# Key Questions 2.1 : Modeling car’s speed

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Key Questions 2.1 : Modeling car’s speed
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?

Review Set up and explain how you would use the photogates and timer to find the average speed of the car on the ramp Set up and explain how you would use one photogate on the ramp to find an instantaneous speed of the car at some point on the ramp

Review What does the timer display for you when the A light is on?
B light? Both A and B lights? No lights? Does the timer reset itself? Do you have to run the car down the ramp multiple times to get the time at A, time at B, and the time from A to B?

Investigation 2.1 What Are Models?
Scientific Model Physical Model Conceptual Model Graphical or Mathmatical Model Define these vocabulary words for the students and have them give examples. Examples can be found in the textbook on pp Point out that models are a good way to examine a complex question as smaller questions. Models also demonstrate how variables relate to one another.

Developing Models Does the car travel the same speed the entire way down the ramp? How much faster is it going at the bottom? Twice or three times as fast? Can we develop an experiment to answer this question? After answering these questions have the students describe how they would go about developing a model to answer these questions or to test their predictions. The students should realize that a physical model can be used as an experiment to test variables.

Developing An Experiment
What materials will we need? What are the variables? Which is the independent, and which is the dependent? What do we do with the variables we are not testing? After answering these questions have the students describe how they would go about developing a model to answer these questions or to test their predictions. The students should realize that a physical model can be used as an experiment to test variables.

Developing An Experiment
What data will we record? Time through the photogate Position of photogate What will we need to calculate? Speed of car, d/t (tricky! What is the value for d?) After answering these questions have the students describe how they would go about developing a model to answer these questions or to test their predictions. The students should realize that a physical model can be used as an experiment to test variables.

Run The Experiment Set up the car & ramp and record the data Tips:
Be careful at the top and the bottom of the ramp 10 cm is a good interval between data points Make sure that the students do not place the photogate so high on the ramp that the beam is broken before they release the car. Make sure that they do not place the photogate so close to the bottom that the car does not bounce back up through the beam. Also, as the students begin to graph the data, check to make sure their scales are appropriate for the data and that the correct data is on the axis. Reference the teachers guide #1 p. 29 The students should be directed to their Investigations Manual pp.10 & 11, parts 1 & 2

What variable should be placed on the X axis? What variable should be placed on the Y? What does the graph show? How can we use this graphical model to predict the speed of the car at a position we did not include in our data? Make sure that the students do not place the photogate so high on the ramp that the beam is broken before they release the car. Make sure that they do not place the photogate so close to the bottom that the car does not bounce back up through the beam. Also, as the students begin to graph the data, check to make sure their scales are appropriate for the data and that the correct data is on the axis. Reference the teachers guide #1 p. 29 The students should be directed to their Investigations Manual pp.10 & 11, parts 1 & 2

Use your graphical model to predict the speed of the car at 47.0 cm

Calculate percent error

Summary Is there a cause and effect relationship between the speed of the car and its location on the ramp? How do you know? Is the relationship strong or weak? Is the relationship linear? Is it a direct or inverse relationship ? The students at this point should try to summarize their conclusions by use of scientific vocabulary. It may be useful to direct the students to the textbook p If time permits, a discussion of slope and Y-intercept may be useful prior to the next investigation.

Key Questions 2.2: position vs. time
What is the relationship between speed, distance, and time of the car on the ramp? How can we determine speed from a distance vs. time graph?

Developing An Experiment
What materials will we need? What are the variables? Displacement of the car (distance between variables) Time it takes for that displacement to occur We will collect all the data that is available, so we can use it in the next investigation! After answering these questions have the students describe how they would go about developing a model to answer these questions or to test their predictions. The students should realize that a physical model can be used as an experiment to test variables.

Developing An Experiment
What data will we record? Distance from A to B Time from A to B Time at A Time at B What will we need to calculate? Speed of car at A Speed of car at B After answering these questions have the students describe how they would go about developing a model to answer these questions or to test their predictions. The students should realize that a physical model can be used as an experiment to test variables.

