Block dropped onto spring, how far is spring compressed?

[MikeMike]

block mass m dropped from height h onto spring with K how far does it compress?

what is the formula for this??

studying for final in 3 hours.

 

[KillerCharlie]

Conservation of energy... energy = constant = potential + spring energy = mgh + 0.5*K*x^2, where x is the distance it compresses.

Energy before dropping: mgh (all potential energy, no spring energy)
Energy after dropping: 0.5*kx^2

Energy before = energy after... mgh = 0.5kx^2

Therefore, x = sqrt( (mgh)/(0.5*K) )


There is one important assumption I'm making here though... that x is small compared to h. If this is not true, then that deflection x will cause additional loss in potential energy. If this is an introductory physics course, then I'm sure you can neglect this additional potential energy loss.

If not, x would be found as follows, assuming the top of the uncompressed spring is the datum (the reference line from which you measured h).

Energy before = mgh

Energy after = 0.5*kx^2 + -mgx

So mgh = 0.5*k*x^2 - mgx

Now you solve for x... which is a little messy

 

[MikeMike]

for some reason i know the answer (key) but its double the answer your formula is giving.

almost like they want the full amount the spring moves but do not specify this.

 

[Zim Hosein]

I wish you sat next to me in Physics KillerCharlie! 😱

 

[KillerCharlie]

Originally posted by: MIKEMIKE
for some reason i know the answer (key) but its double the answer your formula is giving.

almost like they want the full amount the spring moves but do not specify this.

What answer are they giving?

 

[MikeMike]

heres the numbers: m = .45kg h=.44m k=8N/m

they give 1.4m

 

[KillerCharlie]

hmmm, you're right... do they say where h is measured from?

 

[MikeMike]

h is .44m above the spring

 

[KillerCharlie]

😕

That's odd... I'm sure I'm doing this correctly. I haven't taken physics in 3 years but I've tutored students some semesters. Unless I did something wrong (since my brain shut off because I just finished finals, woohoo!), then I'd say their answer is incorrect.

 

[SupaDupaCheez]

wow....my head hurts just reading that!

Good luck on that final

 

[MikeMike]

Originally posted by: KillerCharlie
😕

That's odd... I'm sure I'm doing this correctly. I haven't taken physics in 3 years but I've tutored students some semesters. Unless I did something wrong (since my brain shut off because I just finished finals, woohoo!), then I'd say their answer is incorrect.

i think the part thats in parenthesis that says (The block moves back upwards) means assume upward movement as well.

 

[Ausm]

Depends what planet you are on 😉


Ausm

 

[Aznguy1872]

KillerCharlie is correct! Go with what he said.