Calculate Velocity of 3.15 kg Ball Released from Compressed 1.96 m Spring

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The discussion revolves around calculating the velocity of a 3.15 kg ball released from a compressed spring, with the spring's force described by the equation F = 153x + 12.7x^3. After integrating the force over the compression distance, a value of 341 is obtained, which represents the work done on the ball. This work can be equated to the kinetic energy of the ball using the formula W = 1/2 mv^2. The participants clarify that the units of the work done are indeed consistent with energy, confirming that 341 represents the energy transferred to the ball. The final step involves using the work-energy principle to solve for the ball's velocity.
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The force required to compress an imperfect horizontal spring an amount x is given by F = 153x + 12.7x3 , where x is in meters and F in Newtons. If the spring is compressed 1.96 m, what speed will it give to a 3.15 kg ball held against it and then released?

I know that I will need to take the integral from x=0 to x=1.95, which gives me 341. How do I now get the velocity from this? Any suggestions?
 
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What physical interpretation has "341"?
What are it's units, in particular: can it be seen as some form of energy?
 
I would believe it to be the Force as that is what the function is.
 
strugglin-physics said:
I would believe it to be the Force as that is what the function is.
Force*meter=Force??
Think again..
 
Oh duh that is the Work! So I use W=1/2mv^2!

Thanks for the help!
 

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