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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

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## The Car & Ramp

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**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**• 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?**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.**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?**Motion Investigation #1**• Why does the car have a tab on the side?**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**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!**Controlling Variables**• Now Let’s try that experiment again, and this time we will do our best to control all variables except ramp height.**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 How Fast? Match them up!(m/s)**Using a model to predict speed of car**• Turn to investigation 2.1, Foundations of Physical Science Investigation Manual**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**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?**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**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?**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**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**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**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

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