Physics I
Class 01
Introduction
&
1D Motion
Rev. 31-Dec-03 GB
01-1
Welcome to Physics 1
at RPI
Physics 1 is a calculus-based, college-level introductory course in
general physics. For most of you, this is a required course.
Our primary topic in Physics 1 is Newtonian mechanics. We also
introduce the concepts of electric and magnetic fields. These concepts
are further developed in Physics 2. Physics 2 also covers waves and
introductory quantum mechanics.
Physics 1 has a web site:
http://www.rpi.edu/dept/phys/courses/phys1/index.htm
Please add this URL to your “favorites” and check it regularly for
information and announcements.
01-2
Frequently Asked Questions About
the Textbook for Spring 2004
The required textbook is Fundamentals of Physics, Sixth Edition, by
Halliday, Resnick, and Walker.
You should buy the complete Physics 1 package including Problem
Supplement #1 and the CD. You will use the same book and CD in
Physics 2.
If you bought a used textbook without a CD, you can buy just the CD
in the bookstore. If you have a used CD, you should always
download the latest activity files from the Physics 1 web site.
01-3
Format of the Course
 TA and/or instructor go over homework problems due today.
about 20 minutes
 Instructor gives a short lecture covering new material for today.
about 20 minutes
 Teams and/or the instructor work on Problems of the Day based on
the new material.
about 20 minutes
 Teams work on an activity to reinforce the new material.
about 50 minutes
01-4
Our Expectations of You
 Come to class prepared and ready to learn. This includes
– Reading the assigned material for the day.
– Doing the homework problems.
– Going over the class notes before class.
– Paying attention to the professor and TA.
 Bring any problems you are having with the material to your
instructor or the course director as soon as possible.
 Respect your classmates, instructors, and yourself by maintaining
academic integrity at all times. (In other words, don’t cheat!)
01-5
Exams
There will be three unit exams in Physics 1 (see schedule in the
syllabus). These are always given on Tuesday evenings (6-7:25) so
that everyone can take them at the same time. If you have a valid
RPI excuse for not taking the exam at the regular time, there are
conflict exams given the same evening. For special cases, individual
arrangements should be made with the course coordinator as far in
advance as possible.
If you have taken all three unit exams, the final exam is optional. If
you take it, we count it twice and drop the lowest single score to
calculate your exam average from your best four scores.
01-6
Homework
Homework assignments are generally due at the beginning of every
class. Each homework problem set consists of five Regular
Problems and a few Challenge Problems taken from the textbook
and/or Problem Supplement #1. All homework is written and we
request that you follow the format given in the syllabus and on the
Physics 1 web site.
You are responsible for five points of homework for each
assignment. Each Regular Problem is worth one point and each
Challenge Problem is worth two points. We grade the homework
problems on the principles of physics that you use, not the answers,
since we give you all the answers on the web site.
There is homework due for all classes with a few exceptions.
01-7
Activities
We will assign activity teams beginning with class #1 (this class) and
reassign the teams after each exam. Part of the learning experience in
Physics 1 is making your team work efficiently. We expect all team
members to participate actively.
Activities can include any or all of the following:
 Doing experiments and taking measurements.
 Analyzing video clips.
 Running simulations.
 Pencil and paper exercises.
Each student is responsible for submitting an individual activity write-up
at the end of class. These must be done on loose leaf paper, not torn from
a spiral notebook. Include: Name, section number, and class number.
01-8
Activity Exercises
At the end of each regular activity, there will be one or more exercises
based on the material covered that day. These will be similar to exam
questions. You may consult with anyone to answer these, but your final
write-up must be your own. You will be graded on the methods and
explanations as well as the numerical answers to the exercises.
The first part of the activity is worth up to 7 points except for the
exercise(s). The exercise part is worth 3 points. The maximum for any
activity is 10. If you do not come to class, your activity grade for that day
will be 0 unless you have a valid RPI excuse, in which case the activity
does not count for or against your grade but you are still responsible for
all material covered in class.
01-9
Your Grade in Physics I
Your numerical grade in Physics I is based on the following formula:
Exam Grades:
65% (3 unit exam average or the best 4 out of the
the optional final counted twice plus 3 unit exams)
Homework Grade: 10% (drop 5 points worth)
Activity Grade:
25% (drop lowest activity)
Your letter grade is based on your numerical grade with no rounding,
using cut-offs that we determine after the final exam.
Last semester it was 90.00 to 100.00 = A, 80.00 to 89.99 = B etc.
It is highly unlikely that this semester will be different.
01-10
Definitions
Scalar:
Magnitude:
Vector:
A number – positive, negative, or 0.
Absolute value – positive or 0.
Magnitude (or length) and direction
in space.
Time:
Position:
Displacement:
t(scalar)
x (vector)
 
x  x  x 0
Time interval: t  t  t 0
Average or mean velocity is defined as follows:

v avg
 

x  x 0 x


t  t0
t
01-11
Definitions (Continued)
Instantaneous velocity or just “velocity”:


x d x

v  lim

t 0 t
dt
Example: When you take a car trip, you get the

magnitude of v avg by dividing the change in the
odometer (or distance)
 by the hours you drove. You
get many values of v during the trip by checking the
speedometer moment by moment.



v
v

v
If is constant: avg
01-12
Definitions (Continued)
Average acceleration is defined as follows:

a avg
 

v  v 0 v


t  t 0 t
Instantaneous acceleration or just “acceleration”:


