Otterbein University Department of Physics Physics Laboratory 1500-2

EXPERIMENT 1500-2

MOTION DIAGRAMS

APPARATUS

Track and cart, motion detector, LabPro interface. Software: Logger Pro 3.4

INTRODUCTION

In this lab we will explore the motion of objects, and how to efficiently describe this motion. Namely, we will learn how to create motion diagrams (position, velocity or acceleration as a function of time), and how to extract kinematical information from these diagrams. In short, we want to be able to cast the motion of any object in the real, physical world into a two-dimensional plot that captures the essential parameters of the motion. Of course, we can and will also do the opposite: translate the plot into a real, physical motion of an object.

To display the motion diagrams quickly, we will use a motion detector connected to a computer. The motion detector will measure the position of moving objects as a function of time. From the position data, the computer will derive the values of the object’s velocity and acceleration as a function of time. The motion detector uses sonar to measure the distance to an object. It emits a short burst of ultrasound and measures the time for echoes to return to it. Since the velocity of sound is known, the distance can be determined from the echo delay.


The average velocity of the object as a function of time can be determined from the position data using the definition,


This is the average velocity of the ball in the time interval from ti to ti+1. Similarly, once the velocity as a function of time is known, the average acceleration of the ball in the time interval from ti to ti+1 is defined to be

The computer will perform these calculations for you. In practice, the computer also does some averaging of the data as well, to reduce the noise.

SETUP

1. Plug in the LabPro interface, and connect the motion detector to the port Dig/Sonic 1. The LabPro translates the electrical signals from a variety of measuring devices into the digital language of the computer. Put the motion detector on the lab table with the sensor facing the room.

2. Launch Logger Pro by clicking the icon on the desktop that shows a picture of a vernier caliper. Logger Pro collects, displays and analyzes data from the LabPro interface. Let’s adjust some of the settings, to get a feeling for how Logger Pro works.

a. Use a thermometer to determine the room temperature in centigrade. Then under “Experiment” go into “Set up sensors” and click on the motion detector. Enter the temperature in the appropriate field. Logger Pro needs to know this, since the speed of sound in air depends on temperature. Finally, click OK.

b. Click on the button that looks like a clock. Make sure that the mode is set to Real time collect. That tells Logger Pro that time is one of the variables in your experiment. Click on the tab marked Sampling. Set the experiment length to 5 seconds, and the sampling speed to 20 samples/second. Click on the Averaging tab and set the averaging mode to 3 pts. Now Logger Pro will average three data points together when it analyzes your data, in order to reduce the noise.

In the future, you will use pre-programmed setup files, so you won’t always have to go through this procedure; but now you should have a better idea of how Logger Pro works.

3. Check out the motion detector. Click the Collect button. When the motion detector starts to click, place an object (such as your hand) in the ultrasound beam to see if it gives sensible readings. The floor should give a reading of zero, and you should get correct position readings for any object more than 40 cm away from the detector.

The beam of ultrasound makes a cone of about 15°; make sure the object whose position you are measuring is within this cone, and that there are no other objects in the cone that are closer to detector. The motion detector may also be confused by multiple echoes from hard surfaces such as the ceiling and floor. If you get nonsensical distance readings, make sure the motion detector is aimed in the right direction, and that there are no other objects in the way. The problem of echoes can be reduced by reducing the sampling speed, but you don’t want to do that if you don’t have to. Ask the lab instructor or assistant for help if you are unable to get sensible readings from the motion detector.

PART I – MOTION DIAGRAMS

Motion diagrams are plots of position, velocity or acceleration as a function of time. They display the essential parameters of the motion of an object. In this lab, a motion detector plugged into a computer will create these two-dimensional plots for you. The horizontal axis exhibits the independent variable as usual, in this case time. The origin of the time axis, i.e. the moment when t = 0 s, corresponds to the moment when you pressed the “Collect” button to begin taking data. The vertical axis will represent either position or velocity of an object. Note that both quantities change in time, i.e. are functions of time, and therefore dependent variables.

A. Position versus time

Let’s first explore position versus time motion diagrams. What does the computer display on the vertical axis? Position is spatial, i.e. somehow in the room. Where is the position coordinate axis in the space of the physics lab? We have to measure position relative to something; there has to be an origin and a notion both positive and negative directions. Record all answers to the questions. Of course, you are expected to go beyond a simple "yes" or "no" response and provide justification for your answers.

