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Finding work done by object along circular helix: Line Integral

  1. Nov 12, 2009 #1
    1. The problem statement, all variables and given/known data
    An object weighing 1.2 pounds travels along a helix given by x=cost, y=sint, z=4t, 0<=t<=8pi. Find the work done by the object.

    Let's keep this in ft.

    2. Relevant equations
    g=32.174 ft/s2
    f=m*g
    f=w*d

    3. The attempt at a solution

    r(t)=cos(t)i+sin(t)j+4(t)k

    I know I need an F function, but I'm not sure how to find it.

    w=[tex]\int[/tex] F(dot)dr
    w=[tex]\int[/tex]F(r(t)) (dot) r'(t) dt

    Any help would be appreciated, thanks in advance!
     
    Last edited: Nov 12, 2009
  2. jcsd
  3. Nov 12, 2009 #2

    LCKurtz

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    Homework Helper
    Gold Member

    You are working against gravity, which is directed downward. So figure out the force f of gravity on your object and use

    [tex]\vec F = \langle 0,0,-f\rangle[/tex]

    This is the work done by the force, opposite the work done by the object.
     
  4. Nov 16, 2009 #3
    Thank you for your response. This may sound a bit stupid, but I want to make sure I'm getting the right force here...

    Weight is the mass of an object with a force acting upon it. I'm not sure how much the equations f=ma and weight=m*gravity "overlap", if you will. Can I just say 1.2=mass*gravity? That would mean that the force is 1.2 pounds... do you see what I'm confused about here?

    Thanks again for your help!
     
  5. Nov 16, 2009 #4

    LCKurtz

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    1.2 pounds is a unit of force in the English system. And work is measured in foot-pounds which gives the right units for w = fd in the English system.
     
  6. Nov 16, 2009 #5

    Mark44

    Staff: Mentor

    Weight is a force. The formula F = ma gives the force F acting on an object of mass m under an acceleration a.

    In the SI system, a mass of 1 kg at the surface of the earth exerts a force downward of 1kg * 9.8 m/s^2 = 1 Nt. In the English system, a mass of 1 slug at the surface of the earth exerts a force downward of 1 slug* 32 ft/sec^2 = 32 lb.
    They overlap considerably, but the F = ma formula applies more generally for any kind of acceleration, not just that due to gravity.
     
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