name date pre-lab preparation sheet for lab 1: … · 2020. 1. 20. · lab 1 – intro to motion 1...

Lab 1 – Intro To Motion 1

Name_______________________________ Date________________________

PRE-LAB PREPARATION SHEET FOR LAB 1: INTRODUCTION TO MOTION

(Due at the beginning of Lab 1) Directions: Read over Lab 1 and then answer the following questions about the procedures. 1. In Activity 1-1, how do you think graph a will differ from graph b? 2. What can you say in general about velocity versus time for the graphs (i), (ii), and (iii) in Activity 1-3, Question 1-7? 3. Draw your predicted graph for Activity 2-1, step 3, below:

4. In Activity 3-2, how will you find the average velocity? (Tell me the specific method, do not simply write down the definition of an average.) 5. What is a vector? What vector quantities are studied in this lab?


Name_______________________ Date______________ Partners__________________

LAB 1:

INTRODUCTION TO MOTION

OBJECTIVES • To find out how you can measure your motion with a motion detector. • To explore how your motion looks as a position vs. time graph. • To find out how your motion looks as a velocity vs. time graph. • To explore the relationship between velocity vs. time and position vs. time graphs. • To begin to explore acceleration vs. time graphs.

OVERVIEW The study of the mathematical and graphical representation of motion is known as kinematics. In this investigation, you will use a motion detector to plot position vs. time and velocity vs. time graphs of the motion of your body and a cart.

MATERIALS

• Graphical Analysis application

• LabQuest Mini Base

• Go Direct Sensor Cart

• Number line on floor in meters (optional)

• Motion Detector


INVESTIGATION 1: POSITION VS. TIME GRAPHS OF YOUR MOTION The goal of this investigation is to relate the motion of your own body to features on a position vs. time graph.

In this investigation, “position” is short for “position measured from the motion detector.” The motion detector is the origin from which distances are measured. It will detect the closest object directly in front of it (including your arms if you swing them as you walk). The motion detector will not correctly measure anything closer than 15 centimeters. When making your graphs don’t go closer than 15 centimeters from the motion detector.

Activity 1-1: Making Position vs. Time Graphs 1. Place the motion detector so that it points toward an

open space at least 3 m long. Set the switch on your motion detector to Ball/Walk. Connect the motion detector to the LabQuest Mini Base and connect the Base to your computer. Launch Graphical Analysis.

2. Set up the software for data collection. Click to open Data Collection

Settings in the lower left corner and change End Collection to 10 s. If two

graphs are displayed, click View, , in the upper right corner and choose 1 Graph (a graph of position vs. time should be displayed).

3. When you are ready to start graphing distance, click once on the Collect

button.

4. Make position vs. time graphs for the following different walking speeds and directions, and sketch your results:

a. Start at the 0.5-meter mark and

make a position vs. time graph by walking away from the detector (origin) slowly and steadily. Sketch the graph on the right.

b. Make a position vs. time graph by walking away from the detector (origin) medium fast and steadily. Sketch the graph.


c. Make a position vs. time graph by walking toward the detector (origin) slowly and steadily. Sketch the graph.

d. Make a position vs. time graph by walking toward the detector (origin) medium fast and steadily. Sketch the graph.

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

Question 1-2: Describe the difference between the graph you made by walking toward and the one made walking away from the motion detector.

Question 1-3: Predict the position vs. time graph produced when a person starts at the 1-m mark, walks away from the detector slowly and steadily for 5 s, stops for 5 s, and then walks toward the detector at a faster pace. Draw your prediction on the left axes below using a dotted line. Compare your predictions with the others in your group. See if you can all agree. Draw your group’s prediction on the left-hand axes below using a solid line. (Do not erase your original prediction.)

Show your predictions to your instructor and get their initials here________


5. Do the experiment. Move in the way you described in your prediction and

observe the position vs. time graph that you produce. When you are satisfied with your graph, draw your group’s final result on the graph above labeled “Final Result.”

Question 1-4: Is your prediction the same as the final result? If not, describe how you would move to make a graph that looks like your prediction.

Activity 1-2: Matching a Position vs. Time Graph In this activity you will move to match a position graph shown on the computer screen.

1. In Graphical Analysis, click on Graph Tools, , and choose Add Graph Match. Choose Position. A position target graph will be displayed for you to match.

Question 1-5: Describe how you think you would walk to reproduce the target graph.

2. To test your prediction, choose a starting position. Start data collection, then

walk in such a way that the graph of your motion matches the target graph on the screen.

