Force on rope during a rope swing

[mileswiebe]

Well, its been about two years since I had to do a physics problem so I need some help.

A person plans on swinging from a 30 meter long rope from a bridge. They will tie the rope on to the center of the bridge then stretch it out tight and jump off. They'll be at the same height that the rope is tied at when they jump.

The person weighs 100 kg. Obviously they're on earth...

What is the maximum force exerted on the rope during the swing?What if we make the rope "dynamic rope" which stretches. Will this increase or decrease the maximum force on the rope?

I tried this and got about 3000 Newtons. Am I somewhere close?

Thanks,

Miles

 

[Simon Bridge]

They swing from the rope - so the rope is taught throughout?

the max tension will be at maximum centripetal acceleration, r=length of rope.
which will be at max speed - at the bottom of the swing
determine speed from conservation of energy
potential energy lost falling distance r = kinetic energy at the bottom
- this neglects air resistance (which is not negligible - but it's only 30m - so this back-of-envelope calc should be an upper limit).

Once you have the equation (leave substituting the numbers in till the end) you'll be able to answer the second part.

This is kind-of an odd project - presumably you want to be sure not to exceed the breaking strain of your rope?

 

[rohans]

Well, its been about two years since I had to do a physics problem so I need some help.

A person plans on swinging from a 30 meter long rope from a bridge. They will tie the rope on to the center of the bridge then stretch it out tight and jump off. They'll be at the same height that the rope is tied at when they jump.

The person weighs 100 kg. Obviously they're on earth...

What is the maximum force exerted on the rope during the swing?


What if we make the rope "dynamic rope" which stretches. Will this increase or decrease the maximum force on the rope?

I tried this and got about 3000 Newtons. Am I somewhere close?

Thanks,

Miles

i think your anwer is correct

 

[rcgldr]

Seems like the force should be 3 m g, regardless of the length of rope, if the release point is the same as the pivot point.

The peak force at the bottom of the swing = gravity and centripetal force = m ( 1 g + v^2 / h), and v^2 = 2 g h, so the force = m (1 g + 2 g) = 3 m g.

 

[Simon Bridge]

@rcgldr: of course: if the guy just hung there the tension would be mg. There has to be an additional tension off the centripetal acceleration of 2mg. It's fun watching people do the algebra though and see the length of the rope cancel out. Most people intuitively think it matters. Next step is if the rope is stretchy... the path is no longer circular: does it matter?

@rohans: you cannot tell that because the reasoning is left off ... "3000" is what you get from 100x30=3000 but it has MxL dimensions, so that isn't the way to do it. Such a round number could imply approximating g as 10N/kg rather than 9.8N/kg but we don't really know. We are told "I tried this" but are not told what was tried.