physics problem (particle dynamics)

[HyperSlug]

I know some of you have taken or are taking physics so here's a question for you that I couldn't figure out:

A 68 kg sack is attached to a rope that is 6 meters long. The other end of the rope is tied to a hook which is hooked on to the ceiling. If you drop the sack from the ceiling, what is the maximum amount of force placed on the hook?

This is a real world problem and uhh since that 68 kg sack is really me, my life kinda depends on it.

Factor in gravity to account for acceleration due to mass, and you should arrive at your answer.

[HyperSlug]

Oh I forgot to mention also, just use 10 m/s^2 for gravity. If you just use F=ma, then you discard the fact that the sack dropped 6 meters, which is rather important. A sack hanging from the ceiling generates a much lower force than one falling 6 meters.

[Gomer]

first you need to find the velocity after the 6m fall (11 m/s).

Then your impulse force (aka linear momentum) Fbar is m*v. In order to find the force on the hook, you need to be given a delta t (the time it takes the rope to stop you) to do this problem. Then the force F is (m*v)/(delta t). I would assume 15 milliseconds (15 x 10^-3 seconds).

so the force would be (11*68)/.015=3.324 kN

the faster that rope stops you, the greater the force

10 ms = 5 kN

this also assumes you are falling straight down with no initial velocity.

[caddmannq]

As I recall (from 1972, no less....)

Find the terminal velocity, then:

K EQUALS ONE HALF M times V SQUARED

(for a non-elastic rope )

BTW: Is there a tutorial for writing math formulae on VBB script?

[Gomer]

$100 please (consulting fee) =)

[Gomer]

cadd, that formula is for kinetic energy [Joules or (kg*m^2/s^2)]

force is in Newtons or (kg*m)/s^2

[Graham]

HyperSlug,
You say the sack is you and your life depends on it, is the rope round your neck?



G

[caddmannq]

I stand corrected!

[HyperSlug]

Thanks Gomer. 3.3 kN sounds like it would be about right.

Graham: LOL, no the rope is actually tied to a harness for rock climbing. I was modeling a situation that can occur. My gear can support 22 kN and I wanted to be sure that I wasn't even approaching it.