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Spring and object on ramp

  1. Oct 14, 2013 #1
    I figured out where I was going wrong, it was in the trig for getting the force down the ramp. mgsinθ, not mg/sinθ, although I still got the right answer for the last part using mg/sinθ.

    [STRIKE]1. The problem statement, all variables and given/known data

    A spring is set to move along the surface of a frictionless ramp, which is tilted at an angle θ = 60 degrees away from horizontal. A rock of mass M = 5 kg is placed on a spring. As a result, the spring compresses, coming to rest a distance x = 3.875 cm along the ramp away from its original position.

    What is the spring's force constant?

    The rock is pushed down along the ramp an additional distance y = 29 cm. What is the spring's potential energy now?

    The rock is now released, so that the spring flings it up along the ramp. The spring and rock lose contact when the rock reaches the spring's rest length. How far along the ramp beyond this release point does the rock slide? (You may assume that the ramp is large enough that the rock never reaches its top end).

    The set-up looked like this.

    2. Relevant equations

    F=-k/x
    SPE=(1/2)kx2
    KE=(1/2)mv2
    v2=vi2+2ax

    3. The attempt at a solution

    What is the spring's force constant?
    x=0.03875m
    Fg=(mg)/sinθ
    k=((mg)/sinθ)/x=((5kg*9.8m/s2)/sin60°)/0.03875m≈1460 N/m
    The program marked this wrong

    What is the spring's potential energy now?
    x=0.03875m+0.29m=0.32875m
    SPE=(1/2)kx2=(1/2)(1460N/m)(0.32875m)2≈78.9 J
    The program also marked this wrong.

    How far along the ramp beyond this release point does the rock slide?
    v2=2*KE/m=2*78.9 J/5kg≈31.56(m/s)2
    x=v2/(2(g/sinθ))=31.56(m/s)2/(2(9.8m/s2/sin60°))≈1.395m
    The program marked this correct.

    Based on that I'm thinking that either the professor put in the incorrect answers for the first two, or I did something wrong that managed to sort itself out by the last question.[/STRIKE]
     
    Last edited: Oct 14, 2013
  2. jcsd
  3. Oct 14, 2013 #2
    Check ##F_{g_{x}}##. you calculated it wrong.

    $$F_{g_{x}}=-m.g.Sin(θ)$$

    Edit: I guess you just figured it out!!!!!
     
  4. Oct 14, 2013 #3

    D H

    User Avatar
    Staff Emeritus
    Science Advisor

    Yep. You made the same mistake twice, and that resulted in the mistake canceling itself out. Every once in a while two wrongs *do* make aright. Don't count in it, however. Two wrongs more often than not compound the problem rather than canceling it out.
     
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