Determining g on an Incline

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Determining g on an Incline

• Created for CVCA Physics
• By
• Dick Heckathorn
• 1 December 2K3

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Purpose

• The purpose
• of this experiment
• is to find the acceleration
• due to the pull of the earth
• on an object.
• (gravity g).

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Objective 1

• Use a Motion Detector
• to measure the
• speed and acceleration
• of a cart
• rolling down an incline.

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Objective 2

• Determine the
• mathematical relationship between the
• angle of an incline
• and the
• acceleration of the cart
• rolling down the ramp.

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Objective 3

• Determine the value of
• free fall acceleration, g,
• by extrapolating the
• acceleration vs. sine
• of track angle graph.

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Objective 4

• Determine if
• an extrapolation of the acceleration
• vs.
• sine of track angle
• is valid.

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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.

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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?

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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.

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PRELIMINARY QUESTION 4

• Do you think that during Galileos day it was
  possible to get useful data for any of these
  experiments?
• Why?

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Did you?

• Determine the slope of the velocity vs. time
  graph,
• using only the portion
• of the data
• for times
• when the cart
• was freely rolling.

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ANALYSIS 1

• Enter into lists
• of your TI-83 calculator,
• the height of the books,
• the length of the incline
• and the
• three acceleration values.

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ANALYSIS 1

• Did you label
• the list columns
• with
• representative titles?

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Analysis 2

• Create a new
• list column for
• average acceleration
• and let the
• calculator determine it.

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Analysis 3

• Create a new list column
• for the
• angle of the ramp
• relative to horizontal
• And let the calculator
• determine it.

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Analysis 4

• Plot the
• average acceleration
• as a function of
• the angle.
• (Print out the graph)

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Analysis 5

• Determine the
• equation
• for the data.
• (Print this out)

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Analysis 6

• Plot the equation
• that the
• calculator determined
• from the data.
• (Print this out)

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Analysis 7

• Show your
• printout
• to your
• instructor.
• Did you set
• x-min and y-min to zero?

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Analysis 8

• Create a new list column
• for the
• sine of the angle
• of the ramp
• and let the calculator
• determine it.

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Analysis 9

• Plot the
• average acceleration
• as a function of
• the sine of the angle.
• (Print this out)

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Analysis 10

• Repeat
• steps 5 through 7.

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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.)

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Analysis 12

• How well does
• the extrapolated value
• agree with
• the accepted value
• of free-fall acceleration (g  9.8 m/s2)?

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EXTENSION

• Investigate
• how the value of g
• varies around the world.

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g Location Altitude (N/kg) North
Pole 0 9.832 Brussels 102 9.811 New
York 38 9.803 Chicago 182 9.803 Denver 1638 9.79
6 San Francisco 114 9.800 Canal
Zone 6 9.782 Cleveland
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EXTENSION

• For example,
• how does altitude
• affect the value of g?

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Altitude g (m) (N/kg) 0 9.806 1,000 9.803
4,000 9.794 8,000 9.782 16,000 9.757 32,00
0 9.71 100,000 9.60
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EXTENSION

• What other factors
• cause this acceleration
• to vary from
• place to place?

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Latitude g (N/kg) 0 9.7805 15 9.7839 30
9.7934 45 9.8063 60 9.8192 75 9.8287 90 9
.8322
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EXTENSION

• How much can g vary
• at a school in the mountains compared
• to a school
• at sea level?

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Thats all folks!