Find the net force with the given position vector

  1. 1.The position vector of a 3000N helicopter is given by:
    r=(.02 m/(s^3))(t^3)i + (2.2m/s)tj - (0.06 m/(s^2))(t^2)k
    Find the net force on the helicopter at t = 5s.



    2. I really have no clue where to begin.



    3. I started doing this:
    r= (.02m/(s^3))(5s^3)i + (2.2m/s)(5s)j - (.06m/(s^2)*(5s)^2k
    r= 2.5mi + 11m + 1.5m
    then I drew a 3d graph with each axis labeled and two right triangles but have no clue
    where to go from here.
     
  2. jcsd
  3. rl.bhat

    rl.bhat 4,433
    Homework Helper

    The given problem can be written as

    r = a*t^3*i + b*t*j -c*t^2*k

    Find d(r/dt and d^2(r)/dt^2. That gives you the acceleration. Find the magnitude of a.

    Weight of helicopter is given. Find its mass. Then the force on the helicopter = m*a
     
  4. Thank you so mu rl.bhat.

    After the 2nd derivative I get a= (.12m/s^3)(t) - .12m/s^2
    = (.6m/s^2)- .12m/s^2= -.6 m/s^2
    F=m*a m=F/a m=3000n/9.81m/s^2=305.8kg

    m*a=F 305.8 kg * -.6m/s^2=-183.48N Is that thought process correct?
     
  5. rl.bhat

    rl.bhat 4,433
    Homework Helper

    After the 2nd derivative I get a= (.12m/s^3)(t) - .12m/s^2

    It should be

    a= (.12m/s^3)(t)*i - .12m/s^2*k

    Find the resultant a.
     
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