:
In this diagram, I have move the point of attachment of the rope with which A pulls B away from B's hands, to his waist. Similarly, the rope with which B pulls on A is moved to A's waist.
What happens? Now there are two distinct points where A experiences a force of 100 N: one, his hands (where he is pulling on the rope attached to B's waits); and another where the rope that B is pulling on is tied around his waist.
The results is that there are two ropes with a tension of 100N each, that together result in a force of 200N on A (two ropes) offset by a force of 200N from the floor, etc.
This is NOT the same thing as the first diagram, where the point on which B's rope is attached is the hands of A - there is only a single line connecting A and B with a tension of 100 N in that case.
As was pointed out in comments, you can put a spring gauge in series with your rope to measure the tension in it; and now the difference between "a single person pulling on a rope attached to a ring at the wall (taken to be the dotted line) and two people pulling across a curtain (so they cannot see what they are doing) is that in one case, a single spring (with spring constant $k$) expands by a length $l$, while in the second case you find a spring that's twice as long, with constant $k/2$), expanding by $2l$.
These are all different ways to look at the same thing.
- Mass and material strength do not scale equally with size. This is well known, so I'll only illustrate with a few examples.
Imagine a small cylinder of clay 1/2 inch around and 2 inches tall sitting on your desk. It can sit there a while with little deformation. Now imagine a cylinder of the same material 10 feet around and 40 feet tall. It would slump down significantly right away.
Look at the thickness of animal legs over animal size. Evolution would have trimmed off excess material long ago. Note how much thicker elephant legs are relative to overall size than those of a dog or ant.
- The effects of air viscosity are much greater at the small size of a insect than they are to our human-scale experience. The air pushed in front of your hand will push the insect well before it actually hits your hand.
- You can stun insects by whacking them, although it usually takes something a bit faster and more rigid than your hand for something as small as a fly. I found the best way to hunt flys in a apartment in college was to whack them in mid air with a large metal spatula. This would knock them to the ground where they'd lie for a 10-20 seconds, then buzz on like nothing happend. That gives you plenty of time to dispatch them. The long handle of the spatula allowed me to move it faster than I could move my hand.
Best Answer
Yes, if you put the strongest people in the back the rope will be straighter, making it more likely everyone is pulling in the same direction.