自然科學
大學
力學 救救我 謝謝！（第三題不用）
1. Considerathin rod ofuniform linear mass density pL with mass 4/ and
length /, find the gravitational potential。dp/有)。at a perpendicular
distance Afrom the center ofthe rod. You may find the integral in (E.6)
in Appendix E useful
2. A spherical planet of radius 人> consists ofacore of radius 有/ with
uniform density pi. and a thick outer cloud of dust with umiform
density p: Find the force (magnitude and direction) onamass箇inside
the dust cloud ata position ARp from the planetcenter( 吃<訪<記),
3. Use Fermat's principle by applying calculus of variation to minimize
the time oflight passing from medium ofrefractive index jg, to another
medium ofrefractive index >, derive the Snells law ofrefraction:
js光 名2s 銷
4. Consider the Atwood machine oftwo masses connected by amassless
string oflength 7overapulley ofradius gas shown,
(a) Write down the total kinetic energy and potential energy in terms of
the coordinatex Hence obtain the Lagrangian ofthe system.
(b) Derive the Lagrange's equation of motion and hence find the
acceleration ofthe masses.
x
和二
工
