Velocity Lesson Plan

VELOCITY LESSON PLAN Part 1, “Wet” lab. Simple Motion

In this activity we will concentrate on the simplest motion possible and make careful observations. These observations, and the discussions, which follow, will lead you to a scientific definition for the simple motion.

We will use some of the following equipment for this activity.  Meter stick Stop watch  Tape measure Heavy ball (such as a bowling ball)  Graph paper Ruler Bean bags

We will start by looking at a class of simple motions. When faced with a phenomenon that is new to them, scientists first consider the simplest case they can think of, before trying to describe something extremely complicated.

Most people would agree that one of the simplest possible motions is when an object moves in a straight line without speeding up or slowing down. We might call this a uniformly moving object or an object that moves with a constant speed. We will now attempt to describe precisely what it means to move with constant speed.

Activity: Measurements and Graphs a) For our first experience with measurements and graphing, we will be measuring the distance traveled by a rolling ball at specific instants of time. Please put the distance into meters. Let’s work together to measure the distances traveled by a rolling ball at 1 second intervals. Let’s try rolling the ball slowly the first time and then rolling the ball more quickly. i) Briefly describe how we conducted this experiment.

ii) Record the data. b) When scientists make graphs, it is customary to plot the independent variable along the x-axis and the dependent variable along the y-axis.

What is an independent variable?

What is the independent variable for this experiment?

What is a dependent variable?

What is the dependent variable for this experiment?

Follow the directions given in class to graph this data on graph paper. c) Most likely, your points will have some pattern, but will be a little bit scattered about this pattern. Where do you think this scatter comes from? How might you reduce this scatter? Do you think it is possible to eliminate this scatter completely? Explain. d) Scientists are in the business of looking for patterns and simple relationships. Thus, when you see a pattern like the one on the graph you just made, a scientist will often draw a “curve” through the points. This curve represents a mathematical model of what the results of a “perfect” experiment might look like, but will not touch all the points. In this case, your points should lie approximately on a straight line, so the “curve” you draw will be a straight line. Remember, you should not just try and connect the points (no dot-to-dot), but instead, try and draw the “best fit” line that you can between the points. Explain your rationale for determining what the “best fit” is (for those of you who have used r2, remember, close to 1.00 is best).

So, assuming that the small amount of deviation we see with the connecting the points is due to human and experimental error, we would then assume that the overall pattern is a straight line – and it is. e) Find the slope (rise/run) and y-intercept of your best-fit line and record in your lab notebook. f) I feel that it is important that you make your first graphs by hand so that you know how a graph is put together and how to calculate slope, etc. However, for most of the experiments this semester we will use Excel to graph our data. Make a graph this data using Excel, add the trendline and the equation to the graph and turn in a copy of this graph with your carbons. If you don’t remember how to graph in Excel, the appendix “Graphing Help” may be useful.

Using the Motion Detector to Study Motion

In the last section you were introduced to graphical representation and mathematical models. In this section we will introduce you to some of the powerful capabilities of today’s personal computers by interfacing some electronic tools that will help simplify the measurement process.

Tracking Motion with a Motion Sensor

We will be studying the motion of an object using a computer-based laboratory system consisting of a microcomputer, an electronic interface, a sensor, and special software that will help make the output of the electronic interface understandable by humans. One of the sensors we will be learning to use is an ultrasonic motion detector. When the motion sensor is attached to the computer, the distance of an object from the sensor is recorded automatically. Computer software allows you to display these distances almost instantly in the form of a graph. If the distance changes, you will see the graph of the object’s position change instantly. In addition, the software can use a programmed set of rules to calculate two other quantities that are used to describe motion from distance and time measurements. These include velocity and acceleration. We will have more to say about this in the activities to come.

Things to remember when using a motion sensor: 1. Do not get closer than 0.5 meters from the sensor because it cannot record reflected pulses which come back too soon after they are sent. 2. The ultrasonic waves come out in a cone of about 15. They will “see” the closest object. Be sure there is a clear path between the object whose motion you want to track and the motion sensor.

3. The motion sensor is very sensitive and will detect slight motions. You can try to glide smoothly along the floor, but don’t be surprised to see bumps representing your steps in velocity graphs and even larger bumps in acceleration graphs. Try to mentally level out these bumps and focus on the overall big picture.

4. Some objects like bulky sweaters absorb the signal and may not be “seen” very well by a motion sensor. You may want to hold a book in front of you.

To do the activities that follow you should make sure that (a) an interface is plugged into a power source and connected to your computer, (2) the motion sensor is plugged into the interface and (3) that motion software has been located into the memory of your computer. You should then set up the software to record Position vs. Time graphs for about 15 seconds. Your instructor will give you other information that may be useful

In order to be able to use the motion sensor to get some useful data, you must first learn how to use it. The next activity allows you some time to get familiar with the equipment you will be using. You may need to ask your instructor for details on how your motions sensor and software work.

