Physics 105A
Analytical Mechanics
Midterm Review
28 June 2016
Manuel Calderón de la Barca Sánchez
Energy in a Bungee Jump
 A certain physicist of mass m wants to use a bungee cord
with spring constant k. The bungee cord has unstretched
length L. How far down will the physicist fall, assuming
initial speed is zero and a constant g field? Neglect losses
due to friction and air resistance.
Sigh, No
bungees in
1687…
28 June 2016
MCBS
5.3 : Leaving the sphere
 A small mass rests on top of a fixed frictionless sphere.
The mass is given a tiny kick and slides downward under
gravity. At what point does it lose contact with the
sphere? There are at least two ways to do this.
28 June 2016
MCBS
3.4 : Line of Pulleys
 N+2 equal masses hang from a system of pulleys as
shown. What are the accelerations of all the masses?
N masses
28 June 2016
MCBS
Example: Supporting a tube
 Drill a narrow tube, with cross-sectional area A, from the
surface of the earth down to the center. Then line the
cylindrical wall of the tube with a frictionless coating. Then
fill the tube back up with the dirt that you originally
removed. What is the total gravitational force acting on the
dirt in the tube? Let the earth’s radius be R, and assume
a uniform mass density r (an assumption which is not
true, but just for simplicity).
28 June 2016
MCBS
5.2 : Heading to zero
 A particle moves toward x=0 under the influence of a
potential of the form
V ( x)   A | x |
n
 where A>0 and n>0.
The particle has barely enough
energy to reach x=0. For what values of n will it reach
x=0 in a finite time?
28 June 2016
MCBS