Introduction to Motion



Name_______________________________Date____________________________

Pre-Lab for Introduction To Motion

(Due at the beginning of the Lab)

Directions:

Download the general lab instructions, read this lab, and answer the following questions:

1. To which USB port on the computer should you connect the Labpro interface, side or back?

2. For the motion detector to make an accurate measurement, what is the minimum distance it can be from an object?

3. What is the name of the port that connects the motion detector and the Labpro interface?

4. How does the Logger Pro software determine whether the direction of motion is positive or negative? Why is there no negative position?

5. What does the “Store Latest Run” feature do?

6. What is the variable used in a position-time graph to refer to the horizontal axis? What is the variable used to refer to the vertical axis?

Introduction to Motion With Logger Pro

Objective Introduction to Logger Pro and the motion detector; graphical analysis of motion

Materials Laptop computer

Motion detector (black)

Black cable with white plugs to connect motion detector to LabPro

LabPro Interface (green)

Power supply plug for LabPro

Black USB cable to connect LabPro interface to computer

Gray printer cable

2-3 metersticks

Introduction In this investigation, you will use a motion detector to plot a position-time graph of your motion.

• The motion detector is the origin from which positions are measured. Since it cannot “see” objects behind it, it can only plot positive position. It can, however, show both positive and negative displacement, velocity and acceleration. The default setting is that motion away from the detector is positive and motion towards the motion detector is negative.

• It detects the closest object directly in front of it. It will not correctly measure anything closer than 0.20 meter. When making your graphs, don't go closer than 0.20 meter from the motion detector.

Logger Pro Setup

1. Plug in the the green LabPro interface with the small power supply using the nearest electrical outlet at the lab table. Then connect it to the side USB port of the computer with the all black cable.

2. Plug the black motion detector into the DIG/SONIC 1 port of the Labpro with the black cable with white plugs. Use the wide beam setting (top of motion detector).

3. Open the Logger Pro program (red caliper icon on desktop). Open the file Away and Back , L01A1-1, (File – Open - Experiments- Additional Physics- Real Time Physics – Mechanics).

4. Answer the dialog boxes; confirm that you want to use a motion detector.

5. When you are ready to start graphing position, click once on the Collect button on the toolbar.

• To adjust the distance reading: If you have a number line and you want the detector to produce readings that agree, stand at the 1-meter mark on the number line and have someone move the detector until the reading is 1 meter.

• To adjust beam direction, turn the knob (just a little!) on the side of the motion detector

• To adjust graph axes use Autoscale (“A” icon in toolbar). This automatically adjusts the graphs for your data, To undo, use undo under the edit menu.

• To adjust the graph axes “manually”: Click and drag on the axis (wavy arrow), or use the cursor to highlight the high/low value of an axis and change it.

• To change data collection time, click on the clock icon on the toolbar at the top. Do not change sampling rate (not the same as data collection time).

Investigation 1: Position - Time Graphs

Activity 1 Make position-time graphs for different walking speeds and directions.

▪ Clear lab tables of backpacks and books

▪ Don’t swing your arms or bounce up or down while walking.

▪ If you get a straight horizontal line, the detector isn’t seeing you. Adjust detector and beam direction.

▪ If you see big spikes on the data, the beam is hitting a chair, floor, or ceiling before the walker. Adjust beam position and/or detector.

▪ “Steadily” means at a constant speed. Don’t speed up or slow down.

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Questions 1. Describe the difference between the graph you made by walking away slowly and the one made by walking away more quickly.

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2. Describe the difference between the graph made by walking toward and the one made walking away from the motion detector.

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Activity 2 Non-Linear Position- Time Graphs

Can you make a curved position-time graph? Try to make each of the graphs shown below.

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Describe how you must move to produce a position-time graph with each of the shapes shown.

Graph A answer:______________________________________________

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Graph B answer:______________________________________________

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Graph C answer:______________________________________________

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Activity 3 Equation of a Line

Make a linear position vs. time graph as before. Direction isn’t important, but it should be linear starting at t=0 (start walking before the program starts graphing). When you get a good graph (i.e. both axes and y-intercept visible), store latest run to keep data displayed and PRINT your graph to the printer (Attach to lab).

Find the equation of the line your walking produced. Don’t forget the y intercept. Do not use the linear fit function. Write your equation (neatly) on your graph. The variable for the y-axis is “x” since it’s the position axis (yes I know it’s weird). The variable for the x-axis is “t”; it’s the time axis. Also, write your equation below, using the same variable convention:

Equation: _____________________________________________

Explain what you did to find the equation:

What are the units of the slope?

Your equation should be the format: x = mt + b, where m is the slope and b is the y-intercept. Explain what m and b actually tell you about the moving object.

m ____________________________________

b _____________________________________

Investigation 2: Velocity-Time Graphs

Activity 1 Making Velocity Graphs

1. Open the experiment file called Velocity Graphs, L01A2-1 (File – Open - Experiments- Additional Physics- Real Time Physics – Mechanics)..

2. Graph your velocity for different walking speeds and directions.

a. Make a velocity graph by walking away from the detector slowly and steadily (i.e. constant speed). Repeat until you get a graph you're satisfied with.

Note: Velocity graphs are a lot harder to make than position graphs! Keep your arms by your sides and shuffle your feet to minimize “bounce”. It may be helpful to hold a notebook against you to provide a flat area.

Sketch your result below. (Just draw smooth patterns; leave out bumps that are mostly due to your steps.)You may want to enlarge the velocity axis to get the “big picture”.