2 
v d v d x

a  lim


t  0  t
dt dt 2
01-13
Definitions (Continued)
Beware: The English word “acceleration” does not
have the same meaning as the physics word. In
physics, any change in the velocity vector is an
acceleration!
Some Additional Physics I Terms:
Speed:
Speed Up:
Slow Down:
Magnitude of velocity vector.
Any time the velocity vector’s
magnitude increases.
Any time the velocity vector’s
magnitude decreases.
01-14
Components of Vectors
Any vector can be written in component form:

a  aî  bĵ  ck̂
where î , ĵ, k̂ are unit vectors in the X, Y, and Z
directions respectively. a, b, c are components.
(Sometimes you will see x̂ , ŷ, ẑ unit vectors.)
The components of a vector are scalars. They can be
positive, negative, or zero.

a  aî
In one dimension:
The magnitude of a one-dimensional vector is the
absolute value of its component: |a|.
If a is negative, the vector points in the negative X
direction.
01-15
Velocity and Acceleration
We will start with 1D motion. We will deal with the
X components of velocity and acceleration, v and a.
a is the slope of the graph of v versus t (time).
slope = a
v
t
01-16
Constant Acceleration
For the special case of constant acceleration, the
graph of v versus t is a straight line. The equation is
v  v 0  a t  t 0 
This is the same equation you had in math class for a
line – [ y  m x  b] – but with different symbols.
v
slope = a
v0
t0
t
01-17
Displacement with
Constant Acceleration
Math Fact: Because velocity is the derivative of
displacement, displacement is the area (integral)
under the graph of v versus t.
displacement = area = rectangle + triangle
rectangle:
height  base  v 0 ( t  t 0 )
triangle:
1
height  base 
2
1
(v  v0 )  (t  t 0 ) 
2
1
[a ( t  t 0 )]  ( t  t 0 )
2
v
v0
t0
t
( x  x 0 )  v 0 ( t  t 0 )  12 a ( t  t 0 ) 2
x  x 0  v 0 ( t  t 0 )  12 a ( t  t 0 ) 2
01-18
Class #1
Take-Away Concepts
1D Equations of Motion for Constant Acceleration
Basic Equations
1. v  v 0  a  t  t 0 
2. x  x 0  v 0 ( t  t 0 )  2 a ( t  t 0 )
1
2
Derived Equations
1
x

x

( v 0  v)(t  t 0 )
3.
0
2
1
2
x

x

v
(
t

t
)

a
(
t

t
)
4.
(compare with 2.)
0
0
0
2
5. v  v 0  2a x  x 0 
2
2
01-19
Class #1
Problems of the Day
_______1.
Which one graph below represents a motion for which it would be incorrect to
use equations 1-5 to solve a one-dimensional motion problem – even if you
broke the motion into two time intervals? Note: The respective graphs are
straight line segments and v = velocity, a = acceleration.
v
A)
v
t
B)
a
C)
t
a
t
D)
t
01-20
Answer to Problem 1 for Class #1
The answer is C. Acceleration is not constant, and so it is incorrect
to use equations 1-5. These apply only for constant acceleration.
Graph B is a simple case of constant acceleration in one time
interval.
Graphs A and D are both the same type of motion, with constant –
but different – acceleration values in two or more time intervals.
Equations 1-5 can still be used. First solve for the motion in the first
interval, then use the position and velocity at the end of the first
interval as initial conditions for equations 1-5 (with a different value
of acceleration) in the second interval. An example of this method is
Problem 39P in Chapter 2 of your textbook.
01-21
Class #1
Problems of the Day
2. A construction worker on a new high-rise building drops a
wrench and it falls 78.4 m to the ground. How fast is it moving
when it hits, assuming no air resistance? Use g = 9.8 m/s2.
01-22
Answer to Problem 2 for Class #1
The first step is to determine a coordinate system. We can pick any direction as the
+X direction that makes the problem easier. In this case, we pick X = 0 as the vertical
position of dropping the wrench and X = 78.4 as the place where it hits the ground.
Then acceleration is positive, a = +9.8 because +X is in the down direction.
What variables do we know? x0 = 0, v0 = 0, t0 = 0 (start the clock when the wrench
drops), x = 78.4 and a = 9.8 . We don’t know v (what the problem asks for) or t.
Method A: Use eq. 2 to solve for t: 78.4 = 0.5 * 9.8 * t2 . t = 4.0 . Then use eq. 1 to
solve for v: v = 4.0 * 9.8 = 39.2 m/s.
Method B: We realize that we know everything in eq. 5 except v, which is what we
want. v2 = 2.0 * 9.8 * 78.4 . v = sqrt(1536.64) = 39.2 m/s.
01-23
Activity #1
Software Loading / 1D Motion
Objectives of the Activity:
1. Making sure Physics I software is installed and
working correctly on your laptop.
2. Understanding the basic operation of the motion
detector, cart, and track. (We will use these a lot.)
3. Learning general rules and guidelines that will
apply to all Physics I activities.
4. Review of 1D motion.
01-24
Optional Material
at the End of the Lecture Notes
At the end of most lecture notes, there will
be a section of extra material. This is for the
interest of students who would like to get
some additional depth from the course.
We will not be testing on this material and
you are free to skip it.
01-25
Class #1 Optional Material
Deriving the Other Equations
Equation 3:
3a. Solve 1 for a:
v  v0
a
t  t0
3b. Substitute 3a into 2 and simplify.
Equation 4:
4a. Solve 1 for v0: v 0  v  a ( t  t 0 )
4b. Substitute 4a into 2 and simplify.
Equation 5:
5a. Solve 1 for (v-v0):
v  v0  a (t  t 0 )
x  x0
5b. Solve 3 for (v+v0): v  v 0  2
t  t0
2
v
5c. Multiply 5a by 5b and bring 0 to r.h.s.
01-26