Finding the amplitude of a vertical spring

In summary, the conversation discusses the use of equations to solve for the velocity of lemons dropped from a certain height, the elongation of a spring at equilibrium point, and the COE equation. The speaker is unsure if their reasoning for the COE equation is correct and is seeking clarification on how to define m and x in the equation. They also mention that the formatting of their post may not be ideal.
  • #1
dnglified1
2
1
Homework Statement
Please see attached file
Relevant Equations
Et = Et'
GPE = mgh
SPE = 1/2kx^2
KE = 1/2mv^2
The question asks for a bunch of stuff, but I have everything except part d down.
a) Setting the mass of lemons as m1, I used m1*gh = 1/2mv^2, solving for v of the lemons as v = √2gh, where h is the height at which it is dropped. Then, I used COM and had this equation (not 100% sure if right):
m1*√2gh = (m1 + mp)*vf, and isolated for vf = (m1*√2gh)/(m1 + mp)

b) Setting the equilibrium point at zero, I used kx = mp*g to get x = 0.0054 meters of elongation.

c) Setting Fnet as 0, I used kx = m1*g to get x = m1*g/k

d) This is what I have for the COE equation:

1/2(m1 + mp)vf^2 + mgx = 1/2kx^2

My reasoning for this is that the total energy stored in the spring at max displacement should be equal to the initial kinetic energy of the whole system plus the GPE the spring has due to it not being completely compressed. I solved for x and since x = 2A, A = 0.5x. But I am not getting the expression that is expected. I don't know if the entire thing is wrong or if it is just a math issue.
 

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  • #2
Apologies for formatting, it's my first non-introductory post :)
 
  • #3
dnglified1 said:
1/2(m1 + mp)vf^2 + mgx = 1/2kx^2
How are you defining m and x there?
Remember that, for the spring PE to be 1/2kx^2, x must be the displacement from the spring's relaxed length.
 

FAQ: Finding the amplitude of a vertical spring

What is a vertical spring?

A vertical spring is a type of mechanical spring that can stretch or compress in a vertical direction. It is typically made of a flexible material, such as metal or rubber, and is used to store and release energy.

Why is it important to find the amplitude of a vertical spring?

The amplitude of a vertical spring represents the maximum distance that the spring can stretch or compress from its equilibrium position. This information is important for understanding the behavior and capabilities of the spring.

How do you find the amplitude of a vertical spring?

The amplitude of a vertical spring can be found by measuring the maximum distance that the spring stretches or compresses when a known force is applied to it. This can be done by attaching a weight to the end of the spring and measuring the displacement.

What affects the amplitude of a vertical spring?

The amplitude of a vertical spring can be affected by various factors, such as the material and thickness of the spring, the amount of force applied, and any external factors that may influence the movement of the spring.

What is the relationship between amplitude and frequency in a vertical spring?

The amplitude and frequency of a vertical spring are inversely proportional, meaning that as the frequency increases, the amplitude decreases and vice versa. This relationship is described by Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from its equilibrium position.

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