Lafayette College
Department of Physics
April 21, 2009
Physics 131 LevelIIHomework Set Section 1
Youmay discuss these problems with one or twoother students (or with your instructor), but
your final solutions should be written out by you alone. Under no circumstances should you see
another student’swritten solutions. If you have discussed these problems with anyone you must
acknowledge the collaboration at the beginning of the corresponding problem. Homework is due
in my office by 3:30 PM on the due date and solutions will then be made available on the course
web site. No homework will be accepted after this time.
Youare expected to carefully explain how, starting from basic principles, you have arrivedat
your answers. Please do not use paper with edges frayed from being ripped out of a spiral bound
notebook. If the papers are illegible or disorganized, we reservethe right to return these papers
without being graded. Unless instructed otherwise, all answers should be correct to 3 or 4 sig.
figs.
Assignment Week 12: Due Friday,April 24, 2009
Problem 1: Using the diagrams givenout in class, find the torque on the torsional fiber for the
suspended dumbbell.
Problem 2: Consider a space probe in a circular orbit about the Sun with a radius of R.Show
that the kinetic energy of the orbit is half of the magnitude of the potential energy of the orbit.
Problem 3: Consider the Sun, Earth, and Moon system. Look at twosituations in which all
three bodies line up. The first case puts the moon between the Earth and the Sun and the second
puts the Earth between the Moon and the Sun. Find the net gravitational force on the Moon due
to the other twobodies. In doing so, compare in each case the relative strengths of the two
forces.
Extra Credit Problem. Do not attempt unless you knowwhat you are doing.
Problem 4: Consider a space probe in an elliptical orbit about the Sun. Let Rpbe the dis-
tance of closest approach to the Sun (the perihelion), and let Rabe the furthest distance from the
Sun (The aphelion). Let $K0be the kinetic energy the probe would have ifitwere in a circular
orbit of radius Rp,let
α
K0be the kinetic energy it actually has at the perihelion and let
β
K0be
the kinetic energy it has at the aphelion. Using conservation of energy and conservation of angu-
lar momentum, find the values of
α
and
β
in terms of Rpand Ra.Indoing this calculation, con-
vert both equations to forms that involvethe kinetic energy,then scale the kinetic and potential
energies by K0.Solvefor
α
and
β
in terms of Rpand Ra.Find the numerical values of
α
and
β
for a Hohmann transfer orbit (see problem 12.86 in the text) between the Earth and Mars and al-
