Maximum compression of a spring?

In summary, the conversation discusses different attempts at finding the maximum compression of a spring when a 2 kilogram block is dropped onto it from a height of 0.45 meters. The first attempt involved using the amplitude of the simple harmonic motion, but this was found to be incorrect. The second attempt involved using conservation of energy, but the resulting value was also incorrect. After receiving help, it was discovered that the potential energy at maximum compression should be calculated as mg(h+x) instead of mgh. This provided the correct solution.
  • #1
eri139
15
2
Homework Statement
A 2 kilogram block is dropped from a height of 0.45 meter above an uncompressed spring. The spring has an elastic constant of 150 newtons per meter and negligible mass. The block strikes the end of the spring and sticks to it. Determine the maximum compression of the spring.
Relevant Equations
U = 1/2kx^2, K = 1/2mv^2, U = mgh, F = kx
I found the amplitude of the simple harmonic motion that results (0.367, and I know this is correct because I entered it and it was marked as a correct answer), and assumed it would be the same value for the maximum compression since x(t) = Acos(wt). And, since the maximum value of cosine is 1, then the maximum value of x(t) would be A. But it's not correct. I also tried doubling this value, since I think the amplitude is the distance from the equilibrium position...so I'd double it to find the total compression. This is still incorrect.

Then I tried conservation of energy. I know the block has a potential energy of mgh, or 2 x 9.8 x 0.45. I made that equal to the energy of a spring, which is 1/2 x 150(x^2). Setting both equal to each other, I get 0.343, which is also incorrect.

Please help! I don't know what other approach to take for this question.
 
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  • #2
eri139 said:
Homework Statement:: A 2 kilogram block is dropped from a height of 0.45 meter above an uncompressed spring. The spring has an elastic constant of 150 Newtons per meter and negligible mass. The block strikes the end of the spring and sticks to it. Determine the maximum compression of the spring.
Homework Equations:: U = 1/2kx^2, K = 1/2mv^2, U = mgh, F = kx

I found the amplitude of the simple harmonic motion that results (0.367, and I know this is correct because I entered it and it was marked as a correct answer), and assumed it would be the same value for the maximum compression since x(t) = Acos(wt). And, since the maximum value of cosine is 1, then the maximum value of x(t) would be A. But it's not correct. I also tried doubling this value, since I think the amplitude is the distance from the equilibrium position...so I'd double it to find the total compression. This is still incorrect.

Then I tried conservation of energy. I know the block has a potential energy of mgh, or 2 x 9.8 x 0.45. I made that equal to the energy of a spring, which is 1/2 x 150(x^2). Setting both equal to each other, I get 0.343, which is also incorrect.

Please help! I don't know what other approach to take for this question.
At maximum compression, the potential energy decreased by mg(h+x) instead of mgh.
 
  • #3
ehild said:
At maximum compression, the potential energy decreased by mg(h+x) instead of mgh.
Thank you so much! that did it!
 

FAQ: Maximum compression of a spring?

What is maximum compression of a spring?

Maximum compression of a spring refers to the point at which the spring has been compressed to its fullest extent without causing permanent deformation or damage.

How is maximum compression of a spring determined?

The maximum compression of a spring can be determined by calculating the spring's elastic limit, which is the maximum amount of stress the spring can withstand without permanent deformation, and then applying a safety factor to ensure the spring does not reach its elastic limit during use.

What factors affect maximum compression of a spring?

The maximum compression of a spring can be affected by factors such as the material and thickness of the spring, the amount of force being applied, and the design of the spring itself.

Why is it important to know the maximum compression of a spring?

Knowing the maximum compression of a spring is important for ensuring the spring is not over-compressed, which can lead to permanent deformation or failure. It is also important for designing and using the spring in a safe and efficient manner.

Can the maximum compression of a spring be increased?

The maximum compression of a spring can be increased by using a higher quality or stronger material, increasing the thickness of the spring, or by changing the design to better distribute the force being applied. However, it is important to consider the spring's elastic limit and safety factors when making any changes to increase its maximum compression.

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