PHYSICS LAB
FREE FALL
Printed Names:
Signatures:
Date:
Lab Section:
Instructor:
GRADE:
PHYSICS DEPARTMENT
JAMES MADISON UNIVERSITY
Revision August 2003
Free Fall
FREE FALL
Part A – Error Analysis of Reaction Time
An important facet of experimentation is error analysis (finding uncertainty). In this section of this lab,
you will be introduced to this concept in relation to measurements of your reaction time. This lab will
also provide instructions and experience using the program Logger Pro in entering and manipulating
data.
OBJECTIVES
§
§
§
To measure and compare the reaction times of your left and right hands.
To develop skills in use of Logger Pro for data entry and analysis.
To become familiar with basic techniques in error analysis and propagation.
MATERIALS
Dell computer
Meter stick
Logger Pro
PROCEDURE
1. Have your partner hold the meter stick vertically in front of you. Place your thumb and
forefinger of your dominant hand on either side of the stick at the 50 cm mark. Make this
measurement as accurately as you can.
2. Your partner will release the meter stick. Try to grab the stick as it falls as quickly as possible.
Try not to anticipate the drop and do not move your hand down with the motion of the stick.
3. Measure the distance the stick has fallen. Make this measurement at least to the nearest
millimeter. Record your data with pencil and paper. Complete 10 trials.
4. Enter your data into an Excel spread sheet. You will need a column for the distance (reaction
distance). Add a column for the uncertainty in the measured distance and a comment or text box
comment justifying these numbers. Make an educated guess. Do not use a mathematical
formula. Consider the measurement and decide how well you can make a measurement of the
reaction distance. (Note you may decide to use a single value as an estimate for all your
measured distances. You may decide to use a different value for each measurement. There is no
correct answer. Your justification is important. Be sure that you have made a good argument to
justify your educated guess.) Your data sheet will be your report for this lab so label columns
and include comments with text boxes whenever necessary.
5. Calculate your reaction time.
a. d = ½ g (∆t)2 is the equation relating the distance an object will fall from rest as a
function of time. Rearrange the equation to solve for ∆t. ∆t is reaction time.
b. Add a column deltaT and use Excel formulas to calculate.
ANALYSIS
1. Use Excel to find the Mean, Standard Deviation, Standard Deviation of the Mean and Number
of Points for the distance dropped and for the reaction time.
2. Build a table with these results for your dominant hand (see example below.) Include a row that
shows your reaction distance and one for the reaction time. Express results with correct
significant figures, and units.
Free Fall 54
Picket Fence Free Fall
Dominant Hand
Number of Points
Mean
Standard Deviation
Std. Dev. of Mean
Distance Dropped
Reaction Time
3. Repeat the experiment on the same person using the other hand.
Answer these questions in text boxes on the spread sheet.
QUESTIONS
1. Compare the SD in table with your uncertainty for a single measurement (procedure step 4).
Should the values agree ? If so, why don't they agree ? DO NOT CHANGE YOUR
GUESS.
For the following questions assume that the mean is the best guess for your result. Assume that the
SDM is the best estimate for the uncertainty in your result.
2. Is there a statistically significant difference in the reaction time between the two hands? (Justify
your answer.)
3. How many points would be required to reduce the SDM to a value ten times smaller ?
4. How does the uncertainty in the reaction time compare with the uncertainty in the distance?
a. First calculate the percent uncertainty in the distance d, (uncertainty in d)/d x 100. (
Use the SDM and mean calculated on the previous page.)
b. Now calculate the percentage uncertainty in the time t.
c. Construct the following table in Excel.
A: percent uncertainty in
B: percent uncertainty in
Dominant Hand
Non-Dominant Hand
d. (EXTRA CREDIT answer this question after you have finished the entire lab.) Look
through the "Error Analysis Cookbook" at the front of the lab and write a brief
explanation of this result.
Part B - Picket Fence Free Fall
We say an object is in free fall when the only force acting on it is the earth’s gravitational force. No
other forces can be acting; in particular, air resistance must be either absent or so small as to be ignored.
Free Fall
55
Free Fall
When the object in free fall is near the surface of the earth, the gravitational force on it is nearly constant.
As a result, an object in free fall accelerates downward at a constant rate. The magnitude of this
acceleration is usually represented with the symbol g and has been found to be equal to 9.8 m/s2.
Physics students measure the acceleration due to gravity using a wide variety of timing methods. In this
experiment, you will have the advantage of using a very precise timer connected to the computer and a
Photogate. The Photogate has a beam of infrared light that travels from one side to the other. It can
detect whenever this beam is blocked. You will drop a piece of clear plastic with evenly spaced black
bars on it, called a Picket Fence. As the Picket Fence passes through the Photogate, the computer will
measure the time from the leading edge of one bar blocking the beam until the leading edge of the next
bar blocks the beam. This timing continues as all eight bars pass through the Photogate. From these
measured times, the program will calculate the velocities and accelerations for this motion and graphs
will be plotted.
