Why is the energy stored in a spring proportional to 1/2 * distance * force?

In summary, the energy stored in a spring is equal to 1/2 * distance * maximum-force, which is different from the formula for work, force * distance. This is because the force is not constant and varies as the spring is compressed. An approximate answer can be obtained by analyzing the situation in small steps, but an exact answer requires calculus and integrating the instantaneous force over incremental distance.
  • #1
GeneralOJB
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Why is the energy stored in a spring 1/2 * distance * force? Isn't work just force * distance?
 
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  • #2
GeneralOJB said:
Why is the energy stored in a spring 1/2 * distance * force? Isn't work just force * distance?

The full force is not applied for the full distance.

In the simple case of a constant force over a fixed distance you can just multiply force by distance. But in the case of a spring being compressed, the force is not constant.

You could approximate the answer by analyzing the situation in small steps... You compress the spring the first 1/10th of the distance using 1/10th of the full force, the next 1/10th of the instance using 2/10th of the total force and so on. This approach would give you an answer that is pretty close.

An exact answer can be obtained by using calculus and integrating instantaneous force over incremental distance. That answer turns out to be 1/2 * distance * maximum-force
 
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  • #3
Thanks, I understand now.
 

FAQ: Why is the energy stored in a spring proportional to 1/2 * distance * force?

What is the definition of energy stored in a spring?

Energy stored in a spring is the potential energy that is stored in a compressed or stretched spring. This energy is stored due to the elastic potential energy of the spring, which is a result of the deformation of its shape.

How is the energy stored in a spring calculated?

The energy stored in a spring can be calculated using the formula: E = 1/2 * k * x^2, where E is the energy stored, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

What factors affect the amount of energy stored in a spring?

The amount of energy stored in a spring is affected by the spring constant, the displacement of the spring from its equilibrium position, and the mass of the object attached to the spring.

What happens to the energy stored in a spring when the spring is stretched or compressed?

When the spring is stretched or compressed, the energy stored in the spring increases. This is because the potential energy is directly proportional to the displacement of the spring.

How is energy stored in a spring used in everyday life?

Energy stored in a spring is used in everyday life in various applications, such as in clocks, toys, and mechanical devices. It is also used in industries to store and release energy in machines and equipment.

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