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posted by  croberts89 on 11/6/2009 12:39:13 PM  |  status: Closed  |  Earned Karma: 70

Gravity between particle and rod

Course Textbook Chapter Problem Needs by
Calculus Based Physics Fundamentals of Physics Extended (8th) by Halliday, Resnick, Walker 13 16 11/6/2009 at 10:00:00 PM
Question Details:
Particle of mass m1 = 0.67 kg is a distance d = 23 cm from one end of a uniform rod with length L = 3.0 m and mass M = 5.0 kg.

What is the magnitude of the gravitational force F on the particle from the rod?

I can do the problem with a sphere, but am unsure how to calculate the gravitational pull from a rod. Any help as to the method to approach this problem would be appreciated.
~CRR
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(SME)
posted by Nick9 on 11/7/2009 4:53:30 AM  |  status: Live
Asker's Rating: Lifesaver   
Response Details:
  Given :
  
mass of rod  M = 5.0 kg
length of the rod  L = 3.0 m

Mass per unit length of the rod is, m = M / L = 5.0 / 3.0
  d = 23 cm = 0.23 m
Mass of the element of the lnegth dr of the rod is , dm = m dr 
particle of mass m1 = 0.67 kg
Distance between the element of the rod and mass m1 is
dF = G m1 dm / R2
  dF = Gm1 dm/r2 = GMm1/L * dr/r2

integrate, limits: d to d + L

F = GMm1/L*(1/d - 1/(d + L))

= GMm1/[d(d + L)]

 
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