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Spring Problem with Possible Conservation of Energy Concept ?

  1. May 12, 2013 #1
    1. The problem statement, all variables and given/known data
    A block slides from rest down a frictionless ramp which is 4 m long and has a 30 degree angle with respect to the ground. After reaching the bottom of the ramp it slides on a frictionless surface and compresses a spring a distance of 12cm (.12m) before coming to rest momentarily.

    a) What is the speed of the block before striking the spring?
    b) What is the spring constant?


    3. The attempt at a solution

    I wanted to see if I was on the right track....my logic is to use conservation of energy. Setting my initial condition as the block sliding down the ramp and my final condition when it comes to rest after compressing the spring.....So the sum of my initial energy would by equal to the kinetic energy and the sum of my final energy is equal to the potential energy --> 1/2mv2 = mgh

    Solving for v you get v = √(2gh)....I was thinking the "h" is the height of the ramp which can be found using the angle....I got 2m for that. So using 9.8 m/s2 for g and plugging the rest into my equation I got a velocity of 6.2 m/s

    To find the spring constant I figured you could use F = -kx and solve for F. With a free body diagram the only force acting on the block is gravity but without a mass, I don't know how to find the quantity of that force....

    Please help with part b!! And does the work for part a seem correct?? Really appreciate it, I have my final tomorrow and want to be sure I can do these problems correctly!
     
  2. jcsd
  3. May 12, 2013 #2

    rude man

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    Part a good, paret b bad.
    Use energy conservation here too. The spring is compressed, the kinetic energy is changed to spring potential energy.
     
  4. May 12, 2013 #3
    Ok, won't I still need a mass??
    1/2mv2 = 1/2kx2

    Or did I set that up wrong..
     
  5. May 12, 2013 #4

    rude man

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    I believe you're right! You need m for part b.
     
  6. May 12, 2013 #5
    Ok. I'll keep thinking about it. I'm going to see if maybe I need to work in the work-energy theory....maybe I need two equations that can substitute into each other to solve for k
     
  7. May 12, 2013 #6
    no but on compression of the spring another 12cm X cos(angle) has been traveled by the block so you need to put in another energy conservation
     
  8. May 12, 2013 #7
    I'm still not getting it :( Any other hints anyone can give?
     
  9. May 12, 2013 #8

    Dick

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    If they don't give you a mass then you'll have to solve for the spring constant k in terms of the mass m.
     
  10. May 12, 2013 #9
    Got it, thanks for everyone's help. I understand the concepts so I should be good
     
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