Simple Harmonic Motion of a gun

AI Thread Summary
To determine the speed of a ball leaving a toy popgun, the spring constant (k) was calculated as 416 N/m using the force required to compress the spring. The potential energy stored in the spring was identified using the formula PE = 1/2 kx^2, where x is the compression distance. This potential energy is converted into kinetic energy, allowing the use of KE = 1/2 mv^2 to find the ball's velocity. The initial confusion regarding the role of the 75 N force was clarified, emphasizing its use solely for calculating k. The discussion highlights the importance of understanding energy conversion in this context.
peaches1221
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(1)It takes a force of 75 N to compress the spring of a toy popgun 0.18 m to "load" a 0.14 kg ball. With what speed will the ball leave the gun?

I used the equation F=kx
I solved for K and I got 416 N/m

Then I used the equation omega = square root(K/M)
I solved for omega and i got 54.5.

Is this correct? It seems wrong to me. Please help, any suggestions will be greatly appreciated.
 
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Hint: This is not a S.H.M. problem.
f= -k*x
k>> 416 N/m
This is not necessary.
 
The spring energy is converted into kinetic energy. Do you know what the spring energy is now that you know K? Can you figure out the velocity with this?
 
Thank you both for your help. I'm still not sure if I completely understand this problem

PE= 1/2kx^2
where I know k because it is 416 N/M and X=.18. so I would solve for the PE.

Then you're saying if the spring energy is converted to kinetic energy, then is KE=PE?
thus KE= 1/2mv^2 and then I would have to solve for v?

But I still don't think this is right because where is the 75N coming in?
 
You used it to find K, did you not?
 
Yeah, I'm an idiot. Thanks for your help.
 

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