Phys 3201 Assignment #8 Spring 2006
This assignment is due in class on Wednesday, March 29th.
1. A spacecraft is sent to explore the moon (radius R
and mass M). Initially, the spacecraft is parked in a
circular orbit of radius 3R(orbit 1).
(a) Find the boost ∆vrequired to put the spacecraft
in an elliptic orbit which just skims the Moon’s surface
(orbit 2). Assume a single, short burn.
(b) Find the minimum boost ∆vneeded, once in orbit
2, for the craft to escape the Moon’s gravitational field.
1
2
2. Consider a binary star system in which the two stars revolve about each other in an
elliptical orbit. Their distance of closest approach is Rand their maximum separation is 5R.
Suppose that the stars have masses 3Mand 2M, respectively.
(a) Make a sketch of the situation, indicating the system center of mass, the distance of
closest appraoch, and the distance of maximum separation; (b) Find the reduced mass of
the system; (c) Find the semi-major axis of the elliptical orbit for the equivalent one-body
problem; (d) Compute the period of the orbit.
3. Find the center of mass of a thin uniform-density half-disk of mass Mand radius R.
4. A thin stick of length Llies on the x-axis with one end at x= 0 and the other at x=L.
The density of the stick is not uniform. Instead, its mass per unit length is given by
λ=µ(2L2
−x2)
where µis a constant.
(a) If the total mass of the stick is M, calculate the constant µ.
(b) Find the center of mass. Express your answer as Xcm =cL, where cis a number.
5. (Thornton & Marion problem 9-21) A flexible rope of length 1.0 m slides from a frictionless
table top. The rope is initially released from rest with 30 cm hanging over the edge of the
table. Find the time at which the left end of the rope reaches the edge of the table. (See
textbook for figure.)
