# Maximum Compression for a Block on Spring

• Abu
In summary, the conversation discusses the use of Newton's laws and conservation of energy to solve a problem involving a block compressing a spring. The speaker initially uses Newton's laws and gets an answer half of the correct answer, but learns that this is because the equation used was at the equilibrium position and does not account for the block's non-zero velocity. The correct method is using conservation of energy, where the maximum compression can be found by setting the kinetic energy to zero. This method is simpler and more effective than trying to find the point of maximal elastic force using Newton's laws.
Abu
Homework Statement
A spring of negligible mass has force constant k = 800 N/m. You place the spring vertically with one end on the floor. You then lay a 1.6 kg block on top of the spring and release the book from rest. Find the maximum distance the spring will be compressed
Relevant Equations
F = kx
Hi everyone, just a quick question..

I tried this problem using Newtons laws, not conservation of energy, and I got an answer exactly half of what the correct answer is, and I'm not sure why. Here is what I did:

Net force = zero once the spring is compressed, therefore

mg - kx = 0
mg = kx
mg/k = x
1.6(9.8)/800 = x
x = 1.96 cm

The actual answer is 3.92 cm however, and I don't know why.

If I do this problem using conservation of energy, I get the correct answer but I can't explain why my Newtons laws method is wrong.

When you let go of the block and it starts compressing the spring, the spring will start oscillating. The equation you were using is at the equilibrium position where gravity and elastic force cancel. However, once block reaches this position, it will have non-zero velocity, so it will move past this point and compress the spring further, until it's velocity drops to zero. At this point, elastic force will be bigger than gravity, so it will push the block up, hence it will oscillate.

Therefore, since the energy is conserved, in order to get the maximum compression, you need the equation where kinetic energy is zero, so by substituting correct potential energy for gravity and elastic force, you get the right answer, as you did. In order to get that same point via Newton's law, you'd need to search for the point where elastic force is maximal, not the point where it cancels with gravity. This would prove more complicated than using energy conservation in my opinion, so that's why this exercise is most likely intended to be done using energy conservation.

Hope that helps.

Abu
Antarres said:
When you let go of the block and it starts compressing the spring, the spring will start oscillating. The equation you were using is at the equilibrium position where gravity and elastic force cancel. However, once block reaches this position, it will have non-zero velocity, so it will move past this point and compress the spring further, until it's velocity drops to zero. At this point, elastic force will be bigger than gravity, so it will push the block up, hence it will oscillate.

Therefore, since the energy is conserved, in order to get the maximum compression, you need the equation where kinetic energy is zero, so by substituting correct potential energy for gravity and elastic force, you get the right answer, as you did. In order to get that same point via Newton's law, you'd need to search for the point where elastic force is maximal, not the point where it cancels with gravity. This would prove more complicated than using energy conservation in my opinion, so that's why this exercise is most likely intended to be done using energy conservation.

Hope that helps.
Thank you so much for your fast reply. Your response helped me a lot, I really appreciate it! Thanks!

You're welcome!

## 1. What is maximum compression for a block on spring?

The maximum compression for a block on spring is the distance that the block can be compressed from its equilibrium position when a force is applied to it.

## 2. How is the maximum compression for a block on spring calculated?

The maximum compression for a block on spring can be calculated using the formula: x = F/K, where x is the maximum compression distance, F is the applied force, and K is the spring constant.

## 3. What factors affect the maximum compression for a block on spring?

The maximum compression for a block on spring is affected by the mass of the block, the spring constant, and the magnitude of the applied force.

## 4. What is the relationship between the maximum compression and the spring constant?

The maximum compression is directly proportional to the spring constant. This means that as the spring constant increases, the maximum compression also increases.

## 5. How does the maximum compression change if the mass of the block is doubled?

If the mass of the block is doubled, the maximum compression for the block on spring will be halved. This is because the mass is inversely proportional to the maximum compression, meaning that as the mass increases, the maximum compression decreases.

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