Physics 2211 Mechanics Lecture 1 Knight: 1'1 to 1'7 Motion Concepts

1
Physics 2211 - MechanicsLecture 1 (Knight
1.1 to 1.7)Motion Concepts

• Dr. John Evans
• Professor of Physics
• jevans3_at_gpc.edu
• or
• jevans_at_agnesscott.edu

2
Stop-Motion Photography
We can superimpose all the frames to create
astop-motion picture that shows the
progressionof positions as equal intervals of
time pass.
The equal spacing of the images indicates that
the carhas a constant velocity.
3
Change and Motion
A stationary ball on the ground.Same position at
all times. Velocity0.
A skateboarder rolling on a sidewalk.Images are
equally spaced. Velocityconstant.
A sprinter starting the 100 meter dash. Image
spacing grows. Velocity increasing.
A car stopping for a red light. Image spacing
shrinks. Velocity decreasing.
The actual images can be replaced by dots
showing successive positions.
4
Images to Dots to Motion
5
Motion Diagrams
Velocity Constant
Accelerating
Decelerating
6
Motion in Two Dimensions
7
Adding Vectors
8
Subtracting Vectors
9
Finding Dr rf-ri
10
Sams Motion
11
Dr in Motion Diagrams
12
Velocity
Average speed Distance/Time Example 15
miles/½ hour 30 mph
Generalization velocity
Speed is a scalar (1D) quantity. Velocity is a
vector (3D) quantity.
13
Motion and Velocity Vectors (1)
14
Motion and Velocity Vectors (2)
Velocity is changing in both Magnitude and
direction.
Velocity is changing in magnitude.
Jake throws a ball to Jim.
15
Acceleration
Definition
Acceleration Changing
Acceleration Constant
16
Changing Words to Symbols

• Sketch the situation. Not just any sketch. Show
  the object at thebeginning of the motion, at the
  end, and at any point where the character ofthe
  motion changes. Very simple drawings are
  adequate.
• Establish a coordinate system. Select your axes
  and origin tomatch the motion.
• Define symbols. Use the sketch to define
  symbols representingquantities such as position,
  velocity, acceleration, and time. Every
  variableused later in the mathematical solution
  should be defined on the sketch.Some will have
  known values, others are initially unknown, but
  all should begiven symbolic names.
• List known information. Make a table of the
  quantities whosevalues you can determine from
  the problem statement or that can be
  foundquickly with simple geometry or unit
  conversions. Some quantities are impliedby the
  problem, rather than explicitly given. Others are
  determined by yourchoice of coordinate system.
• Identify the desired unknowns. What quantity or
  quantities will allowyou to answer the question?
  These should have been defined as symbols in step
  3. Dont list every unknown only the one or two
  needed to answer the question.

17
Example Weather Rocket
Q A small rocket used for meteorological
measurements of the upper atmosphere is launched
vertically with an acceleration of 30 m/s2. It
runs out of fuel after 30 s. What is its maximum
altitude?

• What is the rockets velocity atmaximum
  amplitude.
• Velocity goes to zero.
• What happens at t30 sec?Does rocket stop?
• No. Acceleration changes.
• What is the acceleration aftert30 sec? Is it
  positive or negative?
• Negative. a1y-g

18
Additional Material from Section 1.9
19
Standard International Units

• Standard International (SI) Units (also known as
  MKS)
• Time second s
• Length meter m
• Mass kilogram kg

Definition 1 second 9,192,631,770
oscillations of the radio waves absorbedby a
vapor of cesium-133 atoms. Definition 1 meter
is the distance traveled by light in
1/299,792,458 of a second. Definition 1
kilogram is the mass of the international
standard kilogram, apolished platinum-iridium
cylinder stored in Paris. (It is currently the
only SI unitdefined by a manufactured object.)
Unit
Conversions 1 in 2.54 cm 1 cm 0.3937 in 1
mi 1.609 km 1 km 0.621 mi 1 mph 0.447
m/s 1 m/s 2.24 mph Note the English pound
unit is a measure of force, not mass. A
kilogram has a weight of 2.2046 pounds at
standard gravity.

English Units(Used only in USA, Liberia,and
Myanmar)
20
Prefixes

• Standard Prefixes Symbol Examples
• giga- 109 G GHz
• mega- 106 M MHz
• kilo- 103 k kg
• centi- 10-2 c cm
• milli- 10-3 m mm
• micro- 10-6 m mg
• nano- 10-9 n nm
• pico- 10-12 p pF
• femto- 10-15 f fm

21
Unit Conversions
22
Approximate Conversion Factors
23
Scientific Notation
How manysignificantfigures?
24
Some Approximate Lengths
25
Some Approximate Masses
26
Estimating Orders of Magnitude

• Make a rough estimate of the relevant
  quantitiesto one significant figure, preferably
  some power of 10.
• Combine the quantities to make the estimate.
• Think hard about whether the estimate is
  reasonable.

Example How fast does an Olympic sprinter
cross the finishline in the 100 m dash?
Analysis Typical 100 m dash time is 10 s,
so average speed isabout 10 m/s. Sprinters
kick near the finish line, sospeed there is
faster. 50 faster? Maybe. That wouldmean the
finish-line speed is 15 m/s. Reasonable? Yes.
27
Dimensional Analysis (1)
Example
The period P (T) of a swinging pendulum depends
only on the length of the pendulum d (L) and the
acceleration of gravity g (L/T2). Which of the
following formulas for P could be correct ?
P 2? (dg)2
(a)
(b)
(c)
28
Dimensional Analysis (2)
Realize that the left hand side P has units of
time (T ). The right hand side must have the same
units
Try equation (a).
Try equation (c).
Try equation (b).
(a)
(b)
(c)
29
End of Lecture 1

• Before the next lecture, read Knight, Chapters
  1.1 through 2.4