Run The Experiment Set up the car & ramp and record the data Tips:
Be careful at the top and the bottom of the ramp 10 cm is a good interval between photogates Make sure that the students do not place the photogate so high on the ramp that the beam is broken before they release the car. Make sure that they do not place the photogate so close to the bottom that the car does not bounce back up through the beam. Also, as the students begin to graph the data, check to make sure their scales are appropriate for the data and that the correct data is on the axis. Reference the teachers guide #1 p. 29 The students should be directed to their Investigations Manual pp.10 & 11, parts 1 & 2

What variable should be placed on the X axis? TIME A to B What variable should be placed on the Y? DISTANCE A to B What does the graph show? How can we use this graph to find the speed of the car at different places on the ramp? Make sure that the students do not place the photogate so high on the ramp that the beam is broken before they release the car. Make sure that they do not place the photogate so close to the bottom that the car does not bounce back up through the beam. Also, as the students begin to graph the data, check to make sure their scales are appropriate for the data and that the correct data is on the axis. Reference the teachers guide #1 p. 29 The students should be directed to their Investigations Manual pp.10 & 11, parts 1 & 2

Use your graphical model to find the speed of the car at two different places; find the slope between two sets of points on the graph

Key Questions 2.3: acceleration
Is the speed of the car changing as it moves down the ramp? What is acceleration? What is the difference between acceleration and speed?

A quick way to find the value for acceleration on the ramp
Place your ramp in hole #5 from the bottom Use two photogates, and figure out what you need to do to find the value for acceleration on this ramp. How will acceleration be calculated? What data do you therefore need to collect? Make sure that the students do not place the photogate so high on the ramp that the beam is broken before they release the car. Make sure that they do not place the photogate so close to the bottom that the car does not bounce back up through the beam. Also, as the students begin to graph the data, check to make sure their scales are appropriate for the data and that the correct data is on the axis. Reference the teachers guide #1 p. 29 The students should be directed to their Investigations Manual pp.10 & 11, parts 1 & 2

Run A Pre-Experiment When you find your value for acceleration, what will the unit be? cm/s/s or cm/s2 Make sure that the students do not place the photogate so high on the ramp that the beam is broken before they release the car. Make sure that they do not place the photogate so close to the bottom that the car does not bounce back up through the beam. Also, as the students begin to graph the data, check to make sure their scales are appropriate for the data and that the correct data is on the axis. Reference the teachers guide #1 p. 29 The students should be directed to their Investigations Manual pp.10 & 11, parts 1 & 2

Finding acceleration another way
Okay, now how could we use a graph to find the acceleration of the car on the ramp? Construct a speed/time graph and find the slope!

Key Questions 3.1: Newton’s 2nd law
What is a force? How does varying the force on the car, while keeping its mass constant, affect its acceleration? What is the relationship between force, mass, and acceleration?

Modification for 3.1 Rather than collecting more data, simply think this experiment through with the entire class After discussing (use a car/ramp setup to demo as you lead the discussion), give data from teacher’s guide to groups and have them try graphing different combinations of the force, mass, acceleration data

Data for 3.1

Relationship between force, mass, and acceleration

Key Questions 3.2: Weight, Gravity, Friction
• How is motion affected by friction? • Do heavier objects fall faster than lighter objects? • What is friction?

Developing An Experiment
After answering these questions have the students describe how they would go about developing a model to answer these questions or to test their predictions. The students should realize that a physical model can be used as an experiment to test variables.

What happened? Does changing the mass significantly affect the speed of the car? Why or why not?

Key Questions 3.3: Newton’s 3rd law
What do we mean by action and reaction? Why don’t equal and opposite forces cancel each other out? What does Newton’s third law mean to everyday experiences? What is equilibrium, and how does it relate to forces?

Concept development Use the car and ramp to set up an action/reaction situation. Diagram, label forces, and discuss. Use the car and ramp to set up an equilbrium situation (level ramp). Take data on speed of the car and discuss. Use Newton’s 3rd law to discuss everyday scenarios and examples of action/reaction