PHY132
Experiment
3
2-d motion
In this experiment, you will use equations to predict where a ball in parabolic motion will fall
on the floor, and compare this prediction against measurements.
PROCEDURE
1. Set up an inclined tunnel made of paper on a table so that a ball can roll down it, across a
short section of table, and off the table edge. You do not need to make the ramp very high. A
smaller gradient works better. Use tape to secure your ramp.
2. Position the photogates so the ball passes through each of the photogates while rolling on the
horizontal table surface. Connect photogate 1 (the first to detect the ball) to the DIG/SONIC 1
of the LabPro and photogate 2 to the corresponding second port.
3. Mark a starting position on the ramp so that you can repeatedly roll the ball from the same
place. Roll the ball down the ramp through each photogate and off the table. Do a few trial
runs to make sure the ball does not hit either photogate.
4. Open the experiment file 08 Projectile Motion in the folder Physics with Vernier. A data
table and two graphs are displayed; one graph will show the time required for the ball to pass
through the photogates for each trial, and the other will display the velocity of the object for
each trial: you are only interested in this velocity graph.
5. You must enter the distance d (see figure above) between photogates in order for LoggerPro
to calculate the velocity. The program will divide this distance by the time interval t it takes
the ball to roll between gates to get the velocity (v0x = d/t). Carefully measure the distance
from the beam of photogate 1 to the beam of photogate 2. (It may be easier to measure from
the leading edge of photogate 1 to the leading edge of photogate 2.) To successfully predict
the impact point, you must enter an accurate measurement. Enter the distance into LoggerPro
by double clicking on the gate_spacing box: a new window will appear. Enter your value in
meters (do not change to cm). Click
.
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6. To check that the photogates are responding properly click
and roll the ball from the
start point you marked. LoggerPro will plot a velocity point for each instance the ball runs
through the photogates. If no point shows up after the ball has passed, then the order of the
photogates must be inverted. Once this is checked, and to prevent accidental movement of
the photogates, use tape to secure them in place.
7. Estimate, through trials, the position on the floor where the ball lands. Once you are satisfied,
anchor a piece of plain paper on the floor and position carbon paper on top of it such that
after each run you can lift the carbon paper and measure the position of the mark left by the
ball on the bottom paper.
8. During the experiment, take care not to bump any of the photogates, ramp, table or paper on
the floor, or your data will not be precise.
9. Click
collection.
then click
again, to clear the trial data and prepare for the actual data
10. Roll the ball from the start point you marked. Let it roll over the table and hit the floor. It will
leave a mark on the paper under the carbon sheet. Repeat for a total of 12 runs.
Note: Do not click stop after each run. Do so only after the last run or else you will lose all
previous data. The ball may not land on the same spot each time but they should be close.
11. After the last trial, click
to end data collection.
12. You should see 12 data points on the velocity graph, one corresponding to each run. These
show the velocity of the ball as it exits the photogate, just before it rolls off the edge. Click
on the velocity graph. Now click Autoscale from the top menu. Call your instructor to
examine the distribution of points. If there are no stragglers in your distribution, you will stay
with the 12 points. Otherwise, the instructor will help you delete a few points (hopefully not
more than a couple) if necessary. Now select all points in that graph (click and drag mouse to
highlight). Then click on the Statistics button from the top menu. Record the mean value in
the Data Table as the average initial velocity of the ball for this experiment (v0x).
13. Lift the carbon paper and measure the horizontal distance ∆x from the edge of the table to
each point of impact. You may want to use a plumb bob (ask instructor) to accurately project
the edge of the table on the floor, and then measure horizontal distances in respect to that
projected edge. Record them in your Data Table. You should have 10-12 entries for ∆x.
14. Carefully measure the distance from the tabletop to the floor and record it as the vertical
distance |∆y| in the Data Table (units, sig. figs.).
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DATA TABLE
Average initial velocity = v0x =
trial
Measured horizontal distance of ball
∆x (m)
Some 2-d motion equations
∆𝑥⃗ = 𝑣⃗0𝑥 𝑡
𝑡=√
2∆𝑦⃗
−𝑔
Height of table = |∆y| =
ANALYSIS OF EXPERIMENT
15. Calculate the average ∆x and enter it in your Analysis Table. This is your measured
horizontal distance.
