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Minimum compression of a spring.

  1. May 27, 2009 #1
    A toy car with mass 0.043 kg is propelled by a spring with spring constant 92 N/m onto a track. The track contains a vertical loop of radius 0.15 m. Ignore any losses due to friction and use g = 10 m/s2. What is the minimum compression of the spring necessary for the car to complete the loop without leaving the track?

    acceleration = velocity^2/radius= 10(0.15)= velocity^2
    so v^2= 1.5

    Then I use V to get KE = 1/2mv^2
    KE= 1/2(0.043)(1.5)
    KE= 0.03225

    Add PE to the top of the loop PE = mgh
    PE= (0.043)(10)(0.3)
    PE=.0129

    so then the Total E = PE + KE

    TE = 1/2k x^2
    PE+ KE= 1/2k x^2
    .0129+ 0.03225= 1/2 (92) x^2
    0.16125= 1/2 (92) x^2
    0.3225 = 92x^2
    0.003505 = x^2
    x = minimum compression = 0.0592

    Did i do everything correctly or is there a mistake somewhere?
     
  2. jcsd
  3. May 27, 2009 #2

    PhanthomJay

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    Correct that simple math error and everything else looks OK.
     
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