Maximum mechanical energy in the spring-block system

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  • #26
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These two terms together represent the difference in total energy in the lab frame and the total energy in the moving frame.
I understand it now by backward reasoning ,since I know the expression for total energy in lab frame and moving frame . But what if I had approached with this method first .

How do we write total energy in the lab frame ?

Total energy in lab frame = Total energy in moving frame + ???
 
  • #27
TSny
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From an earlier post you had ##E(t) = \frac{1}{2}m(v+v')^2 + \frac{1}{2}kx^2##. In another post, you have expressions for ##x## and ##v'## as functions of time. So, you should be able to get ##E(t)## as an explicit function of time.
 
  • #28
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:sorry:

I was thinking that in post#13 you were giving an alternative way of approaching the problem . But now I realize that the edited part was an alternate/faster way to analyze the expression for the total energy .

Right ?
 
  • #29
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.
 
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  • #30
TSny
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:sorry:

I was thinking that in post#13 you were giving an alternative way of approaching the problem . But now I realize that the edited part was an alternate/faster way to analyze the expression for the total energy .

Right ?
Yes. The first way was to get E(t) explicitly as a function of time. The second was to express E in terms of v and v' and get the answer by inspection.
 
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  • #31
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One last question , am I right in concluding that during the course of motion the work done by external agent pulling the free end would be both positive and negative ? Alternate positive and negative work would be done by the agent .

??
 
  • #32
TSny
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One last question , am I right in concluding that during the course of motion the work done by external agent pulling the freed end would be both positive and negative ? Alternate positive and negative work would be done by the agent .

??
Yes, there are times when the pulling force is doing positive work and times when it is doing negative work. The total work done (starting at t = 0) varies between 0 and 2mv2 over and over again. So, the total work done since the start is never negative.
 
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  • #33
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Thank you very much Sir :smile: .
 

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