## Homework For Lab 2 Changing Motion Answers

**Unformatted text preview: **Name—.________ Date— Partners LAB 2: CHANGING MOTION A cheetah can accelerate from O to 50 miles per hour in 6.4 seconds. —Encyclopedia of the Animal World A Jaguar can accelerate from 0 to 50 miles per hour in 6.1 seconds. —Worlcl Cars OB] ECTIVES 0 To discover how and when objects accelerate. 0 To understand the meaning of acceleration, its magnitude, and its direction. a To discover the relationship between velocity and acceleration graphs. ' To learn how to represent velocity and acceleration using vectors. - To learn how to find average acceleration from acceleration graphs. 0 To learn how to calculate average acceleration from velocity graphs. OVERVIEW In the previous lab, you looked at position—time and velocity—time graphs of the motion of your body and a cart at a constant velocity. You also looked at the ac- celeration—time graph of the cart. The data for the graphs were collected using a motion detector. Your goal in this lab is to learn how to describe various kinds of motion in more detail. You have probably realized that a velocity—time graph is easier to use than a position—time graph when you want to know how fast and in what direction you are moving at each instant in time as you walk (even though you can calculate this information from a position—time graph). It is not enough when studying motion in physics to simply say that "the ob- ject is moving toward the righ ” or “it is standing still." When the velocity of an object is changing, it is also important to describe how it is changmg._'Ihe rate of change of velocity with respect to time is known as the acceleration. To get a feeling for acceleration, it is helpful to create and learn to interpret velocity—time and acceleration—time graphs for some relatively simple motions of LAB 2: CHANGING MOTION 39 dial at about half maximum speed of the fan blade). I?) preserve the batteries, switch on the fan unit only when you are making measurements. 6. Hold the cart with your hand on its side, begin graphing, switch the fan unit on and when you hear the clicks of the motion detector, release the cart from rest. Do not put your hand between the cart and the detector. Be sure to stop the cart before it hits the end stop. Turn off the fan unit. Repeat, if necessary, until you get a nice set of graphs. Adjust the position and velocity axes if necessary so that the graphs fill the axes. Use the features of yOur software to transfer your data so that the graphs will remain persistently displayed on the screen. Also save your data for analysis in Investigation 2. (Name your file SPEEDUP1.XXX, where XXX are your initials.) '7. Sketch your position and velocity graphs neatly on the axes that follow. La~ bel the graphs "Speeding Up I.” (Ignore the acceleration axes for now.) 2 PREDICTION AND FINAL FIESULTS Position (m) Velocity (W‘s) l _. Acceleration (W32) Time (3) Question 1-1: How does your position graph differ from the position graphs for steady (constant velocity) motion that you observed in Lab 1: Introduction to Motion? LAB 2: CHANGING MOTION ' Based on the direction of this vector and the direction of the positive x axis, what is the sign of the acceleration? Does this agree with your answer to Question 1-4? Activity 1-2: Speeding Up More Prediction 1-1: Suppose that you accelerate the cart at a faster rate. How would your velocity and acceleration graphs be different? Sketch your predictions with dashed or different color lines on the previous set of axes. 1. Test your predictions. Make velocity and acceleration graphs. This time ac- celerate the cart with the maximum number of batteries in the battery com- partment (or set the dial to the maximum speed of the fan blade). Remember to switch the fan unit on only when making measurements. Repeat if necessary to get nice graphs. (Leave the original graphs persistently displayed on the screen.) When you get a nice set of graphs, save your data as SPEEDUP2.XXX for analysis in Investigation 2. 2. Sketch your velocity and acceleration graphs with solid or different color lines on the previous set of axes, or print the graphs and affix them over the axes. Be sure that the graphs are labeled "Speeding Up I” and "Speedng Up 2.” Question 1-9: Did the shapes of your velocity and acceleration graphs agree with your predictions? How is the magnitude (size) of acceleration represented on a velocity—time graph? Question 1-10: How is the magnitude (size) of acceleration represented on an acceleration—time graph? INVESTIGATION 2: MEASURING ACCELERATION In this investigation you will examine the motion of a cart accelerated along a level surface by a battery driven fan more quantitativer This analysis will be quantitative in the sense that your results will consist of numbers. You will de- termine the carts acceleration from your velocity—time graph and compare it to the acceleration read from the acceleration—time graph. You will need motion software and the data files you saved from Investiga- tion 1. Activity 2-1: Velocity and Acceleration of a Cart T at Is Speeding Up 1. The data for the cart accelerated along the ramp with half batteries and half dummy cells (Investigation 1, Activity 1-1) should still be persistently on the screen. (If not, load the data from the file SPEEDUP1.XXX.) Display velocity and acceleration, and adjust the axes if necessary. LAB 2: CHANGING MOTION 43 - —- Calculate the change in velocity between points 1 and 2. Also calculate the corresponding change in time (time interval). Divide the change in velocity by the change in time. This is the average acceleration. Show your calculations below. Speeding up Change in velocity (m/s) Tlme interval (5) Average acceleration (m/sz) Question 2-1: Is the acceleration positive or negative? Is this what you expected? Question 2-2: Does the average acceleration you just calculated agree with the average acceleration you found from the acceleration graph? Do you expect them to agree? How would you account for any differences? Activity 2-2: Speeding Up More 1. Load the data from your file SPEEDUP2.XXX (Investigation 1, Activity 1-2). Display velocity and acceleration. 