The Car & Ramp

1. The Car & Ramp CPO Science

2. Key Questions • How do we measure and describe the world around us? • What is speed and how do we measure it? • Can you predict the speed of the car at any given point on the ramp?

3. Overview • Timer Functions • Using the Timer • Measuring Speed • Graphing Speed • Predicting Speed from our Graph

4. CPO Timing System

5. CPO Timing System • How can we measure time accurately? • Using the timer in stopwatch mode; Who can get the fastest time? • The 100 meter race • One runner has a time of 10.01 seconds • Another runner has a time of 10.00 seconds • Who wins?

6. Photogates • How does the Photogate start and stop the timer? Do the speed challenge. • What happens when you block the light beam several times in succession; does the timer reset, or does it add the times? • Plug the second photogate into the B port.

7. How does the timer work like 3 internal stopwatches?

8. Review • How do you start the timer? • How do you stop the timer? • If you block the light beam several times in a row, does the timer start from zero each time, or are the times added? • What does the timer measure when the A light is on? • What does the timer measure when the B light is on? • What does the timer measure when both lights are on?

9. Motion Investigation #1 • Why does the car have a tab on the side?

10. Ramp Height • Design a quick experiment to see what effect ramp height has on the TIME it takes the car to move from Photogate A to Photogate B. • Ramp hole #: 3, 5, 7, 9

11. What Happened? • What are the variables in this experiment? • Distance between A & B • position of A & B • Weight • starting point • friction • start technique • Ramp angle

12. Technique • Practice your drop technique until you get three identical times in a row! This is very important for data collection in the next investigation!

13. Controlling Variables • Now Let’s try that experiment again, and this time we will do our best to control all variables except ramp height.

14. The One-Foot Race

15. 1.Human fast walk 2. Snail 3. Hair growth 4. Continental drift 5. Concorde SST 6. Winner of 100 m dash 7. Tsunami (tidal wave) 8. Running cheetah 9. Fastball pitch (Nolan Ryan, 1974) A. 1.2 x 101 B. 4.5 x 101 C. 7.1 x 102 D. 2.8 x 101 E. 2.0 x 102 F. 3.0 x 10-9 G. 1.0 x 10-3 H. 1.3 x 100 I. 1.0 x 10-9 How Fast? Match them up!(m/s)

16. 1. Human fast walk 2. Snail 3. Hair growth 4. Continental drift 5. Concorde SST 6. Winner of 100 m dash 7. Tsunami (tidal wave) 8. Running cheetah 9. Fastball pitch (Nolan Ryan, 1974) H. 1.3 x 100 G. 1.0 x 10-3 F. 3.0 x 10-9 I. 1.0 x 10-9 C. 7.1 x 102 A. 1.2 x 101 E. 2.0 x 102 D. 2.8 x 101 B. 4.5 x 101 How Fast? Match them up!(m/s)

17. Using a model to predict speed of car • Turn to investigation 2.1, Foundations of Physical Science Investigation Manual

18. Make a Graph of Speed vs. Displacement • Why do we start with this graph? • Only need 1 photogate • Can make predictions with graph • What is the dependent variable, and do we assign it to the X or Y? • What is the independent variable? • Should we connect the data points? • What does the graph tell us about the speed of the car as it rolls down the ramp? • Explain why the graph is a curve

19. Test the Graphical Model • Connect the data points on your graph • Without using the car/ramp setup, predict what the speed of the car at clamp B would be if the photogates were 27 cm apart. • Test your prediction! • Calculate % error

20. The amazing Carnak • Place the Photogate at the 38 cm mark • Turn the timer face down on the table • Run the car down the ramp; DON’T TURN THE TIMER OVER, THAT’S CHEATING • Use your graph and a little algebra to predict the time on the display • Write the time on your white board • Turn the timer over! How close were you? • Calculate % error • THIS IS YOUR GRADE!

21. Position vs. Time • Suppose we want to collect data and graph the relationship between displacement of the car and time (distance vs. time graph). • How do we measure the distance? • How do we measure the time? • What change in our setup is required?

22. Series of Trials • Place photogate A at the top of the ramp, but be sure the wing doesn’t break the beam while the car is at rest. Don’t move A!!! • Place Photogate B at 6 different places along the ramp. • Measure: • Displacement (distance from A to B) • Time A, Time B, Time from A to B

23. Graphing Data • What is the dependent variable? • Displacement; the distance the car moves depends on how much time has elapsed • What is the independent variable? • The time it took the car to move from A to B • Create the d/t graph. • What does the graph tell us about the motion of the car? • Why is the graph a curve?

24. Using a Graph for Predictions • Time to make another prediction! • Place the photogates 55 cm apart. • Turn the timer over and run the car down the ramp • What will the timer read? Make your prediction, check it, and calculate % error • What is your grade on this investigation?

25. Acceleration • What is acceleration? • How could we find the acceleration of the car on the ramp? • Place photogates 20 cm apart at different places on the ramp, and find acceleration • How do accelerations compare at different places on the ramp? • How could I make the acceleration greater?

26. Testing Different Variables • What other combination of variables have we not yet graphed and investigated? • Speed of car vs. elapsed time • Do we need to run more trials to collect data for this? • No, we need to calculate speed at B from previous data • Calculate speed at B for each of the trials in investigation #3

27. More Graphing • What is the dependent variable? • Speed at B; it depends on the time elapsed • What is the independent variable? • Time elapsed from A to B • Create a graph of Speed vs. Time

28. What is different about the “look” of this graph when compared to the other two graphs we created? • It’s a line! What equation describes the relationship between x and y variables for a straight line? • y=mx+b

29. Using the Line Equation • Substitute variable names from our experiment for each of the letters in the equation y=mx+b. • What does y represent? • Speed at b, or VB • What does x represent? • Time elapsed, or tAB • What does b represent? • This is a challenge! Check out the other data we collected and see if you can figure it out • Speed at A, or VA

30. What does m represent? • Slope of the line • How do you find the slope? • Change in y over change in x • What quantity is defined as the change in speed over time? • Acceleration!

31. Rearanging the Equation • Write the equation of the line using the physics variables • VB = at + VA • Physical Science teachers will recognize this as a= (Vf – Vo)/t • You have just used a graph to show the relationship between 4 different physical variables! You derived the equation for finding acceleration! • Use your graph to find b (VA) & m (a)

32. Prediction Vs. Experiment • For each of the following times, use your equation to find the speed at B and plot these data points on your experimental graph of speed vs. time • T= 0.2000, 0.3000, 0.4000, 0.5000 • Find VB for each of these times • Plot the ordered pairs on your experimental graph • How close does your prediction match your experiment?

33. Summary • In many situations, like the car/ramp, the distance, speed, time, and acceleration are all important variables. • We know how to relate speed, distance, and time s = d/t; but without acceleration. • We know how to relate speed, time, and acceleration a = (Vf – Vo)/t; but without distance. • How do we relate all four variables for a more general description of motion?

34. See handout with explanation of finding area under speed/time graph