Accelaration due to Gravity

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ACCELERATION DUE TO GRAVITY READ the instructions!

Today’s lab: carry out good measurements. You can do your calculations later.

Next week’s lab: do the formal lab write up.

Objectives: 1. To predict the shape of the motion graphs for a falling ball and then to check

your predictions by doing the experiment. 2. To study the acceleration due to gravity of objects that experience air friction. Method: Position, velocity, and acceleration graphs will be displayed on a computer using

data sent from a motion detector placed on the floor and protected by wire basket. A ball and two other objects, a Frisbee and a set of coffee filters, will be released so that they move vertically above the motion detector. The resulting motion graphs will be used to check your predicted graphs and the graphs will be analyzed and compared to theory.

Apparatus: motion detector mini basketball Frisbee & coffee filters computer wire basket step stool (share it with others) Section LD01 will do the lab set up. Section LD02 will do the lab clean up. This ensures we share the task and everyone gets some help from others. Section LD01: set up carefully. Once you are done with your lab, please ensure that the lab apparatus is intact. Patience during the lab set up is important. Take a few extra moments to ensure that you have a good and study set up. So in this case, please ensure that you have secured the metal cage to the floor. Do not use excess amount to tape for this. Physics analysis of the lab doesn’t depend on this but if we do not secure the cage, it moves every time the ball or projectile hits it. It messes with the motion sensor alignment and you have to adjust everything for every run. Section LD02: please use the apparatus with care. Remove the metal cage, use the motion sensor with care while removing them from under the cage and disconnecting them from the computer. Cleanly wrap the cords as needed. Put the balls, Frisbees, coffee filters back in the basket/tote bag. Put the motion sensor and cables on the front table. Throw away the tap. The only set up that should not be dismantled is the one on the front, middle table. Precautions:

(1) Your safety and that of others is always important. So always exert caution in the lab. (2) Patience during the data acquisition is important. You may have to do several trials to get

a good data set. When you drop the projectile, it reaches ground very quickly. So try to get a good data run and select the useful part of your graph for analysis. Determine what is a “useful part of the graph” and why.

(3) Try to drop things from more than 2 meters height above the motion sensor.

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Formal Lab Write-up Alert!! This lab will be written up as a formal lab write-up. The lab will take two class periods: during the first class period, you will conduct the experiment and complete the Observations, Data, and Analysis Sheet, which you will turn in at the end of lab. During the second class period (next week), you will be given time to work on your formal (typed) lab write-up, and the instructor will provide guidance for you to conduct the proper analyses. SET UP. 1. Place the motion detector on the floor and protect it with the wire basket. If necessary, you

may have to unplug the detector and run the cable through the side of the basket and then re- plug the detector.

2. Open the file called AccGravity from Desktop. The computer screen should show four

graphs, Position, Velocity, Acceleration and Velocity & Acceleration. The time axis of each graph should be from 0 to 2 seconds. The position axis should be from 0 to 2 meters, the velocity axis from -10m/s to 10 m/s, and the acceleration axis from -11 m/s2 to 11 m/s2. The last graph, Velocity & Acceleration, has the same axis as the acceleration graph.

3. At the top of the screen is a button labeled Collect. When you click on this button, you will

hear a few clicks as the software prepares to make measurements. Then you will hear rapid clicking (almost a buzz) as sonic pulses are sent out by the motion detector and data is collected and plotted on the four graphs.

4. Test the measurement System. As a test of the measurement system, hold the flat side of the

Frisbee above the motion detector, click on Collect, and move the Frisbee up and down by hand, noting the results plotted on the screen. Consult with your instructor if you have problems.

5. Follow the instruction on the Data Sheet. FORMAL LABORATORY REPORT (next class: will be explained later) Once your data sheet is complete, begin work on the formal laboratory report, as described in the introduction. In the discussion section, be sure to address the following question:

The theory of air resistance predicts that as an object moves faster and faster through the air, the resistive force becomes greater and greater and the rate of change of the velocity must decrease, eventually becoming zero. That is, as the object falls, its acceleration decreases and eventually becomes zero and the velocity of the falling object becomes constant. This constant velocity is called terminal velocity. Examine the motion graphs for the falling coffee filters. Is there any evidence for this type of motion or for terminal velocity? Comment and explain.