2. Sketch the velocity and acceleration graphs or print and affix the graphs. Use dashed lines on the previous set of axes. 3. Use the analysis feature of the software to read acceleration values, and find the average acceleration of the cart from your acceleration graph. Acceieration values (mlsz) __ _H_ _E_ 2 Average (mean) acceleration: m/s 4. Calculate the average acceleration from your velocity graph. Remember to use two points as far apart in time as possible, but still having typical values. LAB 2: CHANGING MOTION 45 Record the equation of the fit line, and compare the value of the slope (c) to the acceleration you found in Activity 2-1. Question E2-6: What is the physical meaning of in? Question E2-7: How do the two values of acceleration that you found in this extension agree with each other? Is this what you expected? Find the average acceleration for the motion in your SPEEDUP2.XXX file from the acceleration—time and velocity—time graphs using the same methods. Com- pare the values to those found in Activity 2-2 by averaging 10 values. INVESTIGATION 3: SLOWING DOWN AND SPEEDING UP In this investigation you will look at a cart moving along a ramp or other level surface and slowing down. A car being driven down a road and brought to rest when the brakes are applied is a good example of this type of motion. Later you will examine the motion of the cart toward the motion detector and speeding up. In both cases, we are interested in how velocity and acceleration change over time. That is, we are interested in the shapes of the velocity—time and accelera- tion—time graphs (and their relationship to each other), as well as the vectors rep- resenting velocity and acceleration. You will need the following materials: 0 computer-based laboratory system 0 motion detector 0 RealTime Physics Mechanics experiment configuration files 0 cart with very little friction 0 smooth ramp or other level surface 2—3 m long 0 fan unit attachment with batteries Activity 3-1: Slowing Down In this activity you will look at the velocity and acceleration graphs of the cart moving away from the motion detector and slowing down. 1. The cart, ramp, and motion detector should be set up as in Investigation 1. Use the maximum number of batteries (or set the dial to the maximum speed). The fan should be pushing the cart toward the motion detector. LAB 2: CHANGING MOTION 47 FINAL RESULTS Velocity (mls) Acceleration (misa) O I ['0 4. Neatly sketch your results on the previous axes, or print the graphs and af- fix them over the axes. Label your graphs with o A at the spot where you started pushing. 0 B at the spot Where you stopped pushing. 0 C the region where only the force of the fan is acting on the cart 0 D at the spot where the cart came to rest (and you stopped it with your hand). Also sketch on the same axes the velocity and acceleration graphs for Speed- ing Up 2 from Activity 1-2. Question 3-1: Did the shapes of your velocity and acceleration graphs agree with your predictions? How can you tell the sign of the acceleration from a velocity—time graph? Question 3-2: How can you tell the Sign of the acceleration from an accelera— tion—time graph? Question 3-3: Is the sign of the acceleration (which indicates its direction) what you predicted? How does slowing down while moving away from the detector re sult in this sign of acceleration? (Hint: Remember that acceleration is the rate of change of velocity with respect to time. Look at how the velocity is changing.) LAB 2: CHANGING MOTION 49 PREDICTION Velocity Acceleration Time 1. Test your predictions. First clear any previous graphs. Graph velocity first. ‘ Graph the cart moving toward the detector and speeding up. Turn the fan unit on, and when you hear the clicks from the motion detector, release the cart from rest from the far end of the ramp. ( Be sure that your hand is not between the cart and the detector.) Stop the cart when it reaches the 0.5-m line, and turn the fan unit off immediately. 2. Sketch these graphs or print and affix on the axes below. Label these graphs as "Speeding Up Moving Thward.” FINAL RESULTS Velocity (mfs) ‘ Acceleration (mlsz) LAB 2: CHANGING MOTION 51 Question 3-14: The diagram shows the positions of the cart at equal time in- tervals for the motion described in Question 3-13. At each indicated time, sketch a vector above the cart that might represent the velocity of the cart at that time while it is moving toward the motion detector and slowing down. Assume that the cart is moving at 1‘1 and t4. r4:35 1|3:223 {2:15 11:05 M t' Deotezlt‘or 6 Q G (D A X4 X3 X2 X1 x direction Question 3-15: Show how you would find the vector representing the change in velocity between the times 2 and 3 s in the diagram above. Based on the di- rection of this vector and the direction of the positive x axis, what is the Sign of the acceleration? Does this agree with your answer to Question 3-13? If you have more time, do the following Extension. Extension 73-3: Graphing Slowing Down Toward T ' the Motion Detector Use the motion detector setup to graph the motion of the cart moving toward the motion detector and slowing down, as deScribed in Question 3-13. Print and affix the graph. Question E3-16: Compare the graphs to your answers to Questions 3~13 to 3-15. Activity 3-4: Reversing Direction In this activity you will look at what happens when the cart slows down, reverses its direction and then speeds up in the opposite direction. How does the veloc- ity change with time? What is the cart’s acceleration? The setup should be as shown below—the same as before. The fan unit should have the maximum number of batteries, and should be taped securely to the cart. End stop -' ) \ I Ir.