The Car & Ramp CPO Science

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?

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

CPO Timing System

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? The runner with less time elapsed wins. That would be the blue runner, with a time of 10.01, since this is a shorter amount of time than 10.02.

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. The timer begins timing when the invisible infrared beam of the photogate is broken. The timer stops timing when the beam stops being broken and is once again detected by the receptor unit in the photogate. The timer does not need to be reset. Every time the A beam is broken, it resets automatically and begins timing. Resetting will not interfere with the regular function of the timer, but often students will feel more at ease at the beginning of a trial if the timer reads zero, as opposed to the time from the previous trial. If the timer is reset, there will be no confusion and it will definitely read the results from the intended trial. Plugging in photogate B will enable the timer to record the elapsed time from photogate A to photogate B, the time through A as before, as well as time through B. All three will take place at the same time, each trial.

How does the timer work like 3 internal stopwatches? The timer will record the time through A, the time through B, and the elapsed time from A to B. It will do all 3 for each trial, and the results of these measurements are viewed by pushing the corresponding A and B buttons on the timer. A – displays the time through A ( the amount of time the beam in gate A was broken ) B – displays the time through B ( the amount of time the beam in gate B was broken ) A and B – displays the time from A to B ( the amount of time elapsed from when A was broken to when B was broken ) The timer will reset and begin timing automatically each time the beam in A is broken. INTERESTING – Once a trial has been run, and values for A, B, & A and B have been measured, breaking beam B again will update time through B AND the elapsed time, acting like a lap timer. This means that the timer is always counting, and can add time onto the elapsed time whenever needed. How does the timer work like 3 internal stopwatches?

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? The timer starts timing once the invisible infrared beam on the A photogate has been broken.

Motion Investigation #1 Why does the car have a tab on the side? The tab interrupts the beam and provides a measureable change in distance to determine velocity and acceleration

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

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 To do a scientific experiment, we must vary only one variable at a time to determine the impact of this variable to the system. This is a vital part of the scientific method.

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! The drop technique needs to be consistent so as not to alter the measurement of the impact of another variable being tested. The Best technique? The one you do exactly the same each time. The actual mechanics do not matter as long as it does not impede the movement of the car and is repeated exactly each time.

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

The One-Foot Race

How Fast? Match them up! (m/s) 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) 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

Using a model to predict speed of car Turn to investigation 2.1, Foundations of Physical Science Investigation Manual Follow directions for Inv. 2.1 Using a Scientific Model to Predict Speed

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 The x is the independent variable in this case the position on the ramp. The y is the dependent variable, the speed of the car. Connecting the points with straight lines would be incorrect, as the actual shape is a curve. The graph is a curve because the speed does not increase by the same amount for each equal amount of displacement. If it did, the graph would be a straight line and its slope would be constant. That is not what is taking place however. The speed is increasing by an ever decreasing amount as equal amounts of distance are covered by the car moving down the ramp. This will cause the graph to look like it is beginning to plateau out.

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

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!

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? Follow instructions for Investigation 2.2 in the investigation manual, or for more information consult your Teacher’s Guide for Unit 1 Inv. 2.2.

Series of Trials Displacement (distance from A to B) 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

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? We have a situation here that produces a graph that is a curve. It should be pointed out that this graph is different than the first one we made in a couple of ways. First, only one variable is the same, and second, displacement is on the y axis this time, not the x-axis as it was last time. The distance traveled in each equal amount of time is increasing at an increasing rate. For example, in the first tenth of a second it may have traveled 5 cm. In the second tenth of a second it traveled 8 cm, and in the third tenth 12 cm. This makes the graph continuously increase its slope. If the graph kept going, it almost looks like the graph would approach going straight up.

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?

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?

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

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 Speed vs. Time is the subject for Investigation 2.3 – Acceleration.

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 Reviewing point-intercept form may be required for some people.

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 The y-intercept b represents the car’s initial velocity when it went through photogate A, or VA.

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!

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)

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?

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?

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