Linear Motion - Kinematics

doutfanaticalMechanics

Nov 14, 2013 (3 years and 9 months ago)

65 views

Current Event


Choose an article that is at least 2 pages in length if it is
in a magazine or at least 1 column if it is in a newspaper.
If it is on the internet it should be a 5
-
8 paragraphs.


Read the article and write a summary of what the main
points of the article included.


On Friday we will discuss the articles. You should be
working from your summary during the discussion,
though you can bring the article in if you want to.


You will turn the summary in at the end of the period.
No late summaries will be accepted.


This article should concern either physics, weather,
astronomy or geology. NO BIOLOGY OR MEDICINE!

Linear Motion
-

Kinematics

Key Terms


Speed


Velocity


Acceleration


Free fall


Gravity


Distance


Displacement


Linear Motion


Motion in a straight line


This motion can be described several ways:


Speed


Velocity


Acceleration


Distance


Direction


How can you tell when an object is moving?


All motion is relative


Things that appear to be at rest can move






Motion is Relative


Must compare two objects relative to one
another. Called a frame of reference


How can you tell when an object is moving?


All motion is relative


Things that appear to be at rest can move


Example:


You are sitting in class in your chair


are you
moving?


Although you may be at rest relative to Earth’s
surface, you’re moving about 100,000 km/h
relative to the sun.


Speed

Speed is one way to describe motion. It describes how
fast an object is moving using distance and time.
Average speed is the
total
distance traveled over the
total time and instantaneous speed is the speed at a
particular moment

For example, 30 miles
per

hour means object travels
distance of 30 miles in an elapsed time of one hour. Write
as,

(SPEED) =

(Distance traveled)

(Time elapsed)

30 miles per hour = 30

miles

hour

Practice:

What is the average speed of a cheetah that
sprints 100 meters in 4 seconds? How about if
it sprints 50 meters in 2 seconds?




A car has an average speed of 100 kilometers
per hour. How far does it travel in 30 minutes?


Demo
: Ball Races

Which ball wins the race, A or B?

A

B

Finish

Line

Which ball has the larger average speed?

Which has the larger instantaneous speed at each point.

Velocity


a description of how fast and in what direction


a vector quantity


Constant velocity is constant speed and
constant direction (straight
-
line path with no
acceleration).


Constant speed is steady speed, neither
speeding up nor slowing down.


Different types of velocity and speed


Average velocity/speed


A value summarizing the
average of the entire trip.


All that’s needed is total
displacement/distance and
total time.


Instantaneous velocity


A value that summarizes the
velocity or speed of
something at a given instant
in time.


What the speedometer in
you car reads.


Can change from moment
to moment.


When we say that an object is moving at
constant velocity we mean that it is

1) at rest,

2) moving at an unchanging speed,

3) moving at an unchanging speed in a straight
-
line path,



and that its acceleration is

4) zero.

5) constantly increasing (or decreasing).

6) uniform.


Practice

The speedometer of a car moving east
reads 100 km/h. It passes another car
moving west at 100 km/h. Do they have
same speed? Velocity?


During a certain period of time, the
speedometer of a car reads a constant 60
km/h. Does this indicate a constant
speed? Constant velocity?


Practice Problem


A car going 15m/s accelerates at 5m/s
2

for
3.8s. How fast is it going at the end of the
acceleration?


First step is identifying the variables in the
equation and listing them.

Practice Problem


A car going
15m/s

accelerates at
5m/s
2

for
3.8s
.
How fast
is it going at the
end
of the
acceleration?


t=3.8s


v
i
=15m/s


a=5m/s
2


v
f
=?

Hidden Variables


Objects falling through space can be
assumed to accelerate at a rate of

9.8m/s
2
.


Starting from rest corresponds to a v
i
=0


A change in direction indicates that at some
point v=0.


Dropped objects have no initial velocity.


Practice Problem 2


A penguin slides down a glacier starting from
rest, and accelerates at a rate of 7.6m/s
2
. If it
reaches the bottom of the hill going 15m/s,
how long does it take to get to the bottom?

Acceleration

Define
acceleration

as how fast velocity changes

Acceleration is a rate of a rate (units will have 2 time
values)

(ACCELERATION) =

(Change in Velocity)

(Time interval)

Note: An object accelerates anytime its velocity
changes.

Examples include:


Object speeds up.


Object slows down


Object changes direction (curved path)

Best example of acceleration is objects in free fall

Acceleration

Free
-
fall


falling under the influence of gravity
only

with no air resistance


freely falling objects on Earth gain

speed at the rate of 10 m/s each

second (more precisely, 9.8 m/s
2
)








Gravity


Gravity causes an acceleration.


All objects have the same acceleration due to
gravity.


Differences in falling speed/acceleration are
due to air resistance, not differences in gravity.


g=
-
9.8m/s
2


When analyzing a falling object, consider final
velocity before the object hits the grounds.


Acceleration

Galileo first formulated the
concept of acceleration in his
experiments with inclined
planes.







When we say that an object is being accelerated, we
mean that


1) it is at rest,


2) it is moving,


3) it is either at a state of rest or a state of constant
velocity,


4) its state of motion is changing,

and we define acceleration to be


5) a change in speed.


6) a change in velocity.


7) the rate at which speed changes.


8) the rate at which velocity changes.



An object is accelerating if it moves


1) with constant velocity


2) in a circular path


3) in a straight
-
line path


because it is undergoing a change in its


4) speed.


5) direction


6) net force.


A car increases its speed from 60 to 65 miles per
hour in the same time that a bicycle increases its
speed from rest to 5 miles per hour. In this case the
acceleration is greater for the


1) car,


2) bicycle,


3) is the same for each,


principally because


4) the car undergoes the greater change in velocity.