- WW A Direction of push Prediction 3-3: You start the fan and give the cart a push away from the motion detector. It moves away, slows down, reverses direction, and then moves back to- LAB 2: CHANGING MOTION 53 1 FINAL RESULTS + . Velocity (mls) +2 Acceleration (mlsz) Q | ID Time (s) 3. When you get a good round trip, sketch both graphs on the axes above or print and affix over the axes. Question 3-17: Label both graphs with 0 A where the cart started being pushed. 0 B where the push ended (where your hand left the cart). 0 C where the cart reached its turning point (and was about to reverse di- rection). ' D where you stopped the cart with your hand. Explain how you know where each of these points is. Question 3-18: Did the cart “stop” at its turning point? (Hint: Look at the ve- locity graph. What was the velocity of the cart at its turning point?) Does this agree with your prediction? How much time did it spend at the turning point velocity before it started back toward the detector? Explain. Question 3-19: According to your acceleration graph, what is the acceleration at the instant the cart reaches its turning point? Is it positive, negative, or zero? Is it significantly different from the acceleration during the rest of the motion? Does this agree with your prediction? LAB 2: CHANGING MOTION 55 Name__.__._...____,._..___._____ Date— Partners HOMEWORK FOR LAB 2: CHANGING MOTION 1. An Object moving along + a line (the + position axis) has the accelera- tion—time graph on the right. Acceleration a. Describe how the Object might move to create this graph if it is moving away from the origin. b. Describe how the object might move to create this graph if it is moving toward the origin. c. Sketch with a solid line on the axes on the right a veloc- ity—time graph that goes with the mo- tion described in (a). d. Sketch with a dashed line on the axes on the right a velocity—time graph that goes with the motion described in (b). LAB 2: CHANGING MOTION .57 Acceleration Acceleration Acceleration 5. A car can move along a line (the + position axis). Sketch velocity—time and acceleration—time graphs that correspond to each of the following descrip- tions of the car’s motion. a. The car starts from rest, and moves away from the origin, increasing its speed at a steady rate. : 2 E o a: 8 < - Time LAB 2: CHANGING MOTION .59 d. The car starts from rest, and moves toward the origin, increasing its speed at a steady rate. + Velocity Acceleration Time 2. The car is moving toward the origin at a constant velocity. 2 3 E 2 OJ 8 ﬂ: Time LAB 2: CHANGING MOTION 61 9. For each of the position—time graphs shown, sketch below it the corre- sponding velocity—time and acceleration—time graphs. 7" 0 Time Time Position Position Velocity o + Velocity + C C C E E E e e o g a) 8 g 8 < < < _ Time (a) (W (C) 10. Each of the pictures below represents a car moving down a road. The mo- tion of the car is described. In each case, draw velocity and acceleration vec- tors above the car that might represent the described motion. Label the vec- tors. Also specify the sign of the velocity and the sign of the acceleration. (The positive position direction is toward the right.) a. The driver has stepped on the accelerator, and the car is just starting to move forward. Sign of velocity: Sign of acceleration: b. The car is moving forward. The brakes have @ been applied. The car is slowing down, but has not yet come to rest. Sign of velocity: Sign of acceleration: c. The car is moving backward. The brakes have @ been applied. The car is slowing down, but ‘ has not yet come to re st. Sign of velocity: Sign of acceleration: LAB 2: CHANGING MOTION 63 The graphs on this page represent the motion of objects along a line that is the positive position axis. Notice that the motion of objects is rep- resented by position, velocity, or acceleration graphs. Answer the following questions. You may use a graph more than once or not at all, and there may be more correct choices than blanks. If none of the graphs is correct, answer I. 12. Pick one graph that gives enough information to indicate that the velocity is always negative. Pick three graphs that represent the motion of an object whose velocity is constant (not changing). 13. 14. 15. 16. Pick one graph that deﬁnitely indicates an object has reversed direction. 17. Pick one graph that might possibly be that of an object stand- ing still. Pick 3 graphs that represent the motion of objects whose acceleration is changing. 18. 19. 20. Pick a velocity graph and an acceleration graph that could describe the motion of the same object during the time shown. 21. Velocity graph. 22. Acceleration graph. LAB 2: CHANGING MOTION (9 (h C‘. V ) ) Acceleration Acceleration Acceleration 65 ...

