PASCO ME-9215B User manual

012-06379B
Instruction Manual and
Experiment Guide for
the PASCO scientific
Model ME-9215B
Includes
Teacher’s Notes
and
Typical
Experiment Results
PHOTOGATE TIMER

012-06379B Photogate Timer
®
i
Table of Contents
Page
Copyright, Warranty and Technical Support .................................................... ii
Introduction ...................................................................................................... 1
Operation ......................................................................................................... 2
Accessories for the Photogate Timer ................................................................ 4
10 Copy-Ready Experiments: .......................................................................... 4
Experiment 1: Instantaneous vs Average Velocity .................................... 5
Experiment 2: Kinematics on an Inclined Plane ........................................ 7
Experiment 3: Speed of a Projectile .......................................................... 9
Experiment 4: Newton's Second Law ...................................................... 11
Experiment 5: The Force of Gravity ........................................................ 13
Experiment 6: Conservation of Momentum ............................................. 15
Experiment 7: Kinetic Energy .................................................................. 17
Experiment 8: Conservation of Mechanical Energy ................................. 19
Experiment 9: Elastic-Kinetic Energy ...................................................... 21
Experiment 10: Pendulum Motion ........................................................... 23
Teachers Guide ............................................................................................... 27
Maintenance .................................................................................................. 39

Photogate Timer 012-06379B
®
Copyright, Warranty and Technical Support
Copyright Notice
The PASCO scientific 012-06379B Instruction
Manual is copyrighted with all rights reserved.
Permission is granted to non-profit educational
institutions for reproduction of any part of this
manual, providing the reproductions are used only in
their laboratories and classrooms, and are not sold for
profit. Reproduction under any other circumstances,
without the written consent of PASCO scientific, is
prohibited.
Limited Warranty
For a description of the product warranty, see the
PASCO catalog.
Technical Support
For assistance with any PASCO product, contact
PASCO at:
Address: PASCO scientific
10101 Foothills Blvd.
Roseville, CA 95678-9011
Phone: [phone] (worldwide)
800-772-8700 (U.S)
FAX: [phone]
Web www.pasco.com
email: [email protected]
ii

012-06379B Photogate Timer
1
®
Introduction
Detector
LED: Lights when
beam is blocked
Infrared beam
The PASCO ME-9215B Photogate Timer is an accurate
and versatile digital timer for the student laboratory.
The ME-9215B memory function makes it easy to time
events that happen in rapid succession, such as an air track
glider passing twice through the photogate, once before
and then again after a collision.
The Photogate Timer uses PASCO’s narrow-beam infra-
red photogate (see Figure 1) to provide the timing signals.
An LED in one arm of the photogate emits a narrow infra-
red beam. As long as the beam strikes the detector in the
opposite arm of the photogate, the signal to the timer
indicates that the beam is unblocked. When an object
blocks the beam so it doesn’t strike the detector, the signal
to the timer changes. The timer has several options for
timing the photogate signals. The options include Gate,
Pulse, and Pendulum modes, allowing you to measure the
velocity of an object as it passes through the photogate or
between two photogates, or to measure the period of a
pendulum. There is also a START/STOP button that lets
you use the timer as an electronic stopwatch.
An important addition to your Photogate Timer is the
ME-9204B Accessory Photogate, which must be ordered
separately. It plugs directly into the Photogate Timer and
triggers the timer in the same manner as the built-in pho-
togate. In Pulse Mode, the Accessory Photogate lets you
measure the time it takes for an object to travel between
two photogates. In Gate mode, it lets you measure the
velocity of the object as it passes through the first
photogate, and then again when it passes through the
second photogate.
LED:
Source of infrared
beam
➤➤
➤➤
➤NOTES:
cThe Photogate Timer can be powered using
the included 7.5 V adapter. It will also run
on 4 C-size, 1.5 Volt batteries. Battery in-
stallation instructions are in the Appendix.
dTen ready-to-use experiments are included
in this manual, showing a variety of ways in
which you can use your Photogate Timer.
The equipment requirements vary for differ-
ent experiments. For many of the experi-
ments, you will need an air track (dynamics
carts will also work). Many also require a
ME-9204B Accessory Photogate in addition
to the Photogate Timer. Check the equip-
ment requirements listed at the beginning of
each experiment.
Figure 1: The PASCO Photogate Head
Plug in RJ12 connector
from Photogate timer

