Addition and Subtraction
Using simple trig
Usually avoided in other physics courses
Good only for two 2D vectors and their
resultant or for resolving a 2D vector into
components.
Slow and unwieldy for 3 or more 2D
vectors.
Very difficult with 3D vect
Vectors have magnitude and
direction
r
A
v
B
r r
Symbols: A, B
Without arrow,
r just magnitude
or size. A = | A |
r r r
C=A+B
+ means tail-to-tip
v
B
r
A
r
C
Start
End
= means same start
and end points
OHQ1
OHQ2
Multiplication by a scalar
r
r
F = 3A
r r
Magnitude & Direction Notation
Common
Use Pythagorean Theorem & trig
Direction means with respect to some
convention
0 (positive x direction) in x-y axes
wrt nearest axis on maps (N, E, W, S)
y
A
x
r
A = 6i + 5 j
r
A =| A |= Ax2 + Ax2 = (6) 2 + 52 =
Free Body Diagrams
Principle way to convey your knowledge of a mechanics problem.
Your FBD is your explanation of where your Newtons Equations
come from.
A FBD lets you and the reader check your work efficiently.
It is a mandatory convention of the profes
1. A baseball player throws a ball at a nearby boulder. The ball hits the boulder
with a speed of 41 m/s, and then bounces straight up to a height of 18.0 m.
Assuming that the rotational motion of the ball is negligible, what fraction of
the ball\'s initi
PHYC 1100Y/1290: Introduction to Physics
Department of Physics and Atmospheric Science, Winter 2012
Monday, Wednesday and Friday at 8:35-9:25 and 9:35-10:25 in Dunn 117
Lecturer: Prof. Tom Duck <[email protected]>, Dunn 128; Office hours: Wed 1-4 PM
Lab ins
Motion in One and Two Dimensions-
Vf Vi
t .
Vi + Vf
s=(-2)t
3-.=_
S
.va
_ sign convention for free-fall: up is positive
ll.
.1. 2'
281:
vii: +
viz + 2913
Motion in the x-direction
1. Thedriver ofatar travelling at 25 this sees afallen tree
:9
- gilt
1
Lesson 1: Vectors Part 1
In physics we work with different types of quantities. Some of these quantities require only
a single value to be specified, for example the mass of a car or the walking distance to the
store. We can say that the mass of a car p
1
Lesson 3: Position, Displacement and
Distance Solutions
The following points are used in the first three questions:
2, 4 m, 1,3 m, 2, 5 m
1) Graph the position of the points on a coordinate system.
B
A
C
2) Find the displacement if a particle travels fr
1
Lesson 2: Vectors Part 2 Exercises
Given the following vectors, answer questions 110
1) Multiply 3 with A
2) Multiply 2 with H
3) Obtain the scalar product between A and B
4) Obtain the angle between C and D
5) Obtain the cross product between A and D
6
1
Lesson 2: Vectors Part 2 - Solutions
Given the following vectors, answer questions 1-10
1) Multiply 3 by A
2) Multiply 2 by H
3) Obtain the scalar product between A and B
4) Obtain the angle between C and D
5) Obtain the cross product between A and D
6)
1
Lesson 3: Position, Displacement and
Distance Exercises
The following points are used in the first three questions:
1) Graph the position of the points on a coordinate system.
2) Find the displacement if a particle travels from A to B to C.
3) Find the
1
Lesson 3: Position, Displacement and
Distance
For this first series of lessons we are going to imagine that anything in our world can be
considered a particle. Particles are especially interesting to us because they make problems
easier to solve, since
1
Lesson 1: Vectors Part 1 Exercises
Given the following vectors, answer questions 110:
1) Graph vectors A and B
2) Transform A into the polar form
3) Transform C into the polar form
4) Transform B in the rectangular form
5) Add vectors C and D
6) Add Vec
1
Lesson 2: Vectors Part 2
1 Multiplying a Vector by a Scalar
Multiplying a vector by a scalar is multiplying each component of the vector by the scalar.
The result will be another vector whose magnitude is larger or smaller than the original
vector, but
1
Lesson 4: Velocity and Speed Exercises
Use figure 1 for the first four questions.
Figure 1
1)
2)
3)
4)
Find the average velocity.
Find the instantaneous velocity at t =1, 3 and 5 s
Find the average speed.
Find the instantaneous speed at t = 8 and 13 s
F
Final Examination
PHYSICS 1100
16 December 1997
1.
An object is placed 48.0 cm from a converging lens which has a focal length of
30.0 cm.
(a) Characterize the image formed. Include where the image is, whether it is
real or virtual, erect or inverted, and
Physics 1100
Test #3
March 2002
Use methods shown in class. Show all work.
1.
The U.S.S. Voyager is in circular orbit around a Class M planet. Ensign Kim
reports to Captain Janeway that the planet has a radius of 5840 km, that the
Voyager is 3000 km from
Final Examination
PHYSICS 1100
1.
When sewer pipes are blocked, city engineers often use the following trick to
find where the blockage has occurred. They go to an unblocked end as shown
below and play a pure single frequency tone into the open end. They
Physics 1100
Test #4
March 2002
Use methods shown in class. Show all work.
1.
A physics instructor drops a 75-g ball from a height of 1.50 m. It collides with
the floor and bounces back to a height of 1.25 m.
(a)What is the velocity of the ball just befor
Test #2
PHYSICS 1100
22 October 1997
1.
An asteroid is simply a very large chunk of rock wandering through space.
Between Mars and Jupiter, a large number of these asteroids orbit the Sun and
form what is known as the Asteroid Belt. In the figure below le
Physics 1100
Test #5
April 2002
Use methods shown in class. Show all work.
1.
The charges are Q1 = -2.00 C, Q2 = 6.00 C, and Q3 = 3.00 C.
(a) Find the net electric field (magnitude and direction) at point A on the graph.
(b) If a charge q =-2.00 C is plac
Test #4
PHYSICS 1100
1.
In the diagram below, a block A of mass 3.00 kg is moving to the right when it
collides with block B which has mass 4.50 kg and is not moving. The tabletop
is frictionless and 1.20 m above the floor.
(a) If the collision is perfect
Physics 1100
Test #2
19 February 2002
Use methods shown in class. Show all work.
1.
[10] A ball rolls with velocity of v = 6.00 m/s 2 off the flat roof of a 20-m tall
building. A boy is standing 25 m from the side of the building. The boy starts
running t
Test #2
PHYSICS 1100
22 October 1997
1.
An asteroid is simply a very large chunk of rock wandering through space.
Between Mars and Jupiter, a large number of these asteroids orbit the Sun and
form what is known as the Asteroid Belt. In the figure below le
Physics 1100
Test #1
5 February 2002
Use methods shown in class. Show all work.
1.
[5 Marks] The diagram below represents the velocity (v in m/s) as a function of
time (t in seconds) of a ball moving in a straight line.
a.
Find the average velocity in seg
Test #1
PHYSICS 1100
3 October 1997
1.
[1 Mark] You are given a position versus time graph. What physical quantity is
given by the slope of a line tangent to the curve at time t?
2.
[1 Mark] You are given a velocity versus time graph. What physical quanti