1. The problem statement, all variables and given/known data
Consider a thin rod of mass M and length L. Determine the gravitational potential at a point which is a distance r from the center of the rod and which lies on the midplane of the rod.
Now suppose M is equal to the mass of the Earth and L is equal to the radius of the Earth.
Determine the acceleration due to gravity (of the rod) at a distance r = 0.86 L from the center of the rod.
2. Relevant equations
[itex]\Phi[/itex](r)=[itex]\int[/itex]L/2-L/2[itex]\frac{-G(M/L)}{sqrt(z^2+r^2)}[/itex]dz
U=mgh
3. The attempt at a solution
I calculate the gravitational potential to be -6.91657*10^7 Joules.
mgh=-6.91657*10^7 Joules
g=[itex]\frac{-6.91657*10^7}{m*h}[/itex]
The distance from the rod is r=.86*L but what is m? If I ignore m I get -12.62 m/s^2 which is incorrect.
Suggestions? Thank you!
Consider a thin rod of mass M and length L. Determine the gravitational potential at a point which is a distance r from the center of the rod and which lies on the midplane of the rod.
Now suppose M is equal to the mass of the Earth and L is equal to the radius of the Earth.
Determine the acceleration due to gravity (of the rod) at a distance r = 0.86 L from the center of the rod.
2. Relevant equations
[itex]\Phi[/itex](r)=[itex]\int[/itex]L/2-L/2[itex]\frac{-G(M/L)}{sqrt(z^2+r^2)}[/itex]dz
U=mgh
3. The attempt at a solution
I calculate the gravitational potential to be -6.91657*10^7 Joules.
mgh=-6.91657*10^7 Joules
g=[itex]\frac{-6.91657*10^7}{m*h}[/itex]
The distance from the rod is r=.86*L but what is m? If I ignore m I get -12.62 m/s^2 which is incorrect.
Suggestions? Thank you!
via Physics Forums RSS Feed http://www.physicsforums.com/showthread.php?t=720098&goto=newpost
0 commentaires:
Enregistrer un commentaire