Activity: Playing Around a) To get a feel for the capabilities of the motion sensor, begin by simply standing in front of it. Try walking slowly towards or away from the sensor. Are these measurements similar to or different from the measurements you made with the rolling ball? b) One of the nice aspects of computers that they can do things extremely fast and accurately. Walk with a constant speed towards the sensor. Now walk twice as fast toward the sensor. Try walking away from the sensor. How do these graphs differ? How do they compare with the predictions you made in PRELAB QUESTION #3? Make a careful sketch of these graphs in your lab notebokk (mentally smoothing bumps). Be sure to indicate units and label axes. Have your instructor check your sketches. NOTE: the most important features are if the slope is greater vs. less, + vs. - etc. Therefore, these aspects of the graph must be preserved. c) Look at the following position-time graph. Explain in your lab notebook what you would need to do (in words) to reproduce this graph. Then try and reproduce it. Check your reasoning for a) through c) with a staff member. 4

Position (m) 2

0 2 4 6 8 10 12

Time (s)

So far we have been dealing with “uniform”, or constant velocity motion. When an object moves with a constant velocity, we have seen that the position of the object changes linearly with time, with the slope of the line representing how much the object’s position changes in one second. This became our definition for velocity, at least for the case of uniform motion. We have not yet considered what happens if the object is speeding up or slowing down. What would a position vs. time graph look like then? How can we define velocity? What would a velocity vs. time graph look like? These are some of the questions that we will attempt to answer in the following activities.

Activity: The velocity-time graph a) Notice that the computer software allows you to display two graphs at the same time. Choose two graphs, and let one be a position graph, while the second is a velocity graph. Now walk slowly away from the detector (constant speed), and make careful sketches of the two graphs in your lab notebook.

b) Try walking slowly toward the detector (Constant speed). Again, make careful sketches of the position vs time graph and the velocity versus time graph in your notebook.

c) In your own words, describe how a velocity graph is related to a position graph. Check these against your predictions in pre-lab question #4. Check your results with your instructor.

Activity: Non-Uniform Motion—Experiments

a) Set up the motion detector so that the software is displaying both a position-time graph and a velocity-time graph. Experiment with the following motions in front of the sensor that are not uniform. To simulate speeding up in a car, try starting from rest and then walking towards (or away from) the motion sensor, getting faster and faster as time goes on. Try and obtain a velocity graph that looks linear. (It’s not as easy as it sounds) Show a rough sketch of what you a) position-time and b) velocity-time graphs look like in your notebook (mentally smoothing any spiky areas). The compare to PRELAB question #5 and #6. b) Repeat, but this time try walking toward or away from the detector while slowing down. Again, sketch your two graphs in your notebook. Compare to PRELAB question #7. c) Set up the motion sensor to track the motion of a fan cart. Start the cart at rest, near the motion sensor (at least 0.5 meters away) and let it accelerate away. Describe the velocity-time graph and the position-time graph. Make careful sketches of the two graphs in your notebook. Recall that our definition for velocity (for an object moving with constant speed) had a nice graphical representation. The velocity was equal to the slope of the position-time graph. Can you think of a way of defining velocity when the position-time graph is not a straight line, as is the case with the graphs above? That is, how would you define velocity when the velocity is not constant? d) What about acceleration? Since velocity describes changes in position and acceleration describes changes in velocity, can you define acceleration similar to the way velocity was defined? Give a definition for acceleration when the object’s velocity is changing at a constant rate (this can be graphical or mathematical).

PART II. Simulation. Go to the Moving Man applet by following the “Velocity” link at the bottom of the lesson plan repository (http://www.colorado.edu/physics/phet/simulations/movingman/movingman.jnlp).

Several of the above activities can be practiced and reinforced using “Moving Man” applet. Then we will compare the results below to the results above.

1. Click on the man, and the clock will start. Move the man slowly to the right for about 10 seconds. Try to keep the same speed. Is the velocity positive or negative? ______Is it constant? ______If you velocity is constant, what is the acceleration?______2. Move the man with a constant speed to the left for about 10 seconds. What is the velocity?______What is the acceleration?______3. Sketch the graphs you made in 1 and 2 above. DD

4. Restart. Move the man very slowly to the right and increase its speed very slowly. What is his acceleration?______Decrease his speed. What is the sign of his velocity (+ or -)?_____ What is happening to his velocity? + (increasing) or – (decreasing).___. What is his acceleration? 5. Draw a sketch of the graph you made in 4 above.

A 6. KEY! Is it possible to have a positive velocity and a negative acceleration? Explain.

7. Start the simulation over. Move the man to the left, increasing speed as you go. a. What is the velocity? b. Is he moving faster or slower? c. Is acceleration positive or negative? 8. So. Can you have a negative acceleration but be speeding up? Explain.

9. Practice moving the man by moving the arrows along the right side for position, acceleration, and velocity.

10. Which is easier to control (for instance, move at a constant speed? Move to a selected location. Move with a specific acceleration?)? Moving the man by clicking on the man or with the sliders? Explain.

11. Now that you can control the moving man, see if you can create a distance vs. time graph like in PART 1, Playing Around, C) on the top of page 4. Describe how you created that graph using the moving man.

12. Compare the Moving Man activities 1-11 to the wet lab activities. How were they alike? How were they different? What did you understand better after doing the Moving Man?