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Conservation of Energy on a frictionless incline

  1. Nov 9, 2016 #1
    1. The problem statement, all variables and given/known data
    A 259 g textbook slides up a 22.1° incline that is 2.55 m long. Using conservation of energy and assuming the incline is frictionless, what minimum initial speed is needed to accomplish this?
    mass = 0.259 kg
    Θ = 22.1°
    length of incline = 2.55 m
    2. Relevant equations
    KE = (1/2)*mv2
    PE = mgh

    3. The attempt at a solution
    I solved for height of the incline/ramp using trigonometry where the height is opposite to the angle and the length of the ramp is the hypotenuse:
    h = 2.55*sin(21.5°) = 0.934

    Since the incline is frictionless the kinetic energy at the beginning is equal to the potential energy of when the textbook reaches the top of the ramp:
    KE = PE
    (1/2)*mv2 = mgh
    Isolating for the velocity, the masses cancel out
    v = √2gh
    v = √(2*9.8*0.934)
    = 4.27 m/s

    So I got 4.27 m/s as initial velocity but it doesn't match with any of the answers which are either 4.34 m/s, 7.07 m/s, 3.07 m/s or 6.80 m/s.

    So I was wondering what I did wrong. Was the velocity I was solving for not initial velocity or was the approach completely wrong? or Did I just make some miscalculations that made it not equal to the first answer?
     
  2. jcsd
  3. Nov 9, 2016 #2

    haruspex

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    Notice anything?
     
  4. Nov 9, 2016 #3
    ****, ok I'm very unintelligent, for some reason in my calculations I'm using 21.5 as my degrees I don't know why, thank you for pointing out my obvious mistake though lol.
    Edit: I got right answer thank you lol.
     
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