1. Put the motion detector down on a table or counter so that you are not moving it. While recording data, have a member of your group walk toward and away from the detector. Do this multiple times if you need to do so, but ultimately figure out where the position axis origin is located as well as where the positive and negative values of position are located.

2. Next figure out how the graph tells you which way the person was moving and whether they were moving slowly or quickly.

3. Do your answers change if the person stands still and you move the motion detector back and forth? If so, in what way or ways do you they change? Feel free to explore this question by playing with the detector.

4. Using the apparatus you have and just one person moving, can you create a position versus time graph that has the shape of a circle?

Matching a position versus time plot with actual motion

You should now be able to analyze a plot and write a description of motion that might have created the plot. Also, you should be able to move in such a way that you create the plot, which is what we’ll do next.

5. Keeping the motion detector stationary, walk so that you match the graph below.

Write a description of how you had to move to create this graph. Include qualitative descriptions using words such as: toward, away, slowly, quickly, gradually, etc.

6. Keeping the motion detector stationary, walk so that you match the graph below.

Write a description of how you had to move to create this graph. Include qualitative descriptions using words such as: toward, away, slowly, quickly, gradually, etc.

B. Velocity versus time

Let’s now explore velocity-versus-time motion diagrams. Velocity implies a vector quantity so it must convey both speed (magnitude) and direction. In one-dimensional motion the direction is indicated by assigning a positive or negative sign to the speed. This changes the scalar speed into a velocity vector. Keep this in mind as you work through the exercises that follow.

Matching a velocity versus time plot with actual motion

7. Walk so that you match the graph below. Write down a description of how you had to move to create this graph. Include qualitative descriptions.

8. Walk so that you match the graph below. Write down a description of how you had to move to create this graph. Include qualitative descriptions using words such as: toward, away, slowly, quickly, gradually, etc.

Connecting position and velocity graphs

By now you should have a good understanding of how a person's motion in front of the motion detector translates into a velocity versus time graph on the computer. We will now connect the position-time graph to its corresponding velocity-time graph.

9. Go back to the position-time graph of question 5. On a sheet of graph paper, draw a velocity-versus-time graph that matches this motion.

PART II – CART ON TRACK AT CONSTANT ACCELERATION

Now on to some actual physics, namely the motion of objects under the influence of gravity. We are still only describing motion, i.e. asking how something is moving, and not asking why it moves. That is, we are dealing with kinematics, not dynamics. Since we are not allowed to talk about forces yet, we can cast the influence of gravity entirely into a single, simple statement: objects under the influence of gravity move at constant acceleration. In free fall nothing is holding the objects back, so they are subject to the maximal acceleration, which is a=g=9.8 m/s2. This is a large acceleration, and accordingly, objects move very fast – typically too fast for humans to pay attention to precisely how they fall. (Do they speed up? How?) Back in the days, Galileo didn’t even have a watch at his disposal, so he slowed things down in an ingeniously simple way: he put objects on a very slightly inclined plane. This is basically what we did in the last lab, and we shall use the same setup again. However, we will speed things up by putting two big books under the higher end of the track to be able to safely ignore friction.

This part of the lab is transitional, in that we will qualitatively explore the motion of a cart at constant acceleration, before diving into a full quantitative analysis of an object in free fall.

1. Set up the motion detector at the high end of the track, and load the configuration file which will display position, velocity and acceleration as a function of time.

2. Starting from the low end of the track, push the cart uphill so that it turns around roughly in the middle of the track.

3. Print out the three motion diagrams and describe how they look, focusing on the interesting part, i.e. the time when the cart was actively moving.

4. Determine the slope of the velocity plot with the method we learned in the previous lab. What is its connection to the intercept of the (constant) acceleration plot?

5. Make the incline steeper by putting more books under the high end, i.e. increase the angle of inclination. Push the cart so it goes half-way up again and produce a new set of motion diagrams. Describe what changes and what not (shapes, maxima, slopes, intercepts, etc.)

6. Predict what is going to happen if we increase the incline indefinitely, i.e. the inclination angle become 90 degrees.

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