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b. Make a velocity graph, walking toward the detector slowly and steadily. Sketch your graph.

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Questions 3. How does the shape of velocity vs time graphs differ from those of position vs. time graphs for the same motion (i.e. constant speed)? ______________________________________________________________________________________________________________________________________________________________________________________

4. How are the velocity-time graphs different for motion away and motion toward the detector?

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Activity 2 Where did I start?

Prediction Explain how you can tell from a velocity-time graph where you were, relative to the motion detector, when you started walking and where you were when you stopped?

On the graph below, draw a velocity graph for someone walking at a constant speed of about 0.5 m/s away from the motion detector, starting at 0.5 meters away from the motion detector. Then draw a graph (different color or dashed line) to show someone walking away at the same velocity that started at 1 meter away from the motion detector.

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Set up the motion detector and test your prediction. Make a graph walking away from the motion detector at a constant speed. Use the store latest run feature from the “Experiment” menu so that the graph will remain persistently displayed on the screen. Then make a second graph moving at the exact same speed, but this time start at a different distance from the motion detector. Sketch the two graphs below:

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Question 7. Is there anything on the graph that indicates starting position? What is your conclusion regarding obtaining position information from a velocity-time graph?

Investigation 3: Position and Velocity Graphs

Activity 1 Predicting Velocity Graphs from Position Graphs

1. Predict a velocity graph from a position graph. Open the experiment file Velocity from Position, L01A3-1. Carefully study the position graph shown below and predict the velocity-time graph that would result from the motion. Using a dotted line, sketch your prediction of the corresponding velocity-time graph on the velocity axes.

2. Make the graphs. After each person has sketched a prediction, do your group's best to make a position graph like the one shown below. Walk as smoothly as possible to minimize steps.

When you have made a good duplicate of the position graph, sketch your actual graph over the existing position-time graph.

Use a solid line to draw the actual velocity graph on the same graph with your prediction. (Do not erase your prediction).

3. Store latest run: Use this feature of the software so that the graphs you just made are persistently displayed and you cannot accidentally erase them. Go to “Experiment” on the toolbar and choose “store latest run” from the drop-down menu.

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Activity 2 Determining Mean Velocity from a Velocity Graph and from a Position Graph

1. Select (left mouse click and drag) the non-zero portion of the velocity graph and use the Statistics function to find the average velocity while you were moving (if you stored latest run, the graph is now Run 1):

Average velocity:________ m/s

2. Select the same portion of the position graph, and use the Linear Fit function to find the equation of your motion during that time interval:

slope of the position-time graph:________ m/s

3. Are these values equal (i.e. within .1 m/s of each other)? Explain why they should be (if they are not, make sure you are selecting the correct portion of each graph and try again).

4. PRINT and attach your graph with the analysis boxes showing average velocity and linear fit boxes. Move the analysis boxes so they don’t hide the graphs!

6. In Investigation 2, you determined that you couldn’t obtain position information from a velocity graph. Can you obtain velocity information from a position graph? If so, what information and how?

7. Write a general equation (symbols only) to describe the position (x) of an object with constant velocity, v and initial position, x0 at any time t:

CHECK YOUR UNDERSTANDING:

Part 1: Position-Time Graphs

Sketch the position time graph corresponding to each of the following descriptions of the motion of an object.

1. The object is at rest, but not at the origin.

2. the object moves toward the origin with constant velocity for 5 seconds and then stands still for 5 seconds.

3. The object moves away from the origin, speeding up as it moves (review section on curved graphs).

Answer the following about two objects, A and B, whose motion produced the following graphs. For these questions, the word “ahead” refers to the object that is out in front in the direction of motion

4a. Which object is moving faster?_____

4b. Which starts ahead?_______

4c. What does the intersection mean?

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5a. Which object is moving faster?_____

5b. Which object is moving in a negative direction?

6a. Which object is moving faster?_____

6b. Which starts ahead?_______

Part 2: Velocity-Time Graphs

After studying the velocity-time graphs you have made, answer the following questions. Specify whether or not you are moving at constant speed speeding up or slowing down, and the direction of motion (away or toward origin). Don’t use the word accelerate:

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1. How do you move to create a horizontal line in the positive part of a velocity-time graph?

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2. How do you move to create a straight-line velocity-time graph that slopes up from zero?

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3. How do you move to create a straight-line velocity-time graph that slopes down?

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4. How do you move to make a horizontal line in the negative part of a velocity-time graph?

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5. The velocity-time graph of an object is shown below. Figure out the total displacement of the object. Show your work.

Displacement = ____________ meters.

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6. Both of the velocity graphs below, 1 and 2, show the motion of two objects, A and B. Answer the following questions separately for 1 and for 2. Explain your answers when necessary.

a) Is one faster than the other (exclude t=0s)? If so, which one is faster, A or B?

b) What does the intersection mean?

c) Can one tell which object is closer to the motion detector? If so, which one is closer at t=0 s, A or B?

d) Which object, A or B, is moving in a negative direction (i.e. towards the motion detector)? How can you tell?

1 2

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a._________________ a.____________________

b. __________________ b. __________________

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c. ___________________ c.____________________

d.____________________ d.___________________

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7. Sketch velocity-time the velocity -time graph corresponding to each of the following descriptions of the motion of an object.

8. Draw the velocity graphs for an object whose motion produced the distance-time graphs shown below on the left. Velocity graphs should be numerically correct.

Note: Unlike most real objects, you can assume these objects can change velocity so quickly

that it looks instantaneous with this time scale (i.e. vertical velocity lines are ok).

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