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!