# Height of falling object vs. compression of spring

• HaoPhysics
In summary, the question discusses whether the spring will compress a greater distance when a mass is dropped from a higher height. From a force perspective, the spring should compress the same distance regardless of the height. However, from an energy perspective, the spring will compress a greater distance to match the increased potential energy at the higher height. Therefore, the second explanation is correct as the point of maximum compression is not the equilibrium point.
HaoPhysics
1. Question
Given an idea spring with constant K, a mass of M is dropped onto the spring from a height of H1. The spring compresses D distance.

We take the mass off, and drop the mass again at a height of H2, where H2 is significantly greater than H1. This time, will the spring compress a greater distance or the same distance?

## Homework Equations

F = - k x
and Conservation of energy:
U = mgh, Es = ½kx2, where Es is elastic potential of spring
U = Es

3. Attempt at solution

So if we think about it only in terms of F = -kx, then no matter how high we drop the mass, it should compress the same distance D, because F (gravity) remains the same.

But if we consider it from an energy perspective, then U (gravitational protential) would be greater if the height is greater. And thus the compression must also be greater to match this greater potential energy.

So which one is correct?

The point of maximum compression is not the equilibrium point!

## 1. What is the relationship between the height of a falling object and the compression of a spring?

The height of a falling object and the compression of a spring are directly proportional. As the object falls and gains kinetic energy, it transfers this energy to the spring upon impact, causing it to compress.

## 2. How does the mass of the falling object affect the compression of the spring?

The mass of the falling object does not affect the compression of the spring. The spring will compress the same amount regardless of the mass of the object, as long as the height of the fall remains constant.

## 3. What factors can affect the compression of a spring when an object falls on it?

The factors that can affect the compression of a spring when an object falls on it include the height of the fall, the stiffness of the spring, and any external forces acting on the object or the spring.

## 4. Is there a maximum height from which an object can fall before the spring cannot compress any further?

Yes, there is a maximum height from which an object can fall before the spring cannot compress any further. This is due to the spring reaching its maximum potential energy and not being able to absorb any more energy from the falling object.

## 5. How can the height of a falling object vs. compression of a spring be used in practical applications?

The relationship between the height of a falling object and the compression of a spring is often used in devices such as shock absorbers, pogo sticks, and trampolines. It can also be used in experiments to demonstrate the principles of potential and kinetic energy.

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