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OBSERVATIONS, DATA, AND ANALYSIS SHEET STRAIGHT LINE MOTION Date ____________ Group members: _____________________________________________________________________________

4. ACCELERATION DUE TO GRAVITY Date ____________ Be sure to complete the set up and test as described in the SET UP for this experiment. Since it takes so little time to get experimental data for each trial below, you can repeat the experiment over and over until you get data that looks good to you For each Procedure below, you will acquire and analyze motion data that is displayed as motion graphs on the computer screen. At any time, if you are not sure what information is displayed by the graphs, consult with your instructor. The expected acceleration due to gravity to 3 significant figures in Largo is 9.80 m/s2. PROCEDURE 1. – Acceleration of a Falling Mini-Basketball. 1. Sketch Your Predictions for the Motion Graphs. Before doing the experiment with the falling basketball, imagine

that it is held high above the ground and released from rest so that it falls toward the ground. Discuss with your partners what the position vs. time, velocity vs. time, and acceleration vs. time plots should look like. Ignore any rebound. Sketch each of your predicted plots on the graphs below using a dotted line. Please do not change your predictions after seeing the actual motion plots.

2. Do the Experiment. To test your predictions, hold the basketball high directly above the motion detector (use a

step-stool if needed). Click on Collect and after you hear the “buzz” of data collection, drop the ball from rest. To avoid problems caused by hitting the wire cage, someone can catch or trap the ball just as it hits the cage.

a) View the experimental graphs. Note that the falling motion of the ball is only a small part, perhaps one-third, of the total recorded time data. Pay attention only to that part of the computer plot that represents the “falling motion” that you are studying. Also keep in mind that the recorded velocity vs. time and acceleration vs. time plots may be bumpy. If the velocity results seem too bumpy, repeat the experiment until you get fairly smooth results. The fourth graph, Velocity & Acceleration, allows you to examine both graphs together and to visually compare them. If you have trouble understanding the measured motion plots, consult with your instructor.

b) Sketch the Experimental Graphs (you should also take a picture of the data run you have selected for your

analysis because you will include it in your lab report). After finding the “falling motion” part of each graph, sketch the results for the falling motion only on the above graphs using a solid line. Do not erase your predictions. Smooth out any bumps that appear in the experimental graphs.

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velocity acceleration

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Q1. If your prediction for the graphs above was different from the results, explain the discrepancy. If it was correct, explain why you made the predictions you did.

3. Record Data from the Experimental Graphs. You will record data from the velocity plot and from the position

plot for use later in your analysis.

a) Selecting a portion of the graph. Before analyzing data on a graph, you must select the region that you want to analyze. To select a part of a graph, place the cursor at the upper left of the region you wish to select and, while holding down the left mouse button, scroll the cursor across and down through the region. As you do this, the selected region is highlighted. Be sure the selected region does NOT include any part of the motion that is not the “falling motion”.

b) Velocity Plot. Select the linear region of the velocity plot and fit it to a linear function. To fit the data to a linear function, click on Analyze on the Menu Bar and select Linear Fit…. The program will do a linear regression (like the one done by your calculator) and show the coefficients of the fit. Click OK and the program will display the original graph with a box that gives the slope and y-intercept of the fit (ignore the error information). The program will also plot the linear regression line on the plotted data. The box can be moved to a convenient position by clicking and dragging it. You can remove the box by clicking on the x- mark in the upper left hand corner of the box. Record below the results for slope and y-intercept of your regression analysis with proper units. Use the procedure described in the Uncertainty section in the introduction to estimate the uncertainty of both quantities.

slope _________ y-intercept ___________ Q5. What are the physical meaning of the slope and y-intercept on the v. vs. t graph? Find an experimental value for the acceleration due to gravity, g. Q6: Is it possible to determine the acceleration due to gravity (g) in Largo from your experiment? Explain. Q7. The accepted value for g in Largo is 9.80m/s2. Calculate the discrepancy and percent discrepancy between the accepted value and your measured value of g. Discrepancy:____________________ Percent Discrepancy:____________________ Explain the percent discrepancy in the value of “g” you have determined.

