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Energy changes of a stretched string

  1. Aug 11, 2015 #1
    1. The problem statement, all variables and given/known data
    image.jpg image.jpg

    This is the answer :


    For part d) of this question, I don't understand "stretching/extension reduces and velocity increases/height increases" .

    2. Relevant equations
    Hooke's Law: F=kx

    3. The attempt at a solution
    Ok, so if extension is reduce, then force reduces too. Then how does a decrease in force causes the velocity and height to increase? Does it have something to do with the principle of conservation of energy, where a gain in kinetic energy equals to a lose in gravitational potential energy?
  2. jcsd
  3. Aug 11, 2015 #2
    At a point lower than R , how does spring force compare to force of gravity ?
  4. Aug 11, 2015 #3
    Spring force is more than the force of gravity .
  5. Aug 11, 2015 #4
    So as long as mass is below R , acceleration is ( +ve or -ve ) ? And therefore velocity will always what ?
  6. Aug 11, 2015 #5
    Positive..? I'm not sure.. Therefore, velocity will increase?
  7. Aug 11, 2015 #6
    Yes . ( kx - mg = ma ) , kx > mg .

    Now , a = dv/dt . As a is always positive till before R , dv is always +ve , and hence velocity will increase till R .

    Hope this helps .
  8. Aug 11, 2015 #7
    But how do you know that a is always +ve till before R? And why height increases? Does it got to do with 1/2 mv^2=mgh (gain in kinetic energy=lost in gravitational potential energy) ? And thanks by the way. :)
  9. Aug 11, 2015 #8
    I thought we agreed that -
    It rises because acceleration is upwards . And that's pretty much the only reason .
  10. Aug 11, 2015 #9
    Yeah, I agreed to that one. But the mark scheme also states that the height increases as well. Why?
  11. Aug 12, 2015 #10
  12. Aug 13, 2015 #11
    OK thanks
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