2
Photogate Timer 012-06379B
®
To Operate the Photogate Timer:
cPlug the RJ12 phone connector from the timer into the
RJ12 phone jack on the Photogate Head.
dPlug the 7.5 volt power adapter into the small recep-
tacle on the rear of the timer and into a standard 110
VAC, 60 Hz (or 220/240 VAC, 50 Hz) wall outlet.
ePosition the Photogate Head so the object to be timed
will pass through the arms of the photogate, blocking
the photogate beam. Loosen the clamp screw if you
want to change the angle or height of the photogate,
then tighten it securely.
fIf you are using a ME-9204B Accessory Photogate,
plug the stereo phone plug of the Accessory Photogate
into the large receptacle (see Figure 2) on the rear of
the timer.
gSlide the mode switch to the desired timing mode:
Gate, Pulse, or Pendulum. Each of these modes is de-
scribed below. Switch the MEMORY switch to OFF.
hPress the RESET button to reset the timer to zero.
iAs a test, block the photogate beam with your hand to
be sure that the timer starts counting when the beam is
interrupted and stops at the appropriate time.
jPress the RESET button again. You are ready to
begin timing.
Timing Modes
Gate Mode: In Gate mode, timing begins when the beam
is first blocked and continues until the beam is unblocked.
Use this mode to measure the velocity of an object as it
passes through the photogate. If an object of length L
blocks the photogate for a time t, the average velocity of
the object as it passed through the photogate was L/t.
Pulse Mode: In Pulse mode, the timer measures the time
between successive interruptions of the photogate. Tim-
ing begins when the beam is first blocked and continues
until the beam is unblocked and then blocked again.
With an Accessory Photogate plugged into the Photogate
Timer, the timer will measure the time it takes for an
object to move between the two photogates.
Pendulum Mode: In Pendulum mode, the timer meas-
ures the period of one complete oscillation. Timing be-
gins as the pendulum first cuts through the beam. The
timer ignores the next interruption, which corresponds to
the pendulum swinging back in the opposite direction.
Timing stops at the beginning of the third interruption, as
the pendulum completes one full oscillation.
Manual Stopwatch: Use the START/STOP button in
either Gate or Pulse mode. In Gate mode the timer starts
when the START/STOP button is pressed. The timer
stops when the button is released. In Pulse mode, the
timer acts as a normal stopwatch. It starts timing when
the START/STOP button is first pressed and continues
until the button is pressed a second time.
TIMING DIAGRAMS
Operation
The following diagrams show the interval, t, that is
measured in each timing mode. In each diagram, a
low signal corresponds to the photogate being blocked
(or the START/STOP button pressed). A high signal
corresponds to the photogate being
unblocked (and the START/STOP button unpressed).
Photogate beam
7.5 volt
power adapter
to 120 VAC,
60 Hz
or
220/240 VAC,
50 Hz
Clamp screw: loosen to
adjust photogate angle or
height
MODE DIAGRAM
GATE
PULSE
PENDULUM
Figure 2: Setting Up the Photogate Timer
Photogate Head
Plug in RJ12 connec-
tor from timer
t t t t t t
t t t
tt
Accessory
photogate port
Photogate port
7.5 volt
power port
Rear panel

