basic dynamics question 1

[njlee]

Hi Gurus,

Is there any theories or equations relate force to velocity?

An object, which is tied to a rope, moves in constant velocity. When the rope is taut, what is the tension on the rope at that instant (when the object is instantly stopped/reversed)?

I think the force will be approaching infinite because F=ma and there is zero time for the object to decelerate. However, in real life, it is impossible. I guess the rope would have to be deformed a little bit for the deceleration of the object. how much? how fast? .01 second, .0001 second?

conservation of momentum theory only provides solution of the velocity of the object after impact, not the force, am I right?

What the maximum force resulted from the impact. I'm interested in finding out ways to solve this kind of problem

Thanks for any advice.

Lee

 

[RichLeimbach]

Lee,
You're right on the basics of this. The rope would have to be deformed or else the force would be infinite. Knowing your energy and the spring rate of the rope, it would be possible to calculate the maximum force, acceleration and event time using the F=ma equation (or variations of it).
In my experience, depending on the size and speed of the falling body and the size and construction of the rope, you can get some significant deformations. Even the most rigid rope will deform 2 or 3% before reaching it's breaking strength.

 

[njlee]

Thanks for the response.

I think the hard part will be to determine the rate of deformation and how long the deformation last.

Any knows where can I find this info?

Thanks.

 

[RichLeimbach]

Lee,
You can either test for this yourself (by measuring deformation with various weights on the end of the rope) or you can get it from the manufacturer. Yale Coradge has some good info on their site

http://www.yalecordage.com

that gives some info on deflection and maximum energy absorbtion for various rope materials and braids.