Lab
Range of a Projectile
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The
purpose
of this experiment is to verify that projectiles experience the same acceleration once they are in freefall. You will also collect data to verify the equation for a projectile's range: R = v
_{H}
t.
Materials
1 computer
1 LabPro Interface w/power supply and USB cable
1 motion detector w/communication cable
3 meter sticks
1 large white target paper
5 sheets of carbon paper
Interfacing Setup
Directions
On the floor at the end of your table, tape a piece of target paper so that it is parallel to the edge of the table. Then use a meter stick or plumb line and project the edge of the table onto the paper. Mark that distance from the base of the table - it is your plumb line distance and represents the starting position to measure the ball's range along the target paper.
Measure the distance from the floor to the top of the table: ________ cm
Next place as many sheets of carbon paper as necessary to cover the target paper. Make sure that the carbon paper is "ink side down" so that the golf ball will transfer a mark to the target paper when it strikes the ground. Make sure that you put your names on your target sheet.
Launch the program Logger Pro 3.1 by going to Start → Programs → Grant Tools → Logger Pro 3.1. The program should automatically set up graphs according to the connected sensors. With the motion detector properly connected, the program should display graphs of position versus time and velocity versus time. We will only be examining the position vs time graph displayed on the top right side. The chart on the left side will display the data as it is being collected.
After you have set up your motion detector and rulers (which will act as guides to keep the golf ball rolling "relatively" straight) and you are ready to begin the experiment, hit the "Collect" button
on the top right-hand side of the program window. Data collection will commence immediately. After a few "clicks," one team member will push the golf ball away from the detector, while the other team members monitor the computer screen and watch where the ball hits the target paper.
Remember to roll the ball straight across the table, not at a slant, so that the motion detector can properly track its location towards the edge of the table. Be aware that the detector cannot see the ball when it is within 20 cm. Each time the ball strikes the target paper, lift up the carbon paper and MARK the spot. Each spot is to be numbered so that the range, when measured, can be correlated with that trial's appropriate horizontal velocity. You must have twelve (12) unique velocities or ranges.
PLEASE be careful to alert everyone when a trial is going to commence.
Do NOT assume that everyone is ready. Keep your group working together!
When each trial ends, the person monitoring the computer will use the mouse to mark the section of the graph that delineates the ball's motion along the table between the rulers. As they drag their mouse a gray rectangular shaded area will appear. The area chosen should only include the "good section" of the data - the section with the "smoother slope." Then they will press the "R" key
to display the regression line's statistics. The slope is
0.1000
in the following diagram.
Remember that the team member monitoring the target paper must number the impact points by their trial number. The third member should write down each trial's slope in the data chart before the computer program is rerun for the next trial.
The team member operating the computer should first close each trial's regression window by clicking the small "x" on the upper left hand corner next to "Linear Fit For:" before he starts collecting the next round of data.
Repeat this process until you have a minimum of 12 good trials. "Good" means that no two trials are identical either on the target paper or their slope values. "Good" also means that the data reflects a wide distribution of range values in your impact positions.
Trial
Slope
(m/sec)
Range
(m)
1
2
3
4
5
6
7
8
9
10
11
12
When your group is finished collecting data, clean up your station by:
exiting Logger Pro 3.1 without saving changes,
returning your meter sticks and carbon paper;
folding your target paper into a size approximating an 8½ x 11 sheet of paper and placing your names and period on the outside;
turning in your target paper and data chart; and
unplugging your AC adapter.
The next period will be using the same equipment, so you do NOT need to dismantle the LabPro and the motion detector.
Analysis and Conclusions
1. Based on the height of your table, calculate the time a golf ball dropped from rest from that height would spent in the air. Show your givens, formula, and calculations in the area provided below. Be careful of units!
After measuring the range for each trial, record your information in your data table and the input your data into the EXCEL spreadsheet
range.xls
that accompanies this lab. While at school, remember that you have to open the file called 1-range.xls in your period's folder on the file system and then immediately save it as your own with the title LastnameLastnameLastnameRange.xls
2. After saving your file get a printout of your graph and data table.
3. On your printout, write the line's equation using correct variables and the correct numerical values for its slope and y-intercept. Type in your graph's equation in the textbox provided.
4. Type in your graph's slope in the textbox provided.
5. What physical quantity does the slope of your line represent?
6. In this experiment, what would be the hypothetically "perfect" y-intercept? Justify your answer.
7. Using your results from questions 1 and 3, calculate your experiment's accuracy.
8. True or False? During this experiment, each golf ball spent the same amount of time in the air.
True
False
9. True or False? If a golf ball during one trial had twice the horizontal velocity that it had during a second trial, then the ranges for the two trials should be in a ratio of 2:1.
True
False
10. Let R
_{1}
be the range for a golf ball traveling at a velocity of
v
across our current lab tables. Let R
_{2}
be the range for the same golf ball traveling at the same velocity
v
across a lab table that is twice as high as our lab tables. Which of the following relationships is correct?
R
_{2}
= 2R
_{1}
R
_{2}
=
R
_{1}
R
_{2}
= R
_{1}
R
_{2}
= (½
)R
_{1}
R
_{2}
= ½R
_{1}
On your target paper, be sure to (1) number all of the ball's impact points, and (2) label your base line. Then trim it down as small as possible, fold it and attach it to your cover sheet, data chart, and your EXCEL printout. Please make sure that the target paper can be opened without having to remove the staples and that your group names are on EVERY PAGE of your lab report! Turn your paper work in to the one-way box.
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