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30,000 fleas jumping off an elephant

  1. Mar 31, 2014 #1
    1. The problem statement, all variables and given/known data

    A flea infested elephant with a mass of 3500 kg is standing on a frozen lake wearing frictionless ice skates. If 30000 fast fleas jump off the elephants back (in a horizontal direction) per second, and each flea jumps with a velocity of 10 m/s find the velocity of the elephant using conservation of momentum. Each flea has a mass of 10 milligrams

    2. Relevant equations

    v2 = 2m1/(m1+m2)

    3. The attempt at a solution

    I converted 10 milligrams to kg and multiplied by 30,000 and got .3 kg. I imagined this as an elastic collision of a .3 kg object hitting the elephant at 10 m/s. So, solving for the elephants final velocity.

    v2 = 2(.3)/ (3500+.3)
    v2 = .6/(3500.3)
    v2 = 1.7 x 10^(-4) m/s


    is this correct?
     
  2. jcsd
  3. Mar 31, 2014 #2

    Simon Bridge

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    Keep that up for an hour or so, and the elephant has lost it's entire weight in fleas!

    I don't see the reasoning.
    Your first line seems to suggest that the elephant and a whole seconds worth of fleas are moving at speed v2 as a result of one seconds worth of fleas jumping off at speed 2 units.

    Notice that we are not told how many fleas are infesting the elephant, so you'll need to make an approximation.
    Also - why wouldn't the elephant accelerate?
     
  4. Mar 31, 2014 #3
    ignore how many fleas are infesting the elephant. for this problem we're supposed to assume it is infested with 30,000 fleas and they all jump off the elephant in the same horizontal direction with the same speed and at the same time
     
  5. Mar 31, 2014 #4

    Simon Bridge

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    OK - so what about the reasoning behind your calculation?
    Your first line seems to suggest that the elephant and 30000 fleas are moving at speed v2 as a result of 30000 fleas jumping off at speed 2 units.
     
  6. Apr 1, 2014 #5
    No, the elephant is stationary. the fleas are moving at speed v1 and I'm trying to solve for the final speed of the elephant, v2
     
  7. Apr 1, 2014 #6

    Simon Bridge

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    You gave me:
    v1=10m/s (speed of fleas)
    m=0.3kg (mass of 30000 fleas)
    M=3500kg (mass of elephant)

    Then you wrote: v2 = 2(.3)/ (3500+.3)

    so v2= 2m/(M+m) or (M+m)v2=2m ... the dimensions don't match.

    But why would you try that in the first place?
    What was your reasoning? I won't be able to help you very well if I don't know how you think.

    When you do conservation problems, you follow a pattern.
    This is conservation of momentum: so ...
    Do you know the equation for the momentum of something?
    Do you know the expression for conservation of momentum?

    Before the fleas jump off, what is the net momentum of elephant + fleas?

    After the fleas jump off, the elephant and fleas move in opposite directions ... write expressions for the momentum of the elephant and the momentum of the fleas ... and thus, the net momentum.

    From conservation of momentum, write down an expression which relates the momentum before to the momentum after.

    Solve for v2.
     
    Last edited: Apr 1, 2014
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