012-06379B Photogate Timer
3
®
SPECIFICATIONS
Detector rise time: 200 ns max.
Fall Time: 200 ns max.
Parallax error: For an object passing through the photo-
gate, within 1 cm of the detector, with a velocity of less
than 10 m/s, the difference between the true and effective
length of the object will be less than 1 millimeter.
Infrared source: Peak output at 880 nm; 10,000 hour life.
Figure 3: Timing an Air Track Glider
➤➤
➤➤
➤NOTE: If additional photogate interruptions
occur after the second time is measured, and before
the MEMORY switch is flipped to READ, they too
will be measured by the timer and included in the
cumulative time.
TIMING SUGGESTION
Since the source and detector of the photogate have a
finite width, the true length of the object may not be
the same as the effective length seen by the photo-
gate. This parallax error may be minimized by hav-
ing the object pass as close to the detector side of the
photogate as possible, with the line of travel perpen-
dicular to the beam. To completely eliminate the
parallax error in experimental data, determine the
effective length of the object as follows:
cWith the Timer in Gate mode, push the object
through the photogate, along the path it will fol-
low in the experiment.
dWhen the photogate is triggered (the LED on top
of the photogate comes ON), measure the position
of the object relative to an external reference
point.
eContinue pushing the object through the photo-
gate. When the LED goes OFF, measure the posi-
tion of the object relative to the same external ref-
erence point.
fThe difference between the first and second meas-
urement is the effective length of the object.
When measuring the speed of the object, divide
this effective length by the time during which the
object blocked the photogate.
Memory Feature
When two measurements must be made in rapid succes-
sion, such as measuring the pre- and post-collision veloci-
ties of an air track glider, use the memory function. It can
be used in either the Gate or the Pulse mode.
To use the memory:
cTurn the MEMORY switch to ON.
dPress RESET.
eRun the experiment.
When the first time (t1) is measured, it will be immedi-
ately displayed. The second time (t2) will be automati-
cally measured by the timer, but it will not be shown
on the display.
fRecord t1, then push the MEMORY switch to READ.
The display will now show the TOTAL time, t1+ t2.
Subtract t1from the displayed time to determine t2.
Figure 4: Photogate Timing a Pendulum

4
Photogate Timer 012-06379B
®
The following accessories are available to help extend the
utility of your model ME-9215B Photogate Timer. All
the accessories work equally well with either model. See
the current PASCO catalog for more information.
ME-9204B Accessory Photogate
The stereo phone plug of the ME-9204B Accessory
Photogate plugs into the phone jack on the rear of the
Photogate Timer, giving you two identical photogates
operating from a single timer. With the timer in Gate
mode, you can measure the velocity of an object as it
passes through one photogate, then again as it passes
through the second photogate. With the timer in Pulse
mode, you can measure the time it takes for an object to
pass between the two photogates. (Many of the experi-
ments in this manual are most easily performed using a
Photogate Timer with an Accessory Photogate.)
ME-9207B Free Fall Adapter
For easy and accurate measurements of the acceleration
of gravity, the ME-9207B Free Fall Adapter is hard to
beat. The Free Fall Adapter plugs directly into the phone
plug on the rear of the Photogate Timer. It comes with
everything you need, including two steel balls (of differ-
ent size and mass), a release mechanism, and a receptor
pad. The release mechanism and the receptor pad auto-
matically trigger the timer, so you get remarkably accu-
rate measurements of the free fall time of the steel ball.
ME-9259A Laser Switch
This highly collimated photodetector is identical to a
photogate, except that you use a laser (not included) as
the light source. You can now time the motion of objects
that are far too big to fit through a standard photogate.
Measure the period of a bowling ball pendulum or the
velocity of a car. The Laser Switch operates in all three
timing modes (Gate, Pulse, and Pendulum).
Accessories for the Photogate Timer
The following 10 experiments are written in worksheet form. Feel free
to photocopy them for use in your lab.
NOTE: In each experiment, the first paragraph is a list of equipment
needed. Be sure to read this paragraph first, as the equipment needs
vary from experiment to experiment.
This manual emphasizes the use of an air track, but the air track experi-
ments can also be performed with dynamics carts. Many also require a
ME-9204B Accessory Photogate in addition to a Photogate Timer.
Collision experiments, such as experiments 6 and 7, require four times
to be measured in rapid succession and are therefore most easily per-
formed using two Photogate Timers.
10 Copy-Ready Experiments

