# Compression in Accelerating Springs.

• jimmyw
In summary: Additionally, the compression of the spring is half as much as before because the force is only applied to one end rather than both ends. This is different from the situation described in the post where the compression remains the same because the force is applied to both ends simultaneously. This may be due to a mistake in the calculation or a different setup of the system.
jimmyw
Suppose I have two masses with mass $$M$$ each connected together by a spring with spring constant $$k$$ like this:
[PLAIN]http://img827.imageshack.us/img827/4896/springs1.png

Then I apply a force of $$F$$ at both ends:
[PLAIN]http://img833.imageshack.us/img833/2562/spring2.png

Then using Hooke's law $$F=kx$$, the compression of the spring $$x$$ would be given by:
$$x=F/k$$

So now if I apply the same force $$F$$ just to the right end like this:
[PLAIN]http://img810.imageshack.us/img810/4236/spring3.png

The acceleration of the system is given by Newton's 2nd Law $$F=ma$$
$$F=2Ma$$
$$a=\frac{F}{2M}$$

And the acceleration of the mass on the left is the same as the entire system so the force is:
$$F_{left mass}=Ma$$
$$F_{left mass}=M\frac{F}{2M}$$
$$F_{left mass}=\frac{F}{2}$$

This force must be supplied by the spring so using hookes law:
$$\frac{F}{2}=kx$$
$$x=\frac{F}{2k}$$

This value is half as much as before.

Here is where I'm confused can anyone explain the difference between this and the situation described in this post http://scienceblogs.com/dotphysics/2008/10/fake-vs-real-forces/" where it is said the compression is "the compression is EXACTLY the same before"

What mistakes have I made?

Last edited by a moderator:
jimmyw;2902875 And the acceleration of the mass on the left is the same as the entire system so the force is: [/QUOTE said:
I am not sure ... but its wrong i believe because when you push the mass on right .. the mass on left doesn't have same acceleration until the string can't compress anymore.

Still i would prefer someone more of an expert to justify this.

I'm not worried about that statement.

After the spring has compressed, the acceleration of the mass on the left is the same as the entire system

## 1. What causes compression in accelerating springs?

The compression in accelerating springs is caused by the force applied to the spring, which causes it to compress and store potential energy.

## 2. How does the compression of a spring change with acceleration?

The compression of a spring increases with acceleration, as the force applied to the spring increases, causing it to compress further and store more potential energy.

## 3. What is the relationship between compression and acceleration in springs?

The relationship between compression and acceleration in springs is directly proportional. This means that as acceleration increases, the compression of the spring also increases.

## 4. How does the stiffness of a spring affect its compression during acceleration?

The stiffness of a spring affects its compression during acceleration by determining how much force is required to compress the spring. A stiffer spring will require more force to compress, resulting in less compression compared to a less stiff spring with the same applied force.

## 5. Can the compression of a spring affect its acceleration?

No, the compression of a spring does not directly affect its acceleration. The acceleration of a spring is determined by the force applied to it, not the compression. However, the compression can indirectly affect the acceleration by changing the potential energy stored in the spring, which can then be converted into kinetic energy to accelerate an object attached to the spring.

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