3. If you were not successful, start data collection again when you are ready to begin walking. Repeat this process until your motion closely matches the graph on the screen. Print the graph with your best attempt showing both the target graph and your motion data. Each person in your group should take a turn and produce their own graph.

Question 1-6: How did you adjust your motion to match any sloped parts of the graph you just matched?

Activity 1-3: Other Position vs. Time Graphs

1. Create a graph-match challenge. Click File, , and choose New Experiment. Click Sensor Data Collection. Set up data collection to end

after 5 seconds. Click View, , and choose 1 Graph. Click Graph Tools,

, and choose Add Prediction. Use the Prediction tool to sketch a position vs. time graph. Use straight lines, no curves. Click Save. Challenge another student in your group to match your graph. Sketch the graph with a dashed line, along with the best attempt by a group member to match your position vs. time graph on the same axes. Use a solid line.


2. Can you make a curved position vs. time graph? Describe how you would

make each of the graphs shown below.

Question 1-7: Describe how you must move to produce a position vs. time graph with each of the shapes shown.

o Graph (i) answer:

o Graph (ii) answer:

o Graph (iii) answer:

Question 1-8: What do these curved-line position vs. time graphs have in common?

INVESTIGATION 2: VELOCITY VS. TIME GRAPHS OF YOUR MOTION You have already plotted your position as a function of time using the motion detector. You can also plot how fast you are moving. How fast you move is your speed. It is the rate of change of distance with respect to time. Velocity takes into account your speed and the direction you are moving. When you measure your motion along a line, velocity can be positive or negative.


Activity 2-1: Making Velocity Graphs

1. Set up to graph velocity. Click File, , and choose New Experiment. Click Sensor Data Collection. Set up data collection to end after 5 seconds. Click

View, , and choose 1 Graph. Make sure it is a velocity vs. time graph. 2. Graph your velocity for the following different walking speeds and directions and sketch your results below. Sketch your results on the graphs below. Just draw smooth patterns; leave out smaller bumps that are mostly due to your steps.

a. Make a velocity graph by walking away from the detector slowly and steadily. Try until you are satisfied with the graph you’ve produced.

b. Make a velocity graph by walking away from the detector medium fast and steadily. Sketch your graph.


c. Make a velocity graph by walking toward the detector slowly and steadily. Sketch your graph.

d. Make a velocity graph by walking toward the detector medium fast and steadily. Sketch your graph.

Question 2-1: What is the most important difference between the graph made by slowly walking away from the detector and the one made by walking away more quickly? Question 2-2: How are the velocity vs. time graphs different for motion away and toward the detector? 3. Predict a velocity graph for a more complicated motion and check your

prediction. a. Draw below, using a dotted line, your prediction of the velocity graph

produced if you:

• Walk away from the detector slowly and steadily for 4 s.

• Stop for 4 s.

• Walk toward the detector steadily about twice as fast as before for 4 s.


b. Compare predictions and see if you can all agree. Use a solid line to draw in your prediction.

Prediction

4. Do the experiment. (Be sure to adjust the time scale to 12 seconds.). Repeat

your motion until you think it matches the description. Draw the best graph on the axes below. Be sure the 4-second stop shows clearly.

Final Result

How fast you move is your speed, the rate of change of distance with respect to time. Velocity implies both speed and direction. As you have seen, for motion along a line (the positive x axis), the sign (+ or -) of the velocity indicates the direction. If you move away from the detector (origin), your velocity is positive, and if you move toward the detector, your velocity is negative. The faster you move away from the origin, the greater in magnitude your velocity is, and it is a positive number. The faster you move toward the origin, the greater in magnitude your velocity is, but it is a negative number. That is, -4 m/s is twice as fast as -2 m/s and both motions are toward the origin.


Question 2-3: Draw a vector (a line with an arrow) to represent the velocity of an object moving at -4 m/s. Draw a second vector to represent the velocity of an object moving at -2 m/s. Be sure to include axes for reference to define your directions. How can you visually tell which vector describes which velocity?

Activity 2-2: Matching a Velocity Graph In this activity, you will move to match a velocity graph shown on the computer screen. Each person in the group will repeat this activity to produce two matched graphs.

1. In Graphical Analysis, click on Graph Tools, , and choose Add Graph Match. Choose Velocity. A velocity target graph will be displayed for you to match.

2. Move so as to imitate this graph. You may try a number of times. Work as a team and plan your movements. Get the times right and get the velocities right. Each person should take a turn.

