Max extension of spring/ magnitude of its acceleration

AI Thread Summary
The discussion revolves around calculating the maximum extension of a spring and the corresponding acceleration of a body attached to it. The spring constant is given as 30 N/m, and a 1.1 kg mass is used. The user initially attempts to find the extension using the formula x = mg/k but encounters an error, prompting a request for clarification. A suggestion is made to apply conservation of energy principles, indicating that potential energy in the spring and gravitational potential energy should be equated to find the correct maximum extension. The key takeaway is that the maximum extension requires considering energy conservation rather than just static equilibrium.
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Homework Statement


An ideal spring has a spring constant k = 30 N/m. The spring is suspended vertically. A 1.1 kg body is attached to the unstretched spring and released. It then performs oscillations.


(a) What is the magnitude of the acceleration of the body when the extension of the spring is a maximum in m/s^2

(b) What is the maximum extension of the spring in m?



Homework Equations


kx=mg
=> x=mg/k

a(max)=(A)(w^2)
w=2pi/T
T=2pi*(sqrt(m/k))



The Attempt at a Solution


k=30
m=1.1
a=?
x=?

I have to solve part B (amplitude) before I can solve part A. So, simple algebra sets

x=mg/k
x=(1.1)(9.8) / 30
=.35933 m

But this is wrong according to web assign. Could you tell me what I am doing wrong? Perhaps units or something?

Thank you!
 
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You might want to account for the conservation of energy:

PE = PE

m*g*x = 1/2*k*x²
 
At the minimum extension (starting point) all energy is gravitational; at the maximum extension, all energy is in the spring. This is how you solve b.

Only at the equilibrium point midway between is kx = mg.
 
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