What is the maximum spring displacement?

In summary: Just before you turn the compressed spring sideways, what h does it have, ##h_{weight}## only or ##h_{weight}+h_{impact}##?Just before you turn the compressed spring sideways, it has both ##h_{weight}## and ##h_{impact}##.
  • #1
leafy
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8
Homework Statement
A mass of 1kg is dropped at a height of 6m on an ideal spring. Calculate the maximum spring displacement. Spring constant k=20N/m. Spring length is 5m.
Relevant Equations
F=kx
E= .5kx^2
the mass will drop 1 m before it comes in contact with the spring. I’m stuck afterward. Please help.
The total energy of 1 m is mgh= 1kgx9.8m/ss x 1m = 9.8J
9.8J = .5 x 20N/m x x^2 ---> x = .99 m
the spring is compressed by .99 m ?
 

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  • #2
See PF guidelines: we need you to post an attempt at solution!

Hint: what is your E?
 
  • #3
yes sorry, my attempt is not right, but i should take a shot.
 
  • #4
leafy said:
Homework Statement:: A mass of 1kg is dropped at a height of 6m on an ideal spring. Calculate the maximum spring displacement. Spring constant k=20N/m. Spring length is 5m.
Relevant Equations:: F=kx
E= .5kx^2

the mass will drop 1 m before it comes in contact with the spring. I’m stuck afterward. Please help.
The total energy of 1 m is mgh= 1kgx9.8m/ss x 1m = 9.8J
9.8J = .5 x 20N/m x x^2 ---> x = .99 m
the spring is compressed by .99 m ?
Gravity does not switch off when the mass contacts the spring.
 
  • #5
Thanks for the insight, so we must take gravity into account during the compression.

mg(1m) +mg(x) = .5k(x^2) ---> 0 = 10x^2 - 9.8x - 9.8

x=-.6; x = 1.6

So we take the positive one which is 1.6 m of spring compression? how can i double check this?
 
  • #6
leafy said:
Thanks for the insight, so we must take gravity into account during the compression.

mg(1m) +mg(x) = .5k(x^2) ---> 0 = 10x^2 - 9.8x - 9.8

x=-.6; x = 1.6

So we take the positive one which is 1.6 m of spring compression? how can i double check this?
The only check I can think of is to substitute back into the quadratic. Looks right to me.
 
  • #7
I don't feel comfortable about this answer. The solution should allows us to rotate the spring horizontally at maximum compression and it would yield the same result in term of energy. However, the horizontal position doesn't have a force of mg=10N pressing on it like the vertical position, so something is off. Thanks for helping though.
 
  • #8
leafy said:
The solution should allows us to rotate the spring horizontally at maximum compression
About what axis?
 
  • #9
As the figure shown
 

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  • #10
leafy said:
As the figure shown
I assume you are taking the speed at contact as the same in both orientations. With that axis, the horizontal version does not have any vertical movement of the mass thereafter, so the energy is different.
 
  • #11
leafy said:
I don't feel comfortable about this answer. The solution should allows us to rotate the spring horizontally at maximum compression and it would yield the same result in term of energy. However, the horizontal position doesn't have a force of mg=10N pressing on it like the vertical position, so something is off. Thanks for helping though.
There is the deformation of the vertical spring due to the dead weight of that mass (that will be the neutral point of any subsequent oscillation), let's call it ##h_{weight}##.
And then the deformation due to the velocity of the mass impacting it (that will be the lowest point of any subsequent oscillation), let's call it ##h_{impact}##.

Just before you turn the compressed spring sideways, what h does it have, ##h_{weight}## only or ##h_{weight}+h_{impact}##?

CNX_Calc_Figure_17_03_001.jpg
 
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FAQ: What is the maximum spring displacement?

What is the maximum spring displacement?

The maximum spring displacement refers to the farthest distance the spring can stretch or compress from its equilibrium position.

How is the maximum spring displacement calculated?

The maximum spring displacement can be calculated using Hooke's Law, which states that the displacement is directly proportional to the force applied to the spring and inversely proportional to the spring's stiffness.

What factors can affect the maximum spring displacement?

The maximum spring displacement can be affected by the material and thickness of the spring, the amount of force applied, and the spring's initial length and position.

What happens if the maximum spring displacement is exceeded?

If the maximum spring displacement is exceeded, the spring may become permanently deformed or even break, depending on the material and amount of force applied.

Can the maximum spring displacement be increased?

Yes, the maximum spring displacement can be increased by using a spring with a higher stiffness or by applying a greater force to the spring.

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