Lesson 11: Motion of a Falling Object

Transcription

1 Lesson 11: Motion of a Falling Object 11.1 Observe and find a pattern using your choice of one of the following: 1. The video at this web site: which was shot with a frame rate of 3 fps and a meter stick. 2. One of the multiple exposure photographs at the end of this packet: For the photograph 1 (a computer-generated image), the strobe speed is 2 flashes per second and each unit is 12 mm (1 = 12 mm, 2 = 24 mm). For photograph 2 ( MIT Physics Demos, a real guy dropping a real ball), the strobe speed is also 2 flashes per second and there are 25 cm between the white lines in the photograph. 3. An experiment that you design using available materials. Use the following information to scaffold your lab report. Be sure to include the option that you chose. Your report should also include a title, purpose, materials (only if you design your own experiment), procedure (this will be really short if you don t design your own experiment), data, calculations, graphs, results, and conclusion. Notice this lab is an observational experiment rather than a testing experiment so the hypothesis and prediction parts of the report are not included. a) Describe the motion of the ball based on your observations. Draw a motion diagram to represent these observations. b) Decide on an origin and measure the position of the ball at the beginning of each time interval. How did you decide how to measure the position? Be sure to be consistent. c) What is the instrumental uncertainty in your measurements? Other sources of uncertainty? d) Record the position and time data for the ball in a table. Can you see any patterns? Explain. e) Plot a position versus time graph for this object. What type of function does the trend line resemble? Does this graph represent an object traveling with constant velocity? How do you know? For Review: More about the instrumental uncertainty. Suppose you measure the length of the table to be 2m using a ruler that has centimeter divisions. Half of the smallest division is.5 cm. You can write your measurement as l= 2.m ±.5m..5 cm constitutes.25% of 2 m [ (.5 2) x 1%], thus you can also write the measurement as l = 2.m ±.25%. Notice that using the percentage value of instrumental uncertainty results in a smaller uncertainty value for larger measured quantities if the same instrument is used (for example.5 cm is.25% of 2 m but is 1% of 5 cm, thus when you measure the distance of 5 cm with this ruler, you have 1% uncertainty) Represent and Reason a) Now we will examine graphically how the velocity changes. Calculate the average velocity for the ball for each time interval. Construct and complete a data table that includes the quantities shown below. You may wish to include other quantities and/or calculations depending upon the system you chose for your experiment. Be sure to include uncertainty in your measurements and calculations. Time interval t =t n t n-1 Displacement x = x n x n-1 Average clock reading (t n + t n-1 )/2 Average velocity ΔX/Δt b) What patterns do you notice in the table? What do these patterns indicate about the motion of the falling ball? c) Plot an average velocity versus time graph. Think about which time you should use. Write a function for how the speed changes with time, v(t). d) What is the meaning of the slope of this line? Think about the physical meaning of the slope of the line and name it.

2 e) How would the equation change if the ball were slowing down instead of speeding up? How would your equation change if the ball were initially thrown upwards? f) In general, what is the meaning of the slope of a line? Specifically, what is the meaning of the slope of a position vs. clock reading graph? Of the slope of a velocity vs. clock reading graph? Your lab report will be assessed using the following rubric: Scientific Ability Not Proficient () Partially Proficient (1) Is able to identify No mention of Description of phenomenon to be phenomenon phenomenon is investigated (ie, confusing or purpose ) inaccurate. Is able to represent observations in multiple ways Is able to identify a pattern in the data Is able to represent pattern mathematically Is able to devise explanation for observed pattern Is able to identify sources of experimental uncertainty Is able to identify how experimental uncertainties may affect the data Graphing Observations are not accurately represented by any method No attempt is made to find a pattern No attempt is made to represent pattern mathematically No explanation is given No identification of experimental uncertainties No attempt is made to evaluate experimental uncertainties Graphs are missing or illegible An attempt is made to represent observations in multiple ways; however representations are not consistent with one another or with observations The pattern described is irrelevant or inconsistent with the data The mathematical expression does not represent the trend Explanation is vague, untestable, or inconsistent with the pattern An attempt is made to identify experimental uncertainties, but most are missing, vague, or incorrect An attempt is made to evaluate experimental uncertainties, but most are missing, vague, or incorrect; results may not take uncertainty into account An attempt is made at graphing but there are major errors in variable assignment, consistency, and/or trend lines. Conclusion No conclusions are drawn An attempt is made at a conclusion but relevant points are omitted Details No format considerations/instructions are followed. Report is difficult to read, containing many grammatical and spelling errors. Some attempt made to format correctly, but still contains sizable errors and/or omissions Proficient (2) Description of phenomenon is mostly accurate but is incomplete or contains minor errors. Multiple representations are presented with some inconsistencies The pattern has minor errors or omissions No analysis is made of how well the expression agrees with the data, or some features of the pattern are missing Explanation is mostly complete but does not allow for all observations/aspects of the pattern Most experimental uncertainties are correctly identified Results do take uncertainties into account, but not completely or correctly evaluated Graphs have minor omissions or errors. Conclusion is mostly accurate but contains minor omissions and/or errors Report is clear and coherent but contains minor errors. Advanced Proficient (3) Phenomenon is clearly, accurately stated. Multiple, consistent representations are presented. The patterns accurately represent relevant trends in the data The expression represents the trend and an analysis of the agreement with data is included Explanation is reasonable and complete. All experimental uncertainties are correctly identified. The experimental uncertainty of the final result is correctly, completely evaluated Graphs contain no errors and clearly describe motion of the object. Graphs are consistent with each other and with described patterns. Conclusion contains all required elements with no errors and some elaboration Report is clear, coherent, and contains no relevant errors.