3. Each person should print their best match.

Question 2-4: Describe how you moved to match each part of the graph. For Graph Match 1: For Graph Match 2:

Question 2-5: Is it possible for an object to move so that it produces an absolutely vertical line on a velocity graph? Explain.

INVESTIGATION 3: POSITION AND VELOCITY GRAPHS


You have looked at position vs. time graphs and velocity vs. time graphs separately. Now you will see how they are related.

Activity 3-1: Predicting Velocity Graphs from Position Graphs

1. Click File, , and choose New Experiment. Click Sensor Data Collection.

Set up data collection to end after 5 seconds. Click View, , and choose 2 Graphs. Make sure you have a position vs. time graph and a velocity vs. time graph.

2. Predict a velocity graph from a distance graph. Carefully study the distance graph shown below and predict the velocity vs. time graph that will result from the motion. Using a dotted line, sketch your prediction of the corresponding velocity vs. time graph on the velocity axes.

3. Make the graphs. After each person has sketched a prediction, press

Collect and do your best to make a distance graph like the one shown below. Walk as smoothly as possible.

When you have made a good duplicate of the distance graph, sketch your actual graph over the existing position vs. time graph. Use a solid line to draw the actual velocity graph on the same graph with your prediction. Do not erase your prediction.

Question 3-1: How would the position vs. time graph be different if you moved faster? Slower? Question 3-2: How would the velocity vs. time graph be different if you moved faster? Slower?

Activity 3-2: Estimating and Calculating Velocity In this activity, you will estimate an average velocity from the velocity graph in


Activity 3-1 and then calculate an average velocity using your position graph. 1. Estimate your average velocity from the velocity graph in Activity 3-1. You

are to estimate an average value for velocity while you were walking steadily in Activity 3-1. Click on your velocity graph, read ten values from the velocity graph, and us them to calculate the average (mean) velocity.

Velocity Values (m/s)

1. 3. 5. 7. 9.

2. 4. 6. 8. 10.

Average (mean) Velocity: m/s

Comment: Average velocity during a particular time interval is the change in distance divided by the change in time. By definition, this is also the (average) slope of the position vs. time graph for that time period. As you have observed, the faster you move, the more inclined is your position vs. time graph. The slope of a position vs. time graph is a quantitative measure of this incline, and therefore it tells you the velocity of the object. 2. Calculate your average velocity from your position vs. time graph in Activity

3-1. Click on the position graph to read the position and time coordinates for two points while you were moving. For a more accurate answer, use two points as far away as possible but still typical of the motion, and within the time interval over which you took the velocity readings in step 1.

Position (m) Time (sec)

Point 1

Point 2

Calculate the change in position between points 1 and 2. Also calculate the corresponding change in time (time interval). Divide the change in position by the change in time to calculate the average velocity. Show your calculations in the next table.

3. Draw in the average velocity you just calculated on the velocity graph in Activity 3-1.

Question 3-3: Is the average velocity positive or negative? Is it what you expected? Question 3-4: Does the average velocity you just calculated from the position graph agree with the average velocity you estimated from the velocity graph? Do you expect them to agree? How would you account for any differences?

Change in position m

Time interval sec

Average velocity m/sec


Activity 3-3: Predicting Position Graphs from Velocity Graphs

1. Predict a position vs. time graph from a velocity vs. time graph. Click File,

, and choose New Experiment. Click Sensor Data Collection. Set up data

collection to end after 10 seconds. Click View, , and choose 2 Graphs. Make sure you have a position vs. time graph and a velocity vs. time graph.

2. Carefully study the velocity graph below. Using a dotted line, sketch your prediction of the corresponding position graph on the bottom set of axes. (Assume that you start at the 1-meter mark.)

3. Make the graphs. After each person has sketched a prediction do your best to duplicate the top (velocity vs. time) graph by walking.

When you have made a good duplicate of the velocity vs. time graph, draw your actual result over the existing velocity vs. time graph. Use a solid line to draw the actual position vs. time graph on the same axes with your prediction. (Do not erase your prediction).

Question 3-5: How can you tell from a velocity vs. time graph that the moving object has changed direction? Question 3-6: What is the velocity at the moment the direction changes?


Question 3-7: Is it possible to actually move your body (or an object) to make the vertical lines on the velocity graph that you were trying to match? Why or why not? Question 3-8: Is it possible to actually move your body (or an object) to make vertical lines on a position vs. time graph? Why or why not? What would the velocity be for a vertical section of a position vs. time graph? Question 3-9: How can you tell from a position vs. time graph that your motion is steady (motion at a constant velocity)? Question 3-10: How can you tell from a velocity vs. time graph that your motion is steady?