5) the bicycle has considerably less mass.


6) both undergo equal increases in speed
during
the same interval of time.




Equation for displacement

t
d
v



f
i
v
v
v


2
1
t
v
d



t
v
v
d
f
i


2
1
Practice Problems


A car slows from 45 m/s to 30m/s over 6.2s.
How far does it travel in that time?



A cyclist speeds up from his 8.45m/s
pace. As he accelerates, he goes 325m
in 30s. What is his final velocity?

Equation that doesn’t require v
f



t
v
v
d
f
i


2
1
at
v
v
i
f




t
at
v
v
d
i
i



2
1
)
2
(
2
1
at
v
t
d
i


2
2
1
at
t
v
d
i


Practice Problems

A ball rolling up a hill accelerates at

5.6m/s
2

for 6.3s. If it is rolling at 50m/s initially, how far

has it rolled?

If a car decelerates at a rate of

4.64m/s
2

and it travels 162m in 3s, how fast was it
going initially?

An equation not needing t



t
v
v
d
f
i


2
1
at
v
v
i
f


at
v
v
i
f


t
a
v
v
i
f















a
v
v
v
v
d
i
f
f
i
2
1










a
v
v
d
i
f
2
2
2
1
2
2
2
i
f
v
v
ad


A bowling ball is thrown at a speed of

6.8m/s. By the time it hits the pins 63m

away, it is going 5.2m/s. What is the

acceleration?

The Big 4

at
v
v
i
f


ad
v
v
i
f
2
2
2


t
v
at
d
i


2
2
1


t
v
v
d
f
i


2
1
A plane slows on a runway from 207km/hr

to 35km/hr in about 527m.


a. What is its acceleration?


b. How long does it take?

Ticker Tapes


A common way of analyzing the motion of objects in physics labs is to
perform a ticker tape analysis. A long tape is attached to a moving
object and threaded through a device that places a tick upon the tape
at regular intervals of time


say every 0.1 second. As the object
moves, it drags the tape through the "ticker," thus leaving a trail of
dots. The trail of dots provides a history of the object's motion and is
therefore a representation of the object's motion.










The distance between dots on a ticker tape represents the object's
position change during that time interval. A large distance between
dots indicates that the object was moving fast during that time
interval. A small distance between dots means the object was moving
slow during that time interval. Ticker tapes for a fast
-
moving and a
slow
-
moving object are depicted below.




The analysis of a ticker tape diagram will also reveal if the
object is moving with a constant velocity or with a changing
velocity (accelerating). A changing distance between dots
indicates a changing velocity and thus an acceleration. A
constant distance between dots represents a constant velocity
and therefore no acceleration. Ticker tapes for objects moving
with a constant velocity and an accelerated motion are shown
below.


Uniform Motion



Position vs. Time Graph



Velocity vs. Time Graph





Nonuniform Motion
-

Changing Velocity



Position vs. Time Graph



Velocity vs. Time Graph





Q
: What does the slope
on a
Position vs. Time

Graph tell us?







Q:

What does the slope on a
Velocity vs. Time

Graph tell
us?


A:

The slope on a Position vs. Time
Graph tells us the
velocity
. A positive
slope indicates a positive velocity. A
negative slope indicates a negative
velocity.









A: The slope of a velocity vs. time graph
tells us the
acceleration
. A positive
slope indicates a positive acceleration. A
negative slope indicates a negative
acceleration.

The
slope or gradient

of a distance
-
time graph is
increases with
speed.


distance

time

Question 2

Describe the motion of the three buses X, Y and Z
shown in the graph below.

Uniformly Accelerating Objects


You see the car move
faster and faster. This is a
form of acceleration.


The position vs time graph
for the accelerating car
reflects the bigger and
bigger
D
x values.


The velocity vs time graph
reflects the increasing
velocity.

Velocity
-
time graphs

velocity

time

The
slope

of a
velocity
-
time graph
represents
acceleration
.


constant velocity
or zero acceleration

Constant Velocity


This graph shows that
the velocity:

1.
is 1 m/s.

2.
stays constant at 1 m/s
for 10 seconds.

Activity #1


Predicting the fall time of
a ball


Predict how long it will take for a ball to fall
_____ meters


Show all your work and calculations


Test your hypothesis and actually time the fall


Perform at least 8 trials and find the average
fall time


Plug your time and distance values into an
equation to find the acceleration (a or g) and
see how close your value comes to 9.8 m/s/s

Activity #2


Reaction Time


Use a ruler/meter stick and calculate


your reaction time


Compare this to class/larger sampling size averages


Have one partner hold a ruler/meter stick vertically. The other
partner places their hand at the 0 cm mark. Catch the ruler and
record the distance.


Record the drop distance in cm 5 times and find the average


Calculate your average reaction time using the distance formula,
being careful to make sure your units are converted!


The average reaction time for the general population is
approximately 0.2


0.25 seconds



Activity #3


Tin pan alley


Galileo conducted an experiment similar to this to help him
determine the equation for free fall in relation to distance, time
and gravity.


Attach a set of 6 ½ inch hex nuts to a string so that the nuts will
hit the pie pan at equal time intervals


Place your first hex nut at 15 cm


The falling nuts will accelerate (speed up) as they fall due to
gravity. How will you have to place your hex nuts on the string
so that the “clangs” occur at equal time intervals?


Are there any equations that can help you calculate the proper
distances?


Record the exact spacing between the nuts that resulted in the
clangs occurring at equal time intervals. Show all calculations!!