Solve Bungy Jump Problem: Acceleration at Bottom

[ff93]

You go bungee jumping from a bridge that is 65m high, the bungee cord has an unstretched length of 32m and a spring constant of k=107 N/m
You have a mass of 75kg.

Question: what is the acceleration at the bottom, closest to the ground?

I`ve tried to use 1/2kA²=1/2m_x+1/2kx²
but it doesn´t seem to work for me :(

please help, I´m not asking for U to solve it but at least give me a couple of hints!

 

[Doc Al]

Start by figuring out where the lowest point is. Use conservation of energy.

 

[ff93]

should I use mgh=1/2kx²?

x as how far it stretches from 32m?

and then should I use F=-kx => F=ma and solve out a?

 

[Doc Al]

should I use mgh=1/2kx²?

x as how far it stretches from 32m?

Yes. Hint: Express h in terms of x. (Measure gravitational PE from the lowest point.)

 

[ff93]

you mean mg(x+32)=1/2kx²?

should I then continue with F=-kx => F=ma solve out a?

 

[Doc Al]

you mean mg(x+32)=1/2kx²?

Exactly.

should I then continue with F=-kx => F=ma solve out a?

Be sure to include all forces when applying F=ma.

 

[ff93]

mg(x+32)=1/2kx² gives two answers but I can throw away the negative one, right?

then I used F=-kx+mg => a= (-kx+mg)/m
is that right?

 

[Doc Al]

mg(x+32)=1/2kx² gives two answers but I can throw away the negative one, right?

Right.

then I used F=-kx+mg => a= (-kx+mg)/m
is that right?

Yes, that's fine.

Don't get hung up with signs. You have an upward force of magnitude kx and downward force of magnitude mg. Which direction will the acceleration be in at the lowest point?

 

[ff93]

the direction will be "up",negative
right?

 

[Doc Al]

the direction will be "up",negative
right?

Yes, the acceleration will be up. Which you happen to call negative. I suspect that they only care about the magnitude of that acceleration.

 

[ff93]

thank you for the help!