determining g on an incline created for cvca physics by dick heckathorn 1 december 2k+3
DESCRIPTION
Objective 1 Use a Motion Detector to measure the speed and acceleration of a cart rolling down an incline.TRANSCRIPT
Determining g on an Incline
Created for CVCA PhysicsBy
Dick Heckathorn1 December 2K+3
Purpose
The purposeof this experiment
is to find the accelerationdue to the pull of the earth
on an object.(gravity ‘g’).
Objective 1
Use a Motion Detectorto measure the
speed and accelerationof a cart
rolling down an incline.
Objective 2
Determine themathematical relationship
between theangle of an incline
and theacceleration of the cartrolling down the ramp.
Objective 3
Determine the value offree fall acceleration, g,
by extrapolating theacceleration vs. sineof track angle graph.
Objective 4
Determine ifan extrapolation of the
accelerationvs.
sine of track angleis valid.
PRELIMINARY QUESTION 1
One of the timing devices Galileo used was his pulse.
Drop a rubber ball from a height of about 2 m and try to determine how many pulse beats elapsed before it hits the ground.
PRELIMINARY QUESTION 2
Now measure the time it takes for the rubber ball to fall 2 m, using a wrist watch or calculator timing program.
Did the results improve substantially?
PRELIMINARY QUESTION 3
Roll the cart down a ramp that makes an angle of about 10° with the horizontal.
First use your pulse and then your wrist watch to measure the time of descent.
PRELIMINARY QUESTION 4
Do you think that during Galileo’s day it was possible to get useful data for any of these experiments?
Why?
Did you?
Determine the slope of the velocity vs. time graph,using only the portion
of the datafor times
when the cartwas freely rolling.
ANALYSIS 1
Enter into listsof your TI-83+ calculator,the height of the books,the length of the incline
and thethree acceleration values.
ANALYSIS 1
Did you labelthe list columns
withrepresentative titles?
Analysis 2
Create a newlist column for
average accelerationand let the
calculator determine it.
Analysis 3
Create a new list columnfor the
angle of the ramprelative to horizontalAnd let the calculator
determine it.
Analysis 4
Plot theaverage acceleration
as a function ofthe angle.
(Print out the graph)
Analysis 5
Determine theequation
for the data.(Print this out)
Analysis 6
Plot the equationthat the
calculator determinedfrom the data.(Print this out)
Analysis 7
Show yourprintoutto your
instructor.Did you set
x-min and y-min to zero?
Analysis 8
Create a new list columnfor the
sine of the angleof the ramp
and let the calculatordetermine it.
Analysis 9
Plot theaverage acceleration
as a function ofthe sine of the angle.
(Print this out)
Analysis 10
Repeatsteps 5 through 7.
Analysis 11
On the graph, carry the fitted line out to sin(90o) = 1
on the horizontal axis,and read the value of the
acceleration.(Print out the graph with the
information indicated.)
Analysis 12
How well doesthe extrapolated value
agree withthe accepted value
of free-fall acceleration (g = 9.8 m/s2)?
EXTENSION
Investigatehow the value of g
varies around the world.
Altitude gLocation (m) (N/kg)
North Pole 0 9.832 Canal Zone 6 9.782 New York 38 9.803
Brussels 102 9.811San Francisco 114 9.800
Chicago 182 9.803 Cleveland 210 9.802
Denver 1638 9.796
Altitude g(m) (N/kg)
0 9.8061,000 9.8034,000 9.7948,000 9.782
16,000 9.75732,000 9.71
100,000 9.60
EXTENSION
What other factorscause this acceleration
to vary fromplace to place?
Latitude g(N/kg)
0 9.780515 9.783930 9.793445 9.806360 9.819275 9.828790 9.8322
EXTENSION
How much can ‘g’ varyat a school in the mountains
comparedto a school
at sea level?
That’s all folks!