Picket
fence
Figure 1
OBJECTIVE
§
§
§
To determine the acceleration of gravity (g) by measuring the acceleration of a freely falling
body.
To become more familiar with the concept of velocity and acceleration.
To gain experience in using graphical methods in the analysis of experimental data.
MATERIALS
Power Macintosh or Windows PC
Universal Lab Interface
Logger Pro
Vernier Photogate
Picket Fence
clamp or ring stand to secure Photogate
Free Fall 56
Picket Fence Free Fall
PROCEDURE
BE SURE YOU COLLECT THE DATA BEFORE YOU LEAVE THE LAB. IF THE
ANALYSIS IS INCOMPLETE YOUR INSTRUCTOR MAY REQUIRE YOU TO
COMPETE THE ANALYSIS AT HOME.
1. Fasten the Photogate rigidly to a ring stand so the arms extend horizontally, as shown in Figure 1.
The entire length of the Picket Fence must be able to fall freely through the Photogate. To avoid
damaging the Picket Fence, make sure it has a soft surface (such as a carpet) to land on.
2. Connect the Photogate to the DG 1 input on the LabPro.
3. Prepare the computer for data collection by “Exp 05” from the Intro to Physics folder of Logger
Pro. Two graphs will appear on the screen. The top graph displays distance vs. time, and the lower
graph velocity vs. time.
4. Observe the reading in the status bar of Logger Pro at the bottom of the screen. Block the
Photogate with your hand; note that the Photogate is shown as blocked. Remove your hand and the
display should change to unblocked. If this is not so, consult your instructor.
5. Click
to prepare the Photogate. Hold the top of the Picket Fence and drop it through the
Photogate, releasing it from your grasp completely before it enters the Photogate. Be careful when
releasing the Picket Fence. It must not touch the sides of the Photogate as it falls and it needs to
remain vertical. Click
to end data collection if necessary.
6. Move the data to your Excel spread sheet (new worksheet). Enter values for the uncertainties in
position, velocity, and time as unknown (You may just include a comment). Plot the data. The slope
of a velocity vs. time graph is a measure of acceleration. If the velocity graph has a constant slope,
the acceleration is constant. If the acceleration of your Picket Fence appears constant, fit a straight
line to your data (see FITTING DATA appendix.). Be sure that you have an uncertainty for each
parameter. Cut and paste the parameters from the fit to excel. Be sure to organize and label these
values.
7. To establish the reliability of your measurement, repeat Steps 5 and 6 at least three more times. Do
not use drops in which the Picket Fence hits or misses the Photogate. Record the slopes and initial
velocities in the spread sheet as shown.
Trial
2
Acceleration (m/s )
uncertainty based on fit
Initial Velocity (m/s)
uncertainty based on fit
1
2
3
4
5
6
ANALYSIS
Use text boxes to include text answers in the spreadsheet.
1. From your trials calculate mean value, standard deviation, and the standard deviation of the mean
for the acceleration of the Picket Fence. Record them in an excel data table.
Mean
St. Dev. (SD)
Std. Dev.of Mean (SDM)
Acceleration (m/s-s)
Free Fall
57
Free Fall
2. Plot and describe in words the shape of the velocity vs. time graph of your final successful trial.
How is this related to the shape of the distance vs. time graph?
3. Compare your measurement to the generally accepted value of g (from a textbook or other source).
Do this by determining how well the accepted value lies within your value ± your uncertainty (i.e.,
Accepted Value - Your Value
=
Your Uncer tainty
your Standard Deviation of the Mean) through the following formula:
If this number is less than 3, then you have an experimental value that does not exclude the accepted
value to at least 95% certainty, meaning your experiment did not go against the accepted value.
4. Did you have a systematic error in your data compared with the theoretical value of g? How do
you know? How do you account for this systematic error?
Item
Instuctor's Evaluation
Measured distance dropped and made an
educated guess at uncertainty.
Calculated values for ∆t and correctly calculated
the uncertainty.
Mean, Standard Deviation and Standard Deviation
of Mean for d and ∆t
Reaction time with uncertainty and significant
figures
Question 1 (Difference in right and left hand)
Question 2 (Improve accuracy x10)
Question 3 (Relationship uncertainties in ∆t and d)
Photogate data -> spreadsheet, plotted, fit
Placed fit on plot and evaluated
Tabulated several trials
Mean, Standard Deviation and Standard Deviation
of Mean for g
Examine 1 of the distance vs time graphs
Comparison of distance vs time and velocity vs
time
Comparison g measured to accepted value with
understanding of uncertainty.
Analysis of distance vs time using trendline
Free Fall 58