Max extension of spring/ magnitude of its acceleration

In summary, an ideal spring with a spring constant of 30 N/m is suspended vertically with a 1.1 kg body attached. The body performs oscillations and the maximum extension of the spring can be calculated using the conservation of energy equation PE = PE. When the extension is at its maximum, all energy is in the spring and at the minimum extension, all energy is gravitational. This can be used to solve for the amplitude of the oscillations and then the magnitude of the acceleration of the body can be calculated using the equation a(max) = (A)(w^2).
  • #1
WPCareyDevil
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0

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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  • #2
You might want to account for the conservation of energy:

PE = PE

m*g*x = 1/2*k*x²
 
  • #3
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.
 

1. What is the maximum extension of a spring?

The maximum extension of a spring is the distance it can be stretched from its original length. This distance depends on the material and size of the spring, as well as the amount of force applied to it.

2. How is the maximum extension of a spring calculated?

The maximum extension of a spring can be calculated using Hooke's Law, which states that the force applied to a spring is directly proportional to its extension. This can be represented by the equation F = -kx, where F is the force applied, k is the spring constant, and x is the extension.

3. What factors affect the maximum extension of a spring?

The maximum extension of a spring is affected by the material and size of the spring, as well as the amount of force applied. Other factors that can affect it include temperature, the number of cycles the spring has gone through, and any wear and tear on the spring.

4. What is the magnitude of acceleration of a spring?

The magnitude of acceleration of a spring refers to the rate of change of its velocity as it oscillates back and forth. This is affected by the mass of the object attached to the spring, as well as the spring constant and the amplitude of the oscillation.

5. How is the magnitude of acceleration of a spring related to its maximum extension?

The magnitude of acceleration of a spring is indirectly related to its maximum extension. As the spring is stretched further, the force applied to it increases, causing a greater acceleration. However, this acceleration will decrease as the spring reaches its maximum extension, and will increase again as the spring is compressed back to its original length.

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