Hooke's Law help

[Anonymous No.6110791]

Need help with a Hooke's Law problem.

Pedro Martinez is standing on the planet Baseball (r = 5000 km, m = 7.0 x 10^24 kg) with his favorite spring (k = 100 N/m) in his hand. If he puts a 1.2 kg mass on the end of the spring, how far does it stretch? If he then slowly removes 0.3 kg, how far up does the remaining mass move? What mass would be required to stretch the spring 0.35 m?

[Anonymous No.6110808]

>>6110791
Well where do you think you should start at? Do you know what the formula is? Do you understand how integrals work? What do you have so far, and what is it that you cannot understand.

[Anonymous No.6110856]

I have been given the formula F = kΔd to use. I just don't understand what the Force would be in this problem. Every answer that I have gotten so far seems way to far off.

[Anonymous No.6112275]

>>6110856
call L(t) the lenght of the spring.

Newtonb's law says that :
m*a=sum forces

where a is the acceleration (here a=d/dt(d/dt(L))

->first force is the holoke's one,
F=kΔL
the meaning of ΔL is L(t)-L_0, where L_0 is the length of the spring in its normal state.

since L_0 is just a constant, you can write th acceleration as

a=d/dt(d/dt(ΔL))

-> what are the other forces ?

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then you'll get a differential equation on the variable ΔL. You're only interested by ΔL(t=infinity), which is the math translation of "how far does it stretch"