Determining g on an Incline Created for CVCA Physics By Dick Heckathorn 1 December 2K+3

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

Objective 1 Use a Motion Detector to measure the speed and acceleration of a cart rolling down an incline.

Objective 2 Determine the mathematical relationship between the angle of an incline and the acceleration of the cart rolling down the ramp.

Objective 3 Determine the value of free fall acceleration, g, by extrapolating the acceleration vs. sine of track angle graph.

Objective 4 Determine if an extrapolation of the acceleration vs. sine of track angle is 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 data for times when the cart was freely rolling.

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.

ANALYSIS 1 Did you label the list columns with representative titles?

Analysis 2 Create a new list column for average acceleration and let the calculator determine it.

Analysis 3 Create a new list column for the angle of the ramp relative to horizontal And let the calculator determine it.

Analysis 4 Plot the average acceleration as a function of the angle. (Print out the graph)

Analysis 5 Determine the equation for the data. (Print this out)

Analysis 6 Plot the equation that the calculator determined from the data. (Print this out)

Analysis 7 Show your printout to your instructor. Did you set x-min and y-min to zero?

Analysis 8 Create a new list column for the sine of the angle of the ramp and let the calculator determine it.

Analysis 9 Plot the average acceleration as a function of the sine of the angle. (Print this out)

Analysis 10 Repeat steps 5 through 7.

Analysis 11 On the graph, carry the fitted line out to sin(90 o ) = 1 on the horizontal axis, and read the value of the acceleration. (Print out the graph with the information indicated.)

Analysis 12 How well does the extrapolated value agree with the accepted value of free-fall acceleration (g = 9.8 m/s 2 )?

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

Altitude g Location(m)(N/kg) North Pole Canal Zone New York Brussels San Francisco Chicago Cleveland Denver

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

Altitudeg (m)(N/kg) , , , , , ,

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

Latitudeg (N/kg)

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

That’s all folks!