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Old Oct 7th 2017, 06:43 PM   #1
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Spring slowly lowered vs falling

An object is attached to a vertical spring and slowly lowered to its equilibrium position, this stretches the spring a distance d. If the same object was permitted to fall instead through what maximum distance does the spring stretch?

Right now I am thinking it is mg = kd so d=mg/k
However, I am not sure. Any help is appreciated.

Last edited by alex34; Oct 8th 2017 at 12:32 PM.
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Old Oct 8th 2017, 06:52 AM   #2
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If the object is "slowly lowered" then the greatest extension of the spring is where the spring force, at that extension, is equal to the weight of the force. If the object is dropped then the spring must overcome the kinetic energy of the object as well.
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Old Oct 8th 2017, 09:14 AM   #3
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So for it being slowly lowered would my equation then be, mg = (spring force)(distance) ? mg would serve as the weight of the force.

And for the object being dropped my equation would be (1/2)mv^2=(spring force)(distance) ?

Thanks again.
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Old Oct 8th 2017, 11:04 AM   #4
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An object is attached to a vertical spring and slowly lowered to its equilibrium position, this stretches the spring a distance d. If the same object was permitted to fall instead through what minimum distance does the spring stretch?
sure that's not maximum distance?


let $y=0$ be the position of maximum spring stretch after the mass is dropped (see attached sketch) ...

initial gravitational potential energy = full stretch elastic potential energy

$mg(d+y) = \dfrac{1}{2}k(d+y)^2$

since $(d+y) > 0$ ...

$mg = \dfrac{1}{2}k(d+y)$

$2mg = k(d+y)$

$\dfrac{2mg}{k} = d+y$

since $kd = mg$ ...

$\dfrac{2kd}{k} = d+y \implies d+y = 2d$

... maximum stretch when dropped will be a distance $2d$
Attached Thumbnails
Spring slowly lowered vs falling-spring_prob.jpg  
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Old Oct 8th 2017, 12:31 PM   #5
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Yes my apologies I meant maximum distance. Thank you so much for breaking it down for me!
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Old Oct 8th 2017, 02:29 PM   #6
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Alex34 - spring falls

Hi Alex34,

This problem might be of interest.

Rock Falls on a Spring| THERMO Spoken Here!

Good Luck... TSH
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