Department of Energy Argonne National Laboratory Office of Science NEWTON's Homepage NEWTON's Homepage
NEWTON, Ask A Scientist!
NEWTON Home Page NEWTON Teachers Visit Our Archives Ask A Question How To Ask A Question Question of the Week Our Expert Scientists Volunteer at NEWTON! Frequently Asked Questions Referencing NEWTON About NEWTON About Ask A Scientist Education At Argonne Lifeline Design
Name: Thomas R.
Status: Educator
Age: 60s
Location: N/A
Country: N/A
Date: October 2003

If an object attached to a 6 foot life line weighing 200 pounds falls 6 feet what would be the weight felt by the life line at the end of the fall be? Please show the formula so I can use it in my fall protection class.

The force depends entirely on how much the life line stretches. If it did not stretch at all so the object stopped instantaneously, its acceleration would be infinite and so the force would be infinite. Remember F = ma (Force = mass times acceleration).

If the rope exerted a constant force while it was stretching, it would be easy to calculate the (constant) force exerted on the body. The result is:

F = mg(h+d)/d + mg

Here mg is the weight of the object (say 200 lb), h is the distance it falls before the life line starts slowing its fall (say 6 ft) and d is the distance it falls while the life line is slowing its fall (say 1 ft). The answer is then eight (8) times its weight, or 1600 lb.

More likely, however, the rope stretches like an ideal spring with the retarding force increasing like F = kx, where x is the amount the rope has stretched. The answer is then:

F = 2mg(h+d)/d +mg

With the same numbers, the force is 15 times the weight of the person, or 3,000 lb.

I hope this is clear and answers your question fully. If you would like to see the derivation of these equations, please write again and I will be happy to provide the derivation, which is quite simple.

Best, Dick Plano...

Click here to return to the Engineering Archives

NEWTON is an electronic community for Science, Math, and Computer Science K-12 Educators, sponsored and operated by Argonne National Laboratory's Educational Programs, Andrew Skipor, Ph.D., Head of Educational Programs.

For assistance with NEWTON contact a System Operator (, or at Argonne's Educational Programs

Educational Programs
Building 360
9700 S. Cass Ave.
Argonne, Illinois
60439-4845, USA
Update: June 2012
Weclome To Newton

Argonne National Laboratory