| MadSci Network: Physics |
Yes, the tension on a tug-of-war rope will be different at different points. The tension will be greatest in the middle section (between the two warring teams), and least between the last person and the second to last person.
The tension in a rope is essentially the force that the rope is exerting. The first step in physics problems like this is to draw what is called a free-body diagram. In a free body diagram, you draw the object that you're analyzing (the rope) and all of the forces acting on it. Here's a quick sketch of our rope:
50 50 50 50 50 50 <----<----<------------>---->---->What I attemped to draw was our rope, with three people at each end, each pulling with 50 lbs of force. As you can see, the rope is at equilibrium, i.e. there is an equal amount of force on each side, and the sum of the forces is 0 (50 + 50 + 50 - 50 - 50 - 50 = 0).
To find the tension in the rope, we cut our free body diagram at the point we want to find the tension, and rebalance the forces. So we'll start at the middle where there should be the most tension.
50 50 50 ? <----<----<------|->In order for the diagram to remain balanced, the rope must be pulling with 150lbs of force in the middle, so it has 150lbs of tension. Now let's check the end.
50 ? <----|->Again, to remain balanced, the rope must have 50lbs of tension on it in this section. You'll also see that this works out to be the sum of the forces that we cut off:
50 50 50 50 50
|-<----<------------>---->---->
50 + 50 - 50 - 50 - 50 = -50
Hope that all makes sense. Let me know if you have any other questions about it.
Your Mad Scientist,
Mike Scannell
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