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PROCEDURE 2. – Motion of a Mini-Basketball Tossed Straight Up. This is a more difficult motion to capture using the motion detector. Sketch your predictions before doing the experiment. 1. Sketch Your Predictions for the Motion Graphs. Before doing the experiment, imagine the basketball held low,

just above the ground and is tossed straight upward so that it rises to a maximum height then falls back downward toward the ground. Discuss with your partners what the position vs. time, velocity vs. time, and acceleration vs. time plots should look like for the complete up and down motion of the ball. Sketch each of your predicted plots on the graphs below using a dotted line. Please do not change your predictions after seeing the actual motion plots.

2. Do the Experiment. Test your predictions by doing the experiment. With the basketball held just above the

motion detector, click the Collect button, and after you hear the “buzz” of data collection, toss the ball straight up and allow it to come back down again. You can either catch or trap the ball as it hits the wire basket. You task is to collect data for the entire upward and downward motion of the ball. You can repeat the experiment until you obtain data you want.

a) View the experimental graphs. As above, only pay attention to that part of the computer plot that represents the up and down motion of the ball.

b) Sketch the Experimental Graphs. Sketch experimental results on the above graphs using a solid line. Do not erase your predictions.

Q8. If your prediction for the graphs above was different from the results, explain the discrepancy. If it was correct, explain why you made the predictions you did.

3. Record Data from the Experimental Graphs. As above, select the appropriate velocity region of your motion and

fit it to a linear function and do the same for the appropriate position region and fit it to a quadratic function. Record the results below with proper units and uncertainties. (Since the device used was the same, you may use the same percent uncertainties you found in procedure 1).

velocity plot: slope _________ y-intercept ___________ Q9. Calculate the discrepancy and percent discrepancy between the accepted value of g (9.80m/s2 and your measured value of g. (See the Comparisons section of the introduction). Discrepancy:____________________ Percent Discrepancy:__________________

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PROCEDURE 3. – Falling Objects that Experience More Air Friction. The purpose of this part of the experiment is to observe the motion graphs of falling objects that experience more air friction that the falling ball. You are NOT asked to predict the motion graphs. 1. The Motion of the Frisbee. Hold the Frisbee above the motion detector with its curved edge side facing down

(stand on the step stool if necessary). Click the Collect button and after you hear the “buzz” of data collection, drop the Frisbee from rest. You can allow the Frisbee to hit the wire basket. You want the Frisbee to fall flat through the air. Repeat the experiment, until you get good data

a) Sketch the Experimental Graphs. View the resulting motion graphs and sketch the results on the graphs

below using a solid line. b) Record Data from the Experimental Graphs. Select only the data from the velocity vs. time plot and fit it to a

linear function. Record the results below with proper units and uncertainties. velocity plot: slope _________ y-intercept ___________ Q10. What are the physical meaning of the slope and y-intercept on the v. vs. t graph? Explain whether this acceleration represents the acceleration due to gravity.

2. The Motion of Falling Large Coffee Filters. Select a set of three or four large coffee filters that are pressed together. Hold the filters above the motion detector with the flat side facing down. Click the Collect button and after you hear the “buzz” of data collection, drop the filters from rest. You want the filters to fall flat through the air. You can repeat the experiment until you get a “flat fall”. View the resulting motion graphs. You are looking for evidence that the falling filters reached terminal velocity. If you don’t see evidence of terminal velocity, repeat the experiment, perhaps using fewer filters. If you are not sure what terminal velocity graphs should look like, consult with your instructor.

Sketch the Experimental Graphs. Sketch the results on the graphs below using a solid line. No experimental data

will be recorded using these graphs.

Q11. What are the physical meaning of the slope and y-intercept on the v. vs. t graph? Explain whether this acceleration represents the acceleration due to gravity.

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velocity acceleration

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velocity acceleration

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