INVESTIGATION 4: INTRODUCTION TO ACCELERATION Acceleration is the time rate of change of velocity. Any time the velocity changes, there is an acceleration. In this investigation you will look at velocity and acceleration graphs of the motion of a cart.

Activity 4-1: Velocity and Acceleration of a Cart with Constant Motion As you have seen, it is difficult for a person to move smoothly at a perfectly steady speed. For this last activity, we will use the Go Direct Sensor carts, which do not require the separate Motion Detectors.

1. Click File, , and choose New Experiment. Connect the Sensor Cart to your

computer. If only one graph is displayed, click View, , and choose 2 Graphs (a velocity vs. time and an acceleration vs. time graph).

2. Graph the motion of the cart getting a small push and then moving on its own on the level low-friction ramp. Sketch your results on the following axes.


Question 4-1: When does the cart move at constant velocity: before, during, or after the push? Question 4-1: Compare the average acceleration of the cart while it is coasting to the average acceleration of the cart when you are pushing it with your hand. How is a constant velocity represented on an acceleration vs. time graph?


Name___________________________ Date_______________ Partners_____________________

HOMEWORK FOR LAB 1:

INTRODUCTION TO MOTION

Position vs. Time Graphs Answer the following questions in the spaces provided. 1. What do you do to create a horizontal line on a position—time graph? 2. How do you walk to create a straight line that slopes up? 3. How do you walk to create a straight line that slopes down? 4. How do you move so the graph goes up steeply at first, and then continues up less steeply? 5. How do you walk to create a U-shaped graph?


Answer the following about two objects, A and B, whose motion produced the following position vs. time graphs. 6. a. Which object is moving

faster: A or B?

b. Which starts ahead? Define what you mean by “ahead.”

c. What does the intersection mean? 7 a. Which object is moving faster? b. Which object has a negative velocity according to the convention we have established?

8. a. Which object is moving faster? b. Which object starts ahead? Explain what you mean by “ahead.”


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

9. The object moves with a steady (constant) velocity away from the origin. 10. The object is standing still. 11. The object moves with a steady (constant) velocity toward the origin for 5 seconds and then stands still for 5 seconds. 12. The object moves with a steady velocity away from the origin for 5 seconds, then reverses direction and moves at the same speed toward the origin for 5 seconds. 13. The object moves away from the origin, starting slowly and speeding up.

VELOCITY VS. TIME GRAPHS After studying the velocity vs. time graphs you have made, answer the following questions with terms like “speeding up”, “slowing down” and moving “toward” or “away” from the origin. 1. How do you move to create a horizontal line in the positive part of a velocity vs. time graph?


2. How do you move to create a straight-line velocity vs. time graph that slopes up from zero? 3. How do you move to create a straight-line velocity vs. time graph that slopes down? 4. How do you move to make a horizontal line in the negative part of a velocity vs time graph? 5. The velocity vs. time graph of an object is shown below. Figure out the total displacement by the object. Show your work. Displacement = ________meters

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? If so, which one is faster? (A or B) b) What does the intersection mean?


c) Can one tell which object is “ahead”? (define “ahead”)

d) Does either object A or B reverse direction? Explain.

a) a)

b) b)

c) c)

d) d)

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

7. The object is moving away from the origin at a steady (constant) velocity.


8. The object is standing still. 9. The object moves toward the origin at a steady (constant) velocity for 10 seconds, and then stands still for 10 seconds. 10. The object moves away from the origin at steady (constant) velocity for 10 seconds, reverses direction, and moves back toward the origin at the same speed for 10 seconds.

11. Draw careful graphs below of position and velocity for a cart that: a. moves away from the origin at a slow and steady (constant) velocity for the first 5 seconds. b. moves away at a medium-fast, steady (constant) velocity for the next 5 seconds. c. stands still for the next 5 seconds. d. moves toward the origin at a slow and steady (constant) velocity for the next 5 seconds. e. stands still for the last 5 seconds.


12. Draw the velocity graphs for an object whose motion produced the position vs. time graphs shown below on the left. Position is in meters and velocity is in meters per second. Note: Unlike most real objects, you can assume that these objects can change velocity so quickly that it looks instantaneous with this time scale.

name date pre-lab preparation sheet for lab 1: … · 2020. 1. 20. · lab 1 – intro to motion 1...

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