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

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Homework Help Overview

The problem involves calculating the velocity of a 3.15 kg ball released from a compressed spring, with a specific force function provided for the spring. The spring is compressed by 1.96 m, and participants are exploring the relationship between the work done on the ball and its resulting speed.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the integral of the force function to determine the work done on the ball. Questions arise regarding the interpretation of the calculated value of 341 and its units, with some suggesting it may represent energy.

Discussion Status

The discussion is active, with participants questioning the meaning of the calculated value and its relation to physical concepts such as work and energy. Some guidance has been offered regarding the interpretation of work and its connection to the velocity of the ball.

Contextual Notes

There is a focus on understanding the implications of the force function and the calculations involved, with participants reflecting on the definitions and relationships between force, work, and energy in the context of the problem.

strugglin-physics
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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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