16. Use your values of average v0x and ∆y and the equations for projectile motion as learned in
lecture (also shown below) to calculate a horizontal distance, ∆x. Call this is your predicted
horizontal distance. Record it in your Analysis Table. (g = 9.8 m/s2)
ANALYSIS TABLE
Average measured
∆xmeas
(m)
Predicted
∆xpred
(m)
_________±_______
_________±_______
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Percent difference
(%)
TABLE OF UNCERTAINTIES
v0x (standard deviation of mean, from statistical box)
|y| (meter stick)
xmeas (standard deviation of mean, calculated)
δv0x = 
δy = 
δxmeas = 
You must show the final uncertainties for xmeas and xpred in the Analysis Table.
The uncertainty for xmeas comes directly from the calculation of the standard deviation of the
mean (equation provided in handout given at the start of semester).
The uncertainty for xpred must follow error propagation equations (also in first handout;
example is shown here, but you must learn how to write these formulas on your own during the
semester):
𝑪𝒂𝒍𝒍 𝑷𝟏 =
𝑺𝒐,
𝟐∆𝒚
−𝒈
𝒕 = √𝑷𝟏
𝑭𝒊𝒏𝒂𝒍𝒍𝒚,
𝒕𝒉𝒆𝒏
𝒂𝒏𝒅
𝜹𝑷𝟏 = |𝑷𝟏|
𝜹∆𝒚
∆𝒚
𝒕 𝜹𝑷𝟏
𝜹𝒕 = | |
𝟐 𝑷𝟏
∆𝒙𝒑𝒓𝒆𝒅 = 𝒗𝟎𝒙 𝒕 𝒂𝒏𝒅 𝒕𝒉𝒆𝒏
𝜹∆𝒙𝒑𝒓𝒆𝒅
𝜹𝒗𝟎𝒙 𝟐
𝜹𝒕 𝟐
√
= |∆𝒙𝒑𝒓𝒆𝒅 | (
) +( )
𝒗𝟎𝒙
𝒕
REPORT DUE IN 1 WEEK
For next week you must submit a lab REPORT in the format handed to you at the start of the
semester. Notice that you must show all error calculations in details, and also present the final
errors in the Analysis Table.
In the conclusion, answer the following questions:
1) Did the values of xmeas and xpred agree within their calculated uncertainties? If not,
suggest explanation.
2) Which value would you expect to be smaller: xmeas or xpred? Give an explanation.
Finally, you must also attach the following video analysis exercise to your report (2 pages).
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VIDEO ANALYSIS
Open the experiment file <GalileoNow.cmbl> inside the directory Desktop>MovieClips. This
experiment already contains a movie scaled in meters. Now make the video window as large as
possible. Click at the bottom-right box Sync movie to graph: select the boxes in the window that
pops up, then OK. Go to frame 18. Collect data using the Add Point tool ( ) at the bar on the
right: click on the center of the ball in each frame to record its horizontal and vertical positions.
Note: If you mess up, you can close and re-open the file or start over by choosing Clear All Data
from the Data menu. Alternatively, return to the frame with the badly located point on it, click
the Select Point tool (), and drag the bad point to its proper location with the mouse. Once you
are done collecting data, look at the graphs. Select Curve Fit from the top menu and choose
functions that best match the data in each graph. Remember to select the Time Offset box in the
Curve Fit window. Perform the best fit for each graph.
Answer the following questions and show all calculations.
1) What is the equation that fits the graph Vertical Position vs. Time? Show values.
2) From this best-fit equation, what is the value of the initial vertical velocity of the ball in
frame 18?
3) From this best-fit equation, what is the vertical acceleration of the ball?
4) Using the graph or video, measure how long it took the ball to fall from the edge of the table
(frame 18) to the floor.
5) What is the final vertical velocity of the ball when it is about to touch the ground? Use the
results of questions 2, 3 and 4 to calculate this value. Your result should be close to the
approximate value of 4.4 m/s obtained from the software.
6) Use the time found in question 4, and the equation in question 1 to calculate the vertical
displacement of the ball when it strikes the floor. Then compare its magnitude with the height
of the table measured on the video (use the Photo Distance tool on the bar on the right of the
video to measure the height of the table). Calculate the % difference.
% diff = ______
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7) What is the equation that describes the graph Horizontal Position vs. Time? Show values.
8) From this best-fit equation, what is the initial horizontal velocity when the ball is in frame
18?
9) From this best-fit equation, what is the horizontal acceleration of the ball in the air?
10) What is the final horizontal velocity of the ball when it is about to touch the ground?
11) Use the time found in question 4, and the equation in question 7 to calculate the horizontal
displacement of the ball from the edge of the table (frame 18) to the ground. Compare it
(calculate the % diff) with a direct measurement of x on the video (use the Photo Distance
tool on the bar on the right of the video to measure the distance on the floor from the
projected edge of the table, to the final position on the floor).
% diff = ______
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