{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Physics 325 HW 11 Solutions - Physics 325 homework 11...

Info icon This preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics 325 homework 11 - Solutions Homework due on Thursday 2 December 2010 1.) (15 points) Calculate the gravitational potential due to a thin rod of length l and mass M at a distance R from the center of the rod and in a direction perpendicular to the rod. The expression for calculating the gravitational force is the following; F = G m 1 m 2 r 2 This formula is defined for two point-like objects only. In order to calculate a force due to a finite-size object, we must break the object into infinitesimal volumes, calculate the effect of each, then add these together to get the result.. For this reason, let us consider a small line element dx , located at distance x from the center of the rod. It’s mass is given by dm = λdx , where λ is the line mass density: λ = M/L . The potential due to this line element is then = - G dm x 2 + R 2 = - G λdx x 2 + R 2 where we are considering a unit mass. Adding contributions from all of the pieces, we get φ = rod = - L/ 2 - L/ 2 1 x 2 + R 2 dx Substitute x = R sinh( y ), φ = - GM L sinh - 1 ( l 2 R ) sinh - 1 ( - l 2 R ) dy = - GM L sinh - 1 ( l 2 R ) - sinh - 1 ( - l 2 R ) = - 2 GM L sinh - 1 ( l 2 R ) or equivalently, φ = - 2 GM L ln L 2 R + 1 + L 2 R 2
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
2.) (20 points) Calculate the gravitational field vector due to a homogeneous cylinder ar exterior points on the axis of the cylinder. Perform the calculation... In both cases, all we need to do is (i) break down the cylinder to infinitesimal volume elements dV , (ii) calculate the force/potential due to each piece, and (iii) sum them up to obtain the net force/potential. The most important thing is the choice of coordinate system; you should pick one that respects the symmetry of the system. Here we have a (homogeneous) cylinder, so cylindrical coordinates are good to work with.
Image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern