Gears+and+Speed

(back) []

Worksheet: Gears and Speed

Teeth || Driven Teeth || Gear Ratio
 * Condition || Drive

__Driven__ Driving || Time robot traveled (sec) || Distance Robot traveled (cm) || Average distance robot traveled || Average Speed (cm/sece) || Hypothesis A Predicted Speed (cm/sec) || Hypothesis B Predicted Speed (cm/sec) || 16:16 ||  ||   ||   ||   || 1. ||   ||   || XXXXXXXXXX || XXXXXXXXXXX || 20:12 ||  ||   ||   ||   || 1. ||   ||   ||   ||   || 12:20 ||   ||   ||   ||   || 1. ||   ||   ||   ||   ||
 * Condition 1
 * XXXXXXX || XXXXXXX || XXXXXXX || XXXXXXX || XXXXXXX || 2. || XXXXXXX ||  || XXXXXXXXXX || XXXXXXXXXXX ||
 * XXXXXXX || XXXXXXX || XXXXXXX || XXXXXXX || XXXXXXX || 3. || XXXXXXX ||  || XXXXXXXXXX || XXXXXXXXXX ||
 * Condition 2
 * XXXXXXX || XXXXXXX || XXXXXXX || XXXXXXX || XXXXXXX || 2. || XXXXXXX ||  || XXXXXXXXXXX || XXXXXXXXXX ||
 * XXXXXXX || XXXXXXX || XXXXXXX || XXXXXXX || XXXXXXX || 3. || XXXXXXX ||  || XXXXXXXXXXX || XXXXXXXXXX ||
 * Condition 3
 * XXXXXXX || XXXXXXX || XXXXXXX || XXXXXXX || XXXXXXX || 2. || XXXXXXX ||  || XXXXXXXXXXX || XXXXXXXXXXX ||
 * XXXXXXX || XXXXXXX || XXXXXXX || XXXXXXX || XXXXXXX || 3. || XXXXXXX ||  || XXXXXXXXXXX || XXXXXXXXXXX ||

Introduction to Mobile Robotics > Gears and Speed Investigation

This worksheet is provided for reference only. Be sure that you follow the steps in the online directions, and answer the questions at the appropriate times. Fill out all your answers on a separate sheet of paper.

Condition 1: Take Measurements

Record your calculations: 1. Number of teeth on each gear, reduced gear ratio (see data table on last page of worksheet).

2. Distance traveled in each trial. Condition 1: Calculate Speed

3. Look at the data in your table. i. Did the robot go the exact same distance in all three trials? Why or why not?

ii. Calculate the average distance that the robot went with these gears and this program.

iii. What is the purpose of averaging the three distances?

4. Calculate the robot’s average speed for this gear ratio.

5. Do you have enough information to draw any conclusions about the two hypotheses yet? Explain why or why not?

6. The instructions tell you to measure from the front of the robot to the back of the line.

Why shouldn’t you measure the space “between” the robot and the line (from the back of the robot to the front of the line) instead?

7. Based on the average speed you measured in Condition 1 (Speed 1), what does Hypothesis A predict that the average speed will be for Condition 2? In Condition 2, you will have a 20-tooth gear driving a 12-tooth gear. Fill this in your data table.

Hypothesis A (Speed 1 / Gear Ratio 1) = (Speed 2 / Gear Ratio 2)

Known: Speed 1 = ..........cm/sec

Gear Ratio 1 = ............

Gear Ratio 2 = ............

Find: Predicted Speed 2: ..............cm/sec Record your calculations:

8. Based on the average speed you measured in Condition 1 (Speed 1), what does Hypothesis A predict that the average speed will be for Condition 3? In Condition 3, you will have a 12-tooth gear driving a 20-tooth gear. Fill this in your data table.

Hypothesis A (Speed 1 / Gear Ratio 1) = (Speed 3 / Gear Ratio 3)

Known: Speed 1 = cm/sec

Gear Ratio 1 =

Gear Ratio 3 =

Find: Predicted Speed 3: .................cm/sec

Record your calculations:

9. Based on the average speed you measured in Condition 1 (Speed 1), what does

Hypothesis B predict that the average speed will be for Condition 2? In Condition 2,

you will have a 20-tooth gear driving a 12-tooth gear. Fill this in your data table.

