Max acceleration experienced by the jumper?

[ohheytai]

Design a "bungee jump" apparatus for adults. A bungee jumper falls from a high platform with two elastic cords tied to the ankles. The jumper falls freely for a while, with the cords slack. Then the jumper falls an additional distance with the cords increasingly tense. Assume that you have cords that are 15 m long, and that the cords stretch in the jump an additional 22 m for a jumper whose mass is 80 kg ,the heaviest adult you will allow to use your bungee jump (heavier customers would hit the ground)
what is the maximum acceleration the jumper experiences?
ks = 59.93 N/m
max force of tension = 1318.46
someone please help i have no idea how to do this
i solved for the ks and the max tension but i have no idea how to find acceleration at all i tried F of tension =ma but that is wrong and i tried mg=ma and that's still lwrong someone please help me!

 

[Delphi51]

Free body diagram. What two forces act on the body?
Write that F1 + F2 = ma.
Careful with the signs - be clear on whether up or down is positive and put appropriate signs on the F's.
You should find that the ma is highest when the stretch is greatest.

 

[ohheytai]

F1 would be -mg and F2 would be the force of tension?

 

[ohheytai]

if so its (80)(-9.8)=1318.46N = ma and solving for a would equal 6.68075 m/s^2 righttt?

 

[Delphi51]

That 6.68 is very close to what I found, but I couldn't follow the rest.
Certainly (80)(-9.8)=1318.46N can't be correct.

 

[ohheytai]

sorry i meant (80)(-9.8)+1318.46N = ma haha soo its 6.6 right?

 

[Delphi51]

I get 6.7 or 6.8 depending on the accuracy of g used.

 

[ohheytai]

i just tried all of those they are all wrong :( any idea what's wrong?

 

[ohheytai]

it also says |ay| = ___ g's (acceleration in m/s2 divided by 9.8 m/s2) so I am guessing its not in m/s^2

 

[Delphi51]

Try 6.67/9.8 rounded to the usual number of digits.

 

[ohheytai]

nope still wrong the the answers has units in g's soo yaa idk

 

[Delphi51]

Dividing by 9.8 definitely converts it to G's. I get 0.68.
Were these given or did you calculate them?
ks = 59.93 N/m
max force of tension = 1318.46
The 22 m extension seems a bit large; is it possible the writer meant to say it stretched TO 22 m instead of stretched BY 22 m?

 

[ohheytai]

they we're calculated but they are correct and it is an extension of meters

 

[Delphi51]

How did you get ks = 59.93 N/m?