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I am not exactly sure how the physics work here. If we take a car tow rope, which is manufactured for towing a 3500 kg car and we actually start towing such a car on this rope, what force do we really apply to the rope?

Could the same rope safely withhold an adult person (100 kg) hanging on it?

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1  
Remember a very important point. Climbing ropes are made so that they stretch and elastically absorb the stretch. This is, of course, because if you fall, a rigid rope would bring you to a sudden stop and likely break your body from the snap. Tow ropes are rigid, so your question may hold an intrinsic danger which I consider important to point out. –  Stefano Borini May 31 '11 at 16:30
    
@Stefano Borini: I am fully aware of this fact, but good job pointing it out! –  Richard Rodriguez May 31 '11 at 16:40
    
You will have to find the manufacturer's tensile load rating. Otherwise you will have to test for it first. It is possible to estimate the tensile rating from material and stranding type, but it gets complicated quickly. –  ja72 Jun 1 '11 at 23:23

2 Answers 2

It depends on rolling resistance of wheels, friction resistance in bearings, elevation and acceleration of pulled car.

$ F=F_r+F_f+F_e+F_a $

where:

  • $F$ is total force,
  • $F_r=\frac{N_fb}{r}$ is rolling resistance, $b$ is rolling resistance coefficient, $r$ is radius of the wheel and $N_f$ is normal force,
  • $F_f=\mu N_f$ is friction force and $\mu$ is friction coefficient,
  • $F_e=mg*\sin\alpha$ is part of gravitation force, $\alpha$ is angle of slope, $m$ is mass,
  • $F_a=ma$ is acceleration force, $a$ is acceleration.

    So it depends on bearings condition, tires and surface conditions, and many other variables...

If you want to know whether 3.5 ton rope can lift 100 kg ask sports specialist, especially climbers, whether 100 kg safe rope can pull 3.5 ton car.

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Actually there's three kinds of ropes one might hang an adult human from.

A rock climbing rope is designed with a great deal of stretch. Thus when someone falls the rope decelerates them slowly, thereby lowering the peak force applied to the rope. To find these google "dynamic climbing rope".

Ropes used in rescue are not intended to catch falls. Accordingly they are designed with much less stretch. This makes for a more comfortable ride. To find these, google "low stretch rescue rope" or "static rescue rope".

Ropes used for execution are the third type. With these, safety is not a great concern.

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""With these, safety is not a great concern"" Mhmmmm. ..Depends what has to be safe/secure :=( –  Georg Jun 2 '11 at 9:55

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