# Why mass of spring/string assumed negligible?

• cyt91
In summary, the mass of a spring/string/rope is often assumed to be insignificant when calculating tension. This is because if the spring/string/rope is massless, the tension will be uniform throughout, making the problem easier to solve. However, if the string does have mass, it will also have an acceleration and the F=Ma equation will need to be used. This can make the problem more complicated, potentially resulting in differential equations that are difficult to solve or can only be solved numerically with a computer.
cyt91
In most questions I have encountered involving the calculation of tension in spring/string/rope, we are often asked to assume that the mass of the spring/string/rope to be insignificant. Why is this so? What effect does the mass of the spring/string/rope has on the tension of the spring/string/rope? I checked a few A-level books,none offered any satisfactory explanation.

If the spring/string/rope is massless, then the tension is uniform throughout. (Otherwise, problems become too complicated.)

Also, if the string had mass then it would also have an acceleration when it is connected to a system. You would then be needed to write the F=Ma equation for the string also.

If you don't mind me asking, just how complicated things can be?

I think you'd get a differential equation that either:

1. is much more difficult to solve, or
2. can only be solved numerically (in current practice, with a computer)

With massless springs, it's just sines and cosines.

## 1. Why is the mass of a spring or string assumed to be negligible in physics experiments?

The mass of a spring or string is assumed to be negligible in physics experiments because it is much smaller compared to other objects or masses involved in the experiment. This allows us to simplify calculations and focus on the effects of other forces and masses without being significantly impacted by the mass of the spring or string.

## 2. How is the negligible mass of a spring or string justified in physics equations?

In physics equations, the mass of a spring or string is often represented by the letter "m". However, this "m" is commonly assigned a value of 0, as the mass is considered negligible compared to other masses involved in the experiment. This simplification helps in solving equations and making predictions.

## 3. Can the mass of a spring or string ever be significant in a physics experiment?

In some cases, the mass of a spring or string may not be considered negligible. This can happen when the mass of the spring or string is comparable to the masses of other objects involved in the experiment. In such cases, the mass of the spring or string must be taken into account in calculations and equations.

## 4. How does the negligible mass of a spring or string affect the accuracy of an experiment?

Assuming the mass of a spring or string is negligible may slightly affect the accuracy of an experiment. However, this effect is often considered to be minimal and can be accounted for in the overall margin of error of the experiment. In most cases, assuming the mass is negligible does not significantly impact the results or conclusions drawn from the experiment.

## 5. Are there any exceptions to assuming the mass of a spring or string is negligible?

Yes, there are some exceptions to assuming the mass of a spring or string is negligible. In certain experiments, such as those involving very small masses or high precision measurements, the mass of a spring or string may need to be taken into account. Additionally, in experiments involving elastic collisions, the mass of the spring or string may play a significant role and cannot be assumed to be negligible.

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