NAME: LINEAR KINEMATICS Learning objectives: To increase ...

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14 Νοε 2013 (πριν από 3 χρόνια και 11 μήνες)

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NAME:

__________________________________________



LINEAR KINEMATICS

Learning objectives:

To increase understanding of displacement, speed, velocity, and acceleration and how they are
measured. To increase you ability to utilize Microsoft Excel to
manipulate and graphically display data.


Part I


Video Analysis:
Please download
lab7.xls

from the class website. This is a Microsoft Excel data file with
temporal (time) data on the former world record (WR) holders in the Men's 100m dash (Ben Johns
on, Carl Lewis, Maurice
Greene, Tim Montgomery, Asafa Powell, and Usain Bolt). The data is the time at each 10m interval throughout the race.
Hopefully everyone watched Usain Bolt (Jamaica) set the Olympic and World Record at the 2008 Summer Olympic Game
s
in Beijing. He ran an incredible 9.69 seconds for the distance. Take a second to rewatch this performance if you need.


http://www.flotrack.org/videos/speaker/1401
-
usain
-
bolt/180603
-
2008
-
beijing
-
olympic
-
games
-
mens
-
100m
-
final



If you notice in the
video that Usain Bolt actually starts celebrating prior to the finish. Watch the video again and pause
the video at the exact instant you notice him celebrating. Record that time below that is displayed on the video.









INSTANT of CELEBRATING (sec):

_____________


Ultimately we are going to try to determine what Usain Bolt would have run had he not begun his celebrating before the
finish line. Along the way we are going to be calculating other pieces of temporal kinematics to better understand his
WR
performance. His coach, Glen Mills, said, “If he had continued, the slowest he would have run would have been 9.52,"
1

Is
he right? Let's find out.


1. Cage S. Bolt could have run 9.52 in Olympics, coach says. 2008. Available at:
http://www.reuters.com/article/GCA
-
Olympics/idUSLR7089520080827
.








Part II


Data Analysis:



1.

Open the Excel file and in Cell B15 type “
=B3
-
B2
”. This calculates the time to complete the 10m se
gment from 0


10m. Now copy and paste this value throughout the rest of that table. It will automatically calculate all the 10m
segment times. Highlight any cell within this table and look at the formula given above. You should notice that is
NOT “
=B3
-
B2
”. This is an example of RELATIVE REFERENCING within Excel.


2.

Next we want to calculate the AVERAGE VELOCITY (m/s) at each 10m checkpoint throughout the race. Remember
that velocity = (change in distance) / (change in time). In cell B27 type = “
=10/B15
”. Take a second to think about
what the 10 represents and B15 represents. Notice that this is AVERAGE VELOCITY for this 10m segment and not
the INSTANTANEOUS VELOCITY at 10m


there is a difference. Now copy and paste this value into the rest of the
ta
ble.


3.


Now we want to convert the average velocities into some units that we understand a bit better. Convert the
AVERAGE VELOCITY to miles/hour (mph) for each athlete. You will need to determine the conversion from m/s to
mph.


4.

Finally we want to
calculate AVERAGE ACCELERATION for each 10m segment to determine whether a runner was
speeding up (+ value), maintaining (0), or slowing down (
-

value). Remember that acceleration = (change in
velocity) / (change in time). In cell B51 type ”
=B27/B3
”. Cop
y and paste this value in cells C51, D51, E51, F51, G51
and H51. In cell B52 type “
=(B28
-
B27)/B16
”. Copy and paste this value throughout the remainder of the table.
Think about what the formula represents.


5.

Now we want to really analyze Usain Bolt's per
formance and determine how fast he could have run. First we
need to determine at what exact distance he began celebrating. You should have filled in the time above. Fill in
the table below based upon the given data for his race. Position Before (S1) i
s the last original total time data
point for Bolt BEFORE he started celebrating. For instance, if you thought he started celebrating at 4.3 seconds
(
he doesn’t though
), then S1 would be 30m and T1 would be 3.78 seconds.


Position Before (S1) = _______ m

Split Time Previous (T1) = _____

Position of Celebration (Sp)

Time of Celebration (TC) = _____



6.

Use the AVERAGE VELOCITY during that 10m segment, V
average

during the race to calculate the position at that
exact instance. This is a CONSERVATIVE assessment because this AVERAGE VELOCITY took into account his
slowing down due to celebration but we will go with it.




Position of Celebration (Sp) = S1 + (TC


T1)

* V
average




Position of Celebration (Sp) = ________________ m




Distance Remaining (D) = 100


Sp = __________m


7.

Now compute the AVERAGE LOSS of VELOCITY by all other WR runs excluding Bolt. To do this simply average the
difference of the 80
-
90m velocity

with the 90
-
100m velocity of the other 6 WR trials.





Average LOSS of Velocity in Previous WR Attempts (
AL
) =

_______________ m/s




8.

VERY CONSERVATIVE APPROXIMATION: Let's assume that Usain Bolt would have only decelerated such that his
AVERAGE VELOCITY

over the last 10m

would equal his measured 80
-
90m AVERAGE VELOCITY


AL
.




Bolt's Measured 80
-
90m Average Velocity
(AV
80
-
90
) = ____________




Bolt's Approximated Average Velocity from 90
-
100m
(AVA
80
-
90
) =

AV
80
-
90

-

AL = ___________m/s








Bolt's Ap
proximated Time #1 = Actual Time at 90m + (10m /
AVA
80
-
90
) = ____________ s



9.

CONSERATIVE APPROXIMATION: Let's assume that Usain Bolt was able to maintain his measured AVERAGE
VELOCITY from 80
-
90m (
which probably wouldn't be too difficult considering you n
ow know where he started
celebrating!
).




Bolt's Approximated Time #2 = Actual Time at 90m + (10m /
AV
80
-
90
) = ____________ s



10.

AGGRESSIVE APPROXIMATION: Let's now assume that Usain Bolt MAINTAINED his velocity from 80


100m. This
has occurred in previo
us WR runs.




Bolt's Approximated Time #3 = Actual Time at 80m + (20m /
AV
70
-
80
) = ____________ s




LAB WRITE
-
UP QUESTIONS:
Please type up your solutions to the following questions and supply graphs and references
where you feel appropriate. This
write
-
up is due next week.


1.)

What was Usain Bolt's
AVERAGE VELOCITY

for the entire 100m race (mph)?


2.)

What is your best
estimate

of the fastest
instantaneous

horizontal velocity achieved by Usain Bolt during the 100
m dash and where in the dash did it occu
r?


3.)

Which

10
-
m interval

in the dash did the maximum positive acceleration (towards the finish line) occur for Usain
Bolt? What was this value (give units)?


4.)

Which

10
-
m interval

in the dash did the maximum negative acceleration (away from the finish
line) occur for
Usain Bolt? What was this value (give units)?


5.)

What were your 3 approximations for Usain Bolt's non
-
celebration 100m time?


6.)

Make a plot of 10m Interval Split Times (0
-
10m, 10
-
20m, 20
-
30m, 30
-
40m, 40
-
50m, 50
-
60m, 60
-
70m, 70
-
80m, 80
-
90m, 90
-
1
00m) for Bolt's actual time and your 3 approximations (Very Conservative, Conservative, Aggressive).
(
Look at Excel file in I13 to help with this question
).


7.)

In the summer of 2009 Usain Bolt broke this world record at the IAAF World Championships in Berli
n. What time
did he run?