3 Total: /3 Evaluate your report using this rubric and turn in this self-assessment with your lab report. Worth one extra point.

4 Photo 1: 2 fps; each unit is 12mm.

5 MIT Physics Demos Strobe rate: 2 fps; 25 cm between white lines.

6 Let s Define Another Rate of Change:: Acceleration of an object moving at constant acceleration is equal to the change in velocity of the object divided by the time interval during which this change in velocity occurred. When the object is moving at constant acceleration this ratio is the same for any time interval: a v v 2 1 where v 2 v 1 ( v ) is any change in position during t 2 t 1 the corresponding time interval t 2 t 1 ( t ). The unit for acceleration is m/s/s or m/s 2. So think is acceleration a scalar or vector quantity? How is acceleration related to the Δv arrows of our motion diagrams? 11.3 Represent and reason The motion diagrams in the illustrations below represent the motion of different objects modeled as point-like objects. The arrows are velocity arrows. (+) x I (-) (+) II y I x (-) II (+) I III (-) A different coordinate axis is provided in each situation. An open circle indicates the location of interest. 1. Draw velocity change arrows on each diagram above. 2. Fill in the table that follows. Be sure to make your choices relative to the coordinate axis shown with each motion diagram. Describe the motion in words. Determine the Determine the Determine the sign (+,, or ) sign (+,, or ) sign (+,, or ) of of the position. of the velocity. the acceleration. a) Location I: Location I: Location I: b) Location I: Location I: Location I: c) Location I: Location I: Location I: Location III: Location III: Location III:

7 Axis Title Velocity (m/s) Velocity (m/s) Kreutter: Kinematics Represent and Reason Study the following three graphs taken from actual laboratory data. Determine the acceleration for the motion represented on each graph. What does it mean if the acceleration is positive? Negative? Write the functions v(t) for the following graphs Time (sec) Time (sec) Time (s) Axis Title a) Describe a situation that will match each graph. b) Compare the velocity versus time graphs for objects that move at constant velocity and objects that move with changing velocity. c) What can you say about the acceleration of the moving objects in the graphs? Explain.

8 Velocity (m/s) Kreutter: Kinematics Practice A bus leaves an intersection accelerating at +2. m/s 2. What is the speed of the bus after 5. s? What assumptions did you make? Explain Practice What was the speed of a jogger if she needed 2 seconds to stop at the acceleration of 3 m/s/s? Is the answer realistic? Practice A jogger is running at +4. m/s when a bus passes her. The bus is accelerating from m/s to + 2. m/s in 8. s. The jogger speeds up at the same acceleration. What can you determine about the jogger s motion using these data? Represent and Reason A person on a motorcycle facing south is initially at rest. The motor cycle speeds up from rest to 15 m/s in three seconds. For the next 8 seconds, the motorcycle travels at the same speed. Over the next 12 seconds the motorcycle slows to rest uniformly. Plot an acceleration-versus clock reading graph for the motor cycle. What assumptions did you make about the motorcycle and its motion? Represent and Reason The figure below shows a velocity-versus-clock reading graph that represents the motion of an object, modeled as a point particle (we are not interested in the motion of the feet, head, etc.), moving along a straight path. The positive direction of the position axis is toward the north Time (sec) a) Describe the motion of the object in words. b) When does the object travel at constant velocity? Explain how you know. c) When does the object have a velocity equal to zero? Explain how you know. d) What is the average acceleration for the first three seconds? e) What is the average acceleration for the time interval seconds? f) Plot an acceleration-versus-clock reading graph for the motion of the object. g) At 4.5 seconds, what is the object s acceleration? Velocity? Reflect: What did you learn during this lesson? How is acceleration similar to velocity? How is it different? Why are both concepts important?