Hypothesis B

(Speed 1 x Gear Ratio 1) = (Speed 2 x Gear Ratio 2)

Known:

Speed 1 = .................cm/sec

Gear Ratio 1 = ...............

Gear Ratio 2 = ...................

Find:

Predicted Speed 2: .........................cm/sec

10. Based on the average speed you measured in Condition 1 (Speed 1), what does

Hypothesis B predict that the average speed will be for Condition 3? In Condition 3,

you will have a 12-tooth gear driving a 20-tooth gear. Fill this in your data table.

Hypothesis B

(Speed 1 x Gear Ratio 1) = (Speed 3 x Gear Ratio 3)

Known:

Speed 1 = ..............cm/sec

Gear Ratio 1 = ..............

Gear Ratio 3 = ..................

Find:

Predicted Speed 3: ___cm/sec

11. Number of teeth on each gear, reduced gear ratio (see data table on last page of worksheet).

12. Distance traveled in each trial.

Condition 2: Calculate Speed 13. Calculate the average distance that the robot went with these gears and this program.

14. Calculate the robot’s average speed for this gear ratio.

15. Examine Hypothesis A.

i. From Question 7, what did Hypothesis A predict for the speed of Condition 2?

ii. What was the actual average speed you found using this gear ratio (from Question 14)?

iii. Do these values seem to match closely?

16. Examine Hypothesis B.

i. From Question 9, what did Hypothesis B predict for the speed of Condition 2?

ii. What was the actual average speed you found using this gear ratio (from Question 14)?

iii. Do these values seem to match closely?

17. Compare the two hypotheses.

i. Did Hypothesis A or Hypothesis B do a better job of predicting the effect that changing the gear ratio will have on speed?

ii. Explain your answer to part (i) using numeric evidence.

iii. Is this enough evidence to prove that one hypothesis is incorrect? Explain briefly.

iv. Is this enough evidence to prove that one hypothesis is correct? Explain briefly.

v. Which hypothesis (if any) do you believe has stronger support at this point in time, and why?

18. Number of teeth on each gear, reduced gear ratio for this condition (see data table on last page of worksheet).

19. Distance traveled in each trial.

Condition 3: Calculate Speed

20. Calculate the average distance that the robot went with these gears and this program.

21. Calculate the robot’s average speed for this gear ratio.

22. Examine Hypothesis A.

i. From Question 8, what did Hypothesis A predict for the speed of Condition 3?

ii. What was the actual average speed you found using this gear ratio (from Question 21)?

iii. Do these values seem to match closely?

23. Examine Hypothesis B.

i. From Question 10, what did Hypothesis B predict for the speed of Condition 3?

ii. What was the actual average speed you found using this gear ratio (from Question 21)?

iii. Do these values seem to match closely?

24. Compare the two hypotheses.

i. Did Hypothesis A or Hypothesis B do a better job of predicting the effect that changing the gear ratio will have on speed?

ii. Explain your answer to part (i) using numeric evidence.

iii. Combined with your results from Condition 2 (Question 17), is this now enough evidence to prove that one hypothesis is incorrect? Explain briefly.

iv. Is this now enough evidence to prove that one hypothesis is correct? Explain briefly.

v. If you had to decide right now to support one hypothesis over the other, which would you choose as the correct hypothesis, and why?

25. Summarize the conclusion you reached regarding which of Hypotheses A or B was correct, and explain the steps you followed in order to reach this conclusion.

26. Commonly, two values will be either directly proportional or inversely proportional.

i. Directly proportional values are values that increase and decrease together, always by the same factor. Doubling one value means the other must double as well. Which hypothesis predicted that gear ratios and robot speeds would be directly proportional?

ii. Inversely proportional values are values that increase and decrease oppositely from each other, but always by the same factor. Doubling one value means the other will cut in half. Which hypothesis predicted that gear ratios and robot speeds would be inversely proportional?

iii. Based on your results, did gear ratio and robot speed turn out to be directly proportional, inversely proportional, or neither?

iv. If you did the Wheels and Distance investigation, would you call the relationship between wheel size and distance directly proportional, inversely proportional, or neither?

Gears and Speed Review