Physics 205Final Exam Fall 2003
Solutions
x
M
1) (40 pts) A plane pendulum consists of
a bob of mass m suspended by a massless
rigid rod of length l that is hinged to a sled
of mass M . The sled slides without friction
on a horizontal rail. Gravity acts w
PHYS 203
Princeton University
Final Exam Solution
1. (20 points) Underwater pendulum
A ball of radius a and density b is suspended under water (density
w) on a massless string of length l. You can assume that a<l. The
ball experiences a drag force in th
PHYS 203
Princeton University
Final Exam
Fall 2005
1. (30 points) Toy Car
A toy car is made from a
rectangular block of mass M and
four disk wheels of mass m and
radius R. The car is attached to a
vertical wall by a spring with a
spring constant k. The co
Problem 1
A bead of mass m slides without ction on a wire whose shape is
r
z(r) = a( )4
a
The wire rotates about the z axis with constant velocity !. Earths gravity causes
acceleration g along the z axis.
1. By using cylindrical coordinates, write the Lag
PHYS 203
Princeton University
Final Exam
Fall 2006
1. Death Star (20 pt) A particle of mass m is subject to a central force given by the potential
k
V = 3
( k > 0)
r
a) What is the effective potential? Make a sketch.
Veff =
Veff
Emax
2
k
l
+
3
r
2mr 2
r0