2nd Assignment Phys223: due Wednesday, January 23rd, 2002
1. Consider cylindrical coordinates:
a. Express the unit vectors in cylindrical coordinates in terms of the
Cartesian unit vectors.
b. Express the unit vectors in Cartesian coordinates in terms of
3rd Assignment Phys223: due Wednesday, January 30th, 2002
1. A baseball (radius r=0.0366 m, mass m=0.145 kg) is dropped from rest at the top
of the Empire State Building (height 1250 ft). Calculate
a. The initial potential energy of the baseball,
b. Its f
Todays Menu
Newtonian mechanics: Rectilinear motion
Examples for kinetic and potential energy:
constrained particle
escape speed
Velocity dependent forces
Next session:
Harmonic oscillation (Fowles chapter 3)
Velocity dependent forces
If force can be expr
for a=b=1
100
F(x)
V(x)
E
E-V(x)
50
0
-50
forbidden area where V(x)>E
or E-V(x)<0
-100
-10
-5
0
position x
5
10
100
for a=5, b=1
F(x)
V(x)
E
E-V(x)
50
0
-50
forbidden area where V(x)>E
or E-V(x)<0
-100
-10
-5
0
position x
5
10
1. for k<0 : oscillation
a.
Todays Menu
Newtonian mechanics
Newtons laws
Linear momentum
Conservation of linear momentum
Rectilinear motion: Uniform acceleration under a
constant force
Concepts of kinetic and potential energy
Energy conservation
Next session:
Examples
Newtons three
Todays Menu
Newtonian mechanics: Rectilinear motion
Examples for kinetic and potential energy:
constrained particle
escape speed
Velocity dependent forces
Next session:
Example
Harmonic oscillation
Consequences of energy conservation
The energy conservati
Todays Menu
Coordinate systems
Cylindrical coordinates
Spherical coordinates
Velocity and acceleration in cylindrical and
spherical coordinates
Next session:
Chapter 2: Newtons three laws
Rectilinear motion: Uniform acceleration under a
constant force
1.
Mid-term exam Phys 223.3 on Tuesday, February 12th, 2002
Instructor: Alexander Moewes
No books, no notes, 7 p.m. 9 p.m.,
1. A damped harmonic oscillator with m=10 kg, k=250 N/m, and c=60 kg/s is
subject to a driving force given by F0 cos(t ) , where F0=48
Vector algebra
How to change the coordinate system: the transformation matrix The derivative of a vector Position vector velocity acceleration
in cartesian coordinates
The Transformation matrix
How can a vector be represented in different coordinate syste
1st Assignment Phys223: due Wednesday, January 16th, 2002
r
r
1. Given the vectors: A = ( 4,2,3) and B = (1,3,2) , determine
a. B A ,
b. 3 A B ,
c. the component of B along A ,
d. the unit vector that is perpendicular to the plane A B .
r
r
r
r
r
r
r
r
r
4th Assignment Phys223: due Wednesday, February 6th, 2002
1. On the surface of the moon, the acceleration of gravity is about one-sixth that one
on the earth. What is the half-period of a simple pendulum of length 1 m on the
moon?
2. A spring of stiffness