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Frequently Made Errors in Mechanics - Springs

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In summary, haruspex submitted a new PF Insights post titled "Frequently Made Errors in Mechanics - Springs." The post discusses common mistakes that students make when working with springs, including the incorrect assumption that the tension in one spring will be the same as the tension in another spring connected in series. The post also mentions the benefits of identifying and correcting these errors in improving one's own understanding of the material. Additionally, there is a small typo in the post that is pointed out by another commenter.

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Frequently Made Errors in Mechanics - Springs

Continue reading the Original PF Insights Post.

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QuantumCurt

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Merlin3189

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I think it should beAttempted answer:

When the tension in the first spring is T, the tension in the second spring will also be T.

The two extensions will be ##\frac{T}{k_1} and \frac{T}{k_2}##

Total extension ## = T(\frac{1}{k_1}+\frac{1}{k_2})##

X Total tension = 2T

Overall spring constant ## = \frac{2T}{T(\frac{T}{1}k_1+\frac{1}{k_2})}=\frac{2k_1k_2}{k_1+k_2}##

Overall spring constant ## = \frac{2T}{T(\frac{1}{k_1}+\frac{1}{k_2})}=\frac{2k_1k_2}{k_1+k_2}##

Reference https://www.physicsforums.com/insights/frequently-made-errors-mechanics-springs/

The most common errors made in mechanics when dealing with springs include miscalculating the spring constant, neglecting the effects of friction, ignoring the mass of the spring itself, failing to consider the non-linear behavior of springs under large forces, and not taking into account the energy lost to heat due to internal friction.

The spring constant is a crucial factor in determining the behavior of a spring in a mechanical system. An inaccurate calculation can lead to incorrect predictions and results in the system, potentially causing the system to fail or operate inefficiently. Therefore, it is essential to accurately calculate the spring constant to ensure the system's proper functioning.

One way to minimize the effects of friction on a spring is to use lubricants to reduce the coefficient of friction between the spring and other surfaces. Another way is to design the system in a way that reduces the contact points between the spring and other components. Additionally, using materials with lower coefficients of friction or incorporating bearings can also help minimize the effects of friction on a spring.

To account for the non-linear behavior of springs under large forces, it is necessary to use more advanced mathematical models, such as the Hooke's Law for non-linear springs. Additionally, conducting experiments and gathering data on the spring's behavior under different forces can also help in accurately predicting its behavior in real-world scenarios.

Internal friction in springs causes energy to be lost in the form of heat, which can significantly affect the performance of a mechanical system. Ignoring this energy loss can lead to inaccuracies in calculations and predictions, potentially causing the system to fail. Therefore, it is crucial to take into account the energy lost to heat when dealing with springs in mechanics.

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