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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 ?

- Thread starter bgq
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- #1

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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 ?

- #2

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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.

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 ?

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

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

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AlephZero

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When it is in equilibrium, F1 = F andIf it is at equilibrium so that F1 = F2 = F.

Forces are vector quantities, they have magnitude

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

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jbriggs444

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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,

Be sure to watch your sign conventions. If a spring is being

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.

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