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Simple what is velocity at time t problem

  1. Sep 10, 2012 #1
    Simple "what is velocity at time t" problem

    1. The problem statement, all variables and given/known data

    A helicopter is lifting off. The only forces are air (up) and gravity. What is the vertical speed at time t if it took off at time t=0?

    2. Relevant equations

    g = F(air)/m, g=Δv/Δt

    3. The attempt at a solution

    F(air)/m = Δv/Δt

    v = tF(air)/m, but I'm told that this is wrong. I believe I need to include g. What am I missing?
     
  2. jcsd
  3. Sep 10, 2012 #2

    Simon Bridge

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    Re: Simple "what is velocity at time t" problem

    Draw a free-body diagram for the helecopter.
    The sum of the forces is mass times acceleration... acceleration of the helecopter is not going to be g.
     
  4. Sep 10, 2012 #3

    Andrew Mason

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    Re: Simple "what is velocity at time t" problem

    In order to determine the acceleration you have to add all the forces on the helicopter (ie. by adding the forces as vectors). As Simon points out, the best way to do this is with a vector diagram showing all the forces on the helicopter. Gravity is one of the two forces acting on the helicopter.

    How is the net force (vector sum of all forces) related to the motion of the helicopter?

    AM
     
  5. Sep 10, 2012 #4

    rcgldr

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    Re: Simple "what is velocity at time t" problem

    One missing piece of information is that the upwards force from the air is probably assumed to be constant regardless of the helicopter's vertical speed (not realistic, but probably what the problem statement is assuming).
     
  6. Sep 10, 2012 #5
    Re: Simple "what is velocity at time t" problem

    Yes, I'm pretty sure the F(air) is constant for the purposes of the problem.

    So how about this: F(air) + F(weight) = ma + mg where "a" is the upward acceleration of the helicopter. BUt now I have too many variables to solve just for velocity. I have one Δv/Δt for a and one Δv/Δt for g.

    What am I STILL missing?
     
  7. Sep 10, 2012 #6
    Re: Simple "what is velocity at time t" problem

    Fnet=Fair-mg
    a=Fair/m-g

    For constant Fair and g.
    v0=0
    v(t)=(Fair/m-g)t
     
    Last edited: Sep 10, 2012
  8. Sep 10, 2012 #7

    Simon Bridge

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    Re: Simple "what is velocity at time t" problem

    Sum of the forces equals mass time acceleration.

    Formally:
    1. Pick a direction to be positive.
    2. Put all the forces in a row with + signs between them (some of the forces will be negative) ... then put an = sign .... then put "ma".
    3. then do the algebra.

    i.e.
    with positive = "upwards"

    Fair + (-Fweight) = ma

    Notice that Fweight=mg
    Put Fair=F (saves typing).

    F - mg = ma => a = (F - mg)/m => v(t) = (F - mg)t/m

    Notice: do step #2 like that and you'll never mess up the order.
     
  9. Sep 11, 2012 #8
    Re: Simple "what is velocity at time t" problem

    Thank you! I see that I have been over-complicating it.
     
  10. Sep 11, 2012 #9

    Simon Bridge

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    Re: Simple "what is velocity at time t" problem

    No worries :)
     
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