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Hewitt: Chapter 2 P. 10-27

Giancoli: Chapter 2 P. 21-48

- Displacement, velocity, and acceleration are all vector quantities
- Displacement is change in position. Velocity is the rate of change of position with time. Acceleration is the rate of change of velocity with time. Changes in each property expressed by subtracting initial values from final values.
- A choice of reference frame determines the direction and the magnitude of each of these quantities.

__Learning Objective #1:__ The student is able to express the motion of an object using narrative, mathematical, and graphical representations.

__Learning Objective #2:__ The student is able to design an experimental investigation of the motion of an object

__Learning Objective #3:__ The student is able to analyze experimental data describing the motion of an object and is able to express the results of the analysis using narrative, mathematical, and graphical representations.

__Note Taking Outline:__

It is important for each video to take good notes. Good notes not only record important information but help you to understand/process it. Good notes can also help you to record what you don't understand and get specific help. Finally, good notes are a tremendous test preparation/review tool. **This is a major college preparation skill!** We will be using what is called the Cornell Note Taking Method. The link below takes you to a site that lets you set up and print customized note paper.

Cornell Note Taking Generator Web Site

__I. Graph Matching Lab__

Do Preliminary Questions on blank graph paper (show me your answers)

Perform the Lab

Re-do Preliminary Questions

Do Analysis Questions (separate sheet of paper)

Video: Position - Time Graphs (YouTube)

How can the motion of an object be represented by a position - time graph? Make sure you download and print note sheet.

__II. Lab Challenge:__** **How can we use these graphs to actually measure how fast a person is walking?

Your lab group needs to come up with a way to measure a person's speed using each type of graph. Both a position-time graphs and a velocity-time graph. When you think you have it come and see me before doing it.

Video: Velocity - Time Graphs

See how motion is represented by velocity-time graphs. Take good notes!

__III. MBL HW #1,2__

Worksheet handed out in class. When finished check using the key then show me.

__V. LAB: Modern Galileo Experiment__ Click here to download

1.) Read Lab

2.) Do Preliminary Questions

3.) Discussion with me

4.) Do Lab

5.) Analysis Questions (with calculations) on separate sheet of paper

6.) Discussion with me

__VI. Video: Acceleration__

The idea of acceleration is developed from motion detector graphs of a dynamics cart traveling down an inclined ramp.

__VII. HW: Introduction to Motion: Changing Motion__Handout in class. Skip #1B, 2B, 3, 6, 15, 21-26. Check against the scoring key when done.

**VIII.**Video: Equations of Uniform Accelerated Motion

Very important video for learning how to do more complicated problems with acceleration. Don't forget to download a notes sheet.

__IX.____Galileo Lab Extension #2__

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