# Spring stretched at both ends

• bgq
In summary, when determining the elongation or compression of a spring that is accelerating, you must take the average of the tension or compression forces at the two ends and use that value to calculate the displacement of the spring. This can be done by considering the spring as a series of smaller springs and adding up the displacements from each individual force. It is important to watch for sign conventions and make sure to use the correct formula for calculating tension or compression.

#### bgq

Hi,

Consider a spring of stiffness k and mass m. If we stretch - simultaneously - both ends of the spring by force F1 and F2. What will be the elongation of the spring? Can I add the forces and say that
x = (F1 + F2)/k ?

bgq said:
Hi,

Consider a spring of stiffness k and mass m. If we stretch - simultaneously - both ends of the spring by force F1 and F2. What will be the elongation of the spring? Can I add the forces and say that
x = (F1 + F2)/k ?

No, you can't add the forces. If the forces are unequal, the spring itself will start to accelarate in the direction of the largest force. F = ma applies here, where F is the net force.

To stretch a spring, you always have to exert a force on both sides. Even if you tie the spring to an unmoveable object, the object will still exert the same force on one side of the spring, as the force on the other side, because the spring now can't move, so the net force on it has to be 0

willem2 said:
No, you can't add the forces. If the forces are unequal, the spring itself will start to accelarate in the direction of the largest force. F = ma applies here, where F is the net force.

To stretch a spring, you always have to exert a force on both sides. Even if you tie the spring to an unmoveable object, the object will still exert the same force on one side of the spring, as the force on the other side, because the spring now can't move, so the net force on it has to be 0

If it is at equilibrium so that F1 = F2 = F. Is elongation x = F/k or x = 2F/k?

bgq said:
If it is at equilibrium so that F1 = F2 = F.

When it is in equilibrium, F1 = F and F2 = -F.

Forces are vector quantities, they have magnitude and direction.

Is elongation x = F/k or x = 2F/k?

x = F/k. Adding two forces of magnitude "F" that act in different directions, to get "2F", is meaningless.

• 1 person
The spring may be compressed or elongated even if it is accelerating. My question is how to find the elongation or compression is such a situation.

bgq said:
The spring may be compressed or elongated even if it is accelerating. My question is how to find the elongation or compression is such a situation.

Take the average of the tension (or compression) force at the two ends and compute the amount of elongation or compression based on that.

For instance, consider a spring hanging from one end. The tension at the one end is mg. The tension at the other end is zero. So, on average the tension across the length of the spring is mg/2.

Be sure to watch your sign conventions. If a spring is being pushed from the back with a force of 10 Newtons and pulled from the front with a force of 20 Newtons, that's 20 minus 10 all divided by 2 for an average tension of 5 Newtons.

You can derive this result by treating the original spring as a bunch of smaller springs connected end-to-end and then adding up the displacements that result from the tension or compression experienced by each of the smaller springs.

• 1 person

## What is a spring stretched at both ends?

A spring stretched at both ends is a type of spring where both ends are fixed or attached to a solid object, creating tension and causing the spring to resist force or pressure applied to it.

## What is the purpose of a spring stretched at both ends?

The purpose of a spring stretched at both ends is to store and release energy. When a force is applied to the spring, it compresses or stretches, and when the force is released, the spring returns to its original shape, releasing the energy it stored.

## How does a spring stretched at both ends work?

A spring stretched at both ends works by converting potential energy into kinetic energy. When the spring is stretched, it stores potential energy in the form of elastic potential energy. When the force is released, the stored energy is converted into kinetic energy, causing the spring to return to its original shape.

## What materials are used to make a spring stretched at both ends?

A spring stretched at both ends can be made from various materials such as steel, plastic, rubber, or even natural materials like animal tendons. The type of material used depends on the specific application and the desired properties of the spring.

## What are some common uses of a spring stretched at both ends?

A spring stretched at both ends has a wide range of applications, including in mechanical devices such as door hinges, car suspension systems, and mattresses. They are also used in toys, clocks, and other household items that require tension or resistance to force.