Why is the gravitational potential energy of ideal uniform massive spring mgx/2, not mgx?

Israel Hale 2022-07-23 Answered
Why is the gravitational potential energy of ideal uniform massive spring m g x / 2, not m g x?
L = T V = 1 2 m 3 x ˙ 2 + 1 2 M x ˙ 2 1 2 k x 2 m g x 2 M g x
where m g x / 2 refers to gravitational potential energy of ideal spring. But I do not get why it's m g x / 2 instead of m g x. What is the reason?
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Answers (2)

Kali Galloway
Answered 2022-07-24 Author has 16 answers
x is the extension of the spring. If you extend the spring by a distance x, keeping the other end fixed, its centre-of-mass moves by x 2
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Livia Cardenas
Answered 2022-07-25 Author has 5 answers
If the spring is stretching by an amount of x, its centre of mass is displaced by an amount of x / 2
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