Determining g on an Incline

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

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

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

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

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

6. Objective 4 • Determine if • an extrapolation of the acceleration • vs. • sine of track angle • is valid.

7. 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.

8. 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?

9. 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.

10. PRELIMINARY QUESTION 4 • Do you think that during Galileo’s day it was possible to get useful data for any of these experiments? • Why?

11. 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.

12. 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.

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

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

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

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

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

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

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

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

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

22. Analysis 10 • Repeat • steps 5 through 7.

23. 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.)

24. Analysis 12 • How well does • the extrapolated value • agree with • the accepted value • of free-fall acceleration (g = 9.8 m/s2)?

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

26. Altitude g Location (m) (N/kg) North Pole 0 9.832 Canal Zone 6 9.782 New York 38 9.803 Brussels 102 9.811 San Francisco 114 9.800 Chicago 182 9.803 Cleveland 210 9.802 Denver 1638 9.796

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

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

29. 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

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

31. That’s all folks!