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Caculating the decline angle of a swing

  1. Oct 28, 2009 #1
    1. The problem statement, all variables and given/known data

    The seat of a child’s swing with a mass of 6 kg hangs on lightweight strings that are
    2.5 m long. A dog with mass of 3 kg sleeps on the swing’s seat. The dog jumps from the swing with velocity of 2 m/s in a horizontal direction.
    - How much is the maximum angle of decline when the dog jumps from the seat?

    2. Relevant equations

    G= mv
    W(kinetic)= ½ mv²
    W(gravitational)= mgh

    3. The attempt at a solution

    According to arithmetic:
    cosθ= (l-h) / l → 1- (h/l)

    W(kinetic)= W(gravitational)
    ½ mv²= mgh → h= v² / 2g

    Substitution:
    cosθ= 1- (h/l) = 1- (v² / 2gl)

    Because we have one system, the gravitational force of the dog should equal gravitational force of the swing, I hope this is correct:
    m(dog)*v(dog)= m(seat)*v(seat) → v(seat)= m(dog)*v(dog) / m(seat)

    Another substitution:
    cosθ= 1- (m(dog)²*v(dog)² / 2m(swing)²*gl)
    θ= 11.6º
     
  2. jcsd
  3. Oct 28, 2009 #2

    Delphi51

    User Avatar
    Homework Helper

    I got the same answer, similar method.
     
  4. Oct 28, 2009 #3
    Thank you for revising and helping!
     
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