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Conservation of energy problem! child slides down at angle? check my asnwers?

  1. Oct 21, 2012 #1
    A child whose weight is 267 N slides down a 6.10 m playground slide that makes an angle of 20.0° with the horizontal. The coefficient of kinetic friction between slide and child is 0.10.

    (a) How much energy is transferred to thermal energy?

    (b) If she starts at the top with a speed of 0.534 m/s, what is her speed at the bottom?

    my attempt:

    a)267sin30° - 0.1 x 267 cos 20° = 108.410 J

    b) ƩW = 1/2m(v final)^(2) - 1/2m(v initial)^(2)

    108.410 J = 1/2m(v final)^(2) - 2.845J

    111.255 = 1/2m(v final)^(2)

    .....v final = 2.858 m/s

    The answers are
    a) 153 J
    b) 5.45 m/s

    im not sure what I am doing wrong. can someone please help?

    thanks!

    EDIT:

    I figure out what i did wrong for part a.

    the answer is just mu n
    0.1x267cos(20)x6.1 = 153.047

    I still dont understand part b!? help please!
     
    Last edited: Oct 21, 2012
  2. jcsd
  3. Oct 21, 2012 #2
    You didn't factor in the change in potential energy.
     
  4. Oct 21, 2012 #3
    im not sure what you mean. do u mind showing me the steps?
     
  5. Oct 21, 2012 #4
    The child slides down the slide. That means her height decreased by some amount. She's under the influence of gravity, so she lost some potential energy. The work by friction becomes W=ΔKE+ΔPE.
     
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