What Is the Speed of a Block Launched by a Compressed Spring?

AI Thread Summary
A spring with a stiffness of 3500 N/m launches a 4 kg block from a compressed position of 0.2 m. The discussion revolves around calculating the block's speed when it reaches 1.3 m above its starting position, with participants clarifying the correct application of potential energy equations. Initial calculations yielded an unreasonably high speed, prompting a reevaluation of the signs and values used for displacement. After correcting the stretch and height values, a more realistic speed of approximately 2.366 m/s was determined. The importance of accurately defining the system and surrounding objects, as well as consistent sign usage, was emphasized throughout the conversation.
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Homework Statement


So we have a test this Friday over several topics in modern mechanics. Our professor gave us last year's test to use as a study guide, but hasn't posted the solutions yet. I'm not sure I'm doing this one right so I was hoping someone could check my work! I feel like my number is a bit big.



A spring whose stiffness is 3500 N/m is used to launch a 4 kg block straight up in the classroom. The
spring is initially compressed 0.2 m, and the block is initially at rest when it is released. When the block is 1.3
m above its starting position, what is its speed? Be sure to specify what objects are in your system and what
objects are in the surroundings. Show all your work, starting from fundamental principles and/or definitions

system: block, spring, gravity
surrounding: none

Us = Potential Energy of Spring
Ug = Potential Energy of Gravity
ks = spring stiffness
si & sf = stretch


Homework Equations



Ef = Ei + W

Usf + Ugf + Kf = Usi + Ugi + [STRIKE]Ki[/STRIKE] + [STRIKE]W[/STRIKE]

Kf = Usi - Usf + Ugi - Ugf

.5mvf2 = .5ks(si - sf)2 + mg(yi - yf)

vf2 = (ks(si - sf)2)/m + 2g(yi - yf)

vf = sqrt((ks(si - sf)2)/m + 2g(yi - yf))




The Attempt at a Solution



I might have messed up the stretch, I'm currently looking over it.

I got vf = 44.038 m/s
 
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Seems like you need to double check your s's and y's. Are these potential energies(Us and Ug) supposed to add or subtract? Did you use the correct signs for your s's and y's?
 
I used the quantity -.2 for both si and yi since the spring is compressed. I'm not sure what you are saying. Usf and Ugf should be subtracting.
 
I'm not saying what you did is wrong, but to make sure you are consistent with your signs. What values did you use for delta s and delta y?
 
delta s and delta y = -1.5

The stretch became +2.25 because it was squared

The thing is though that it is si-sf and yi-yf, so it is different I guess you could say.
 
Hmm, I think you can assume all the energy from the spring transfers into the object such that the spring stops decompressing at its equilibrium length. So delta s is just the distance it is compressed, and delta y is how high the block is from where it started.
 
Okay I see what you mean. After the spring is released, the block flies off the spring so Usf is actually just 0, right?

For that, I got Vf = 2.366 m/s which does sound much more realistic haha.
 
I think that's around the value I got as well (don't remember, but it's reasonable). Did you use (-)1.3 for delta y? If not, then your velocity is probably a little low.
 
No, I used -1.5, because when the block is at 1.3, it is 1.5m above the point it started from.
 
  • #10
The problem says clearly that is 1.3 m above the starting position. Not 1.5.
 
  • #11
Yeah you are right. Sorry I haven't slept in a while, so I'm kind of delusional.
 
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