Springs

[IntoTheNewWorld]

Hi guys I'm a bit confused about spring questions 

In VCAA 07, Qn 9,

"In a laboratory class at school, Lee is given a spring with a stiffness of 20 N m^-1 and unstretched length of 0.40m. He hangs it vertically, and attaches a mass to it, so that the new length of the spring is 0.60m"

To calculate the mass, you had to kx to mg

In VCAA 06, Qn 14,

"The natural length of the bungee cord is 10m. Sam stops falling and first comes to rest momentarily when the length of the bungee cord is 18m. What is the spring constant of the bungee cord?"

But in this case, to find k, you have to equate mgh to spring potential energy. Equating kx to mg doesn't work. Could someone please help me understand why I can't just equate kx to mg like in the previous question? Any help greatly appreciated 

[kamil9876]

it's tricky. It's because there is a difference between 'momentarily at rest' and 'hanging'. Hanging implies that you are permanently at rest and so a=0 therefore the net force is zero and so:

0=kx-mg

However when something is momentarily at rest, v=0, but acceleration does not neccesarily equal 0 and so net force is not neccesarily 0. When you imagine it, the net force on Sam in this case is actually not zero since right after this moment he is going to be pulled back up. Basically in this case sam is momentarily at rest because he is at the turning point and so v=0(just like in projectile motion where v=0 at turning point, but as you know in projectile motion v=0 at turning point while the Force is non-zero!)


The sam-rope system is made up of three energies:
E=Total Energy
GP=Gravitational Potential
EP=Elastic Potential
KE=Kinetic Energy


GP+EP+KE=E

(Subscript i means initial)
Initially and and so:

(1)

(subscript f means final)
At the instant we are interested in. Because v=0(momentarily at rest), and so:
(2)

However because (conservation of energy) we can equate (1) and (2):




And so the Elastic Potential Energy at the turning point is the change in Gravitational Potential. So energy analysis simplifies this situation correctly and does not worry about net forces(and hence accelerations) but rather velocities because we are considering kinetic energy.

[IntoTheNewWorld]

Thanks so much kamil, I think I get it now =D

[median]

Would it be necessary to know the weight of the rope in a question like this?