4.1 Forces
There are four known fundamental forces of nature:
(1) the strong nuclear force between subatomic particles;
(2) the electromagnetic forces between electric charges;
(3) the weak nuclear forces, which arise in certain radioactive decay processe
3.1 Vectors and Their Properties
Two vectors A and B can be added geometrically with the triangle method.
The two vectors are drawn to scale on graph paper, with the tail of the second
vector located at the tip of the first.
The resultant vector is the
5.3 Gravitational Potential Energy
The gravitational force is a conservative field.
Gravitational potential energy is another way of accounting for gravitational work
To find the change in gravitational potential energy as an object of mass m moves betwee
7.1 Angular Speed and Angular Acceleration
where
where
The average angular speed
of a rigid object is defined as the ratio of the angular
displacement
to the time interval
, or
is in radians per second (rad/s).
The average angular acceleration
of a rotati
6.1 Momentum and Impulse
The linear momentum of an object of mass m moving with velocity is defined as
Momentum carries units of kg (m/s.)
The impulse I of a constant force F delivered to an object is equal to the product of the force
and the time interva
Terri White
Chapter 5
5.1 Work
The work done on an object by a constant force is W = ( Fcos ) d
o Where F is the magnitude of the force, d is the magnitude of the objects
displacement, and is the angle between the direction of
force F and the displacement
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
Scanned by CamScanner
MATH 128 Winter 2017
Quiz 2 Solutions
Topics: Techniques of Integration and some Applications of Integration
Monday January 30
1. Evaluate the following integral (5 points: 1 for the conjugate, 1 for z and dz, 1 for
work, 1 for resulting function, 1 for a
MATH 128 Winter 2017
Work Sheet 3b (Quiz 3 topics)
Topics: Parametric/Vector Curves, Polar Coordinates, and Sequences & Series
1. (a) Show that the parametric equations
x = x1 + (x2 x1 )t
and
y = y1 + (y2 y1 )t;
(0 t 1)
describe the line segment that join
MATH 128 Winter 2017
Worksheet 4: Convergence tests and power series
1. Determine whether the following series are convergent or divergent. For the convergent
series, determine the sum.
(a)
(b)
X
n=0
X
n=0
n
cos (n) 3
3n+2 + 2 5n+1
42n
X
n 22n
5 e
(c)
MATH 128 Winter 2017
Quiz 3
Topics: Parametric Curves, Polar Coordinates, Sequences, Series
Monday March 6
1. Find the equation of the line that is tangent to the curve described by x = 1 + 4t t2
and y = 2 t3 at the point t = 1. (5 points each: 2 for hand
MATH 128 Winter 2017
Quiz 4
Topics: Convergence Tests, Power Series
Monday March 27, 2017
1. For each of the following series, determine whether it is absolutely convergent, condi[4]
tionally convergent, or divergent.
(a)
X
2n en
2
n=0
Solution (1 for set
MATH 128 Winter 2017
Quiz 1
Topics: Integration by substitution, integration by parts, trigonometric integrals,
trigonometric substitution
Monday January 16
1. Evaluate the following.
(a)
R
(sin 2)esin
2
d (6 points: 1 for z, 1 for dz, 1 for complete subs
MATH 128 Winter 2017
Work Sheet 3a
Topic: Differential Equations
1. Show that the following functions, y(x), is a solution of the given differential equation.
dy
d2 y
= 2y
2
dx
dx
(a) y(x) = c1 ex + c2 e2x ;
Solution: We have y(x) = c1 ex + c2 e2x . Then
Physics tutorial questions
A swimmer steps off a diving board and lands in a pool. If the time to reach the pool
is 1.00s, determine how high the diving board is.
A frog hops out of a helicopter and hits the ground 2.5 seconds later. If the helicopter
was
CHAPTER 3
3.1 Vectors and their properties
A car travels 20.0 km due north and then 35.0 km in a direction 60.0 o west of north,
as in Figure 3.6. Using a graph, din the magnitude and direction of a single vector
that gives the net effect of the cars trip
CHAPTER 1
1.5 Conversion of units
If a car is traveling at a speed of 28.0 m/s, is the driver exceeding the speed limit of
55.0 mi/h?
The traffic light turns green, and the driver of a high-performance car slams the
accelerator to the floor. The accelerom
CHAPTER 2
2.2 Velocity
A turtle and a rabbit engage in a footrace over a distance of 4.00 km. The rabbit runs
0.500 km and then stops for a 90.0-min nap. Upton awakening, he remembers the
race and runs twice as fast. Finishing the course in a total time o
CHAPTER 4
4.3 newtons second law
An airboat with mass 3.50x102 kg, including the passenger, has an engine that produces a
net horizontal force of 7.70x102N, after accounting for forces of resistance (Fig. 4.6).
a) Find the acceleration of the airboat
b) S
Introduction to
Quantum
Information
Processing
CS467 C&O481 PHYS467
Lecture 6
Michele Mosca mmosca@uwaterloo.ca
Lecture 5
1
Spectral decomposition
Often it is convenient to rewrite the density matrix as a mixture of its
eigenvectors.
Recall that eigenvect
Introduction to
Quantum
Information
Processing
CO481 CS467 PHYS467
Michele Mosca
lecture 4
1
Overview
Global Phase
Some circuit notation for measurements
Holevos theorem
Bell Basis and Superdense Coding
Implementing Bell measurements
Postulates of Quantum
Introduction to
Quantum
Information
Processing
CO481 CS467 PHYS467
Michele Mosca mmosca@uwaterloo.ca
Lecture 10
1
Deutsch-Jozsa problem
Suppose
f : cfw_0,1n cfw_0,1 with the promise that
f is either constant or balanced.
Decide if f is constant or balance
From quantum physics to a
new kind of computer
Introduction to
Quantum
Information
Processing
CO481 CS467 PHYS467
Michele Mosca mmosca@uwaterloo.ca
lecture 2
Classical bits (section 1.4 of text)
Probabilistic bits (section 1.4 of text)
Classical Circuit M