012-06379B Photogate Timer
5
®
Experiment 1: Instantaneous Versus Average Velocity
x0
1-2 cm support
x1
Figure 1.1: Setting Up the Equipment
D
D/2 D/2
Card-
board
D
Figure 1.2: Measuring Veloc-
ity in Gate Mode
EQUIPMENT NEEDED:
- Photogate Timer with Accessory Photogate
- Air Track System with one glider.
Introduction
An average velocity can be a useful value. If you know you will average 50 miles per
hour on a 200 mile trip, it’s easy to determine how long the trip will take. On the other
hand, the highway patrolman following you doesn’t care about your average speed over
200 miles. He wants to know how fast you’re driving at the instant his radar strikes your
car, so he can determine whether or not to give you a ticket. He wants to know your
instantaneous velocity. In this experiment you’ll investigate the relationship between
instantaneous and average velocities, and see how a series of average velocities can be
used to deduce an instantaneous velocity.
Procedure
cSet up the air track as shown in
Figure 1.1, elevating one end of
the track with a 1-2 cm support.
dChoose a point x1near the center
of the track. Measure the position
of x1on the air track metric scale,
and record this value in Table 1.1.
If you are using an air track with-
out a scale, use a meter stick to
measure the distance of x1from the edge of the upper end of the track.
eChoose a starting point x0for the glider, near the upper end of the track. With a pencil,
carefully mark this spot on the air track so you can always start the glider from the
same point.
fPlace the Photogate Timer and Accessory Photogate at points equidistant from x1,as
shown in the figure. Record the distance between the photogates as Din Table 1.1.
gSet the slide switch on the Photogate Timer to PULSE.
hPress the RESET button.
iHold the glider steady at x0, then release it. Record time t1,the time
displayed after the glider has passed through both photogates.
jRepeat steps 6 and 7 at least four more times, recording the times as t2
through t5.
kNow repeat steps 4 through 9, decreasing Dby approximately 10 centi-
meters.
lContinue decreasing Din 10 centimeter increments. At each value of D,
repeat steps 4 through 8.

6
Photogate Timer 012-06379B
®
Optional
You can continue using smaller and smaller distances for Dby changing your timing tech-
nique. Tape a piece of cardboard on top of the glider, as shown in Figure 1.2. Raise the pho-
togate so it is the cardboard, not the body of the glider, that interrupts the photogate. Use just
one photogate and place it at x1. Set the timer to GATE. Now Dis the length of the card-
board. Measure Dby passing the glider through the photogate and noting the difference in
glider position between where the LED first comes on, and where it goes off again. Then
start the glider from x0as before, and make several measurements of the time it takes for the
glider to pass through the photogate. As before, record your times as t1through t5. Continue
decreasing the value of D, by using successively smaller pieces of cardboard.
Data and Calculations
c For each value of D, calculate the average of t
1
through t
5
. Record this value as t
avg
.
d Calculate v
avg
= D/t
avg
.This is the average velocity of the glider in going between the two
photogates.
e Plot a graph of v
avg
versus Dwith Don the x-axis.
x1=
D t
1t2t3t4t5tavg vavg
Questions
c Which of the average velocities that you measured do you think gives the closest approximation
to the instantaneous velocity of the glider as it passed through point x
1
?
d Can you extrapolate your collected data to determine an even closer approximation to the in-
stantaneous velocity of the glider through point x
1
? From your collected data, estimate the
maximum error you expect in your estimated value.
e In trying to determine an instantaneous velocity, what factors (timer accuracy, object being
timed, type of motion) influence the accuracy of the measurement? Discuss how each factor
influences the result.
f Can you think of one or more ways to measure instantaneous velocity directly, or is an instanta-
neous velocity always a value that must be inferred from average velocity measurements?
Table 1.1 Data and Calculations

012-06379B Photogate Timer
7
®
Experiment 2: Kinematics on an Inclined Plane
EQUIPMENT NEEDED:
-Photogate Timer -Meter stick
-Ball and ramp, [A ball bearing (approximately 1.8 cm diameter) and a U-channel
ramp (approximately 50 cm long with an inside width of approximately 1 cm) will
work well, but the exact dimensions are not important].
Introduction
In this lab you will investigate how the velocity
of an object varies as it undergoes a constant
acceleration. The object is a ball rolling down
an inclined ramp. Instead of the usual investiga-
tion of velocity as a function of time, you will
measure its velocity as a function of the distance
it has travelled from its starting point.
(➤➤
➤➤
➤Note: This experiment is just as easily per-
formed with a glider on an inclined airtrack.)
Procedure
cSet up the apparatus as shown in Figure 2.1.
dMove the ball slowly through the photogate, using the
meter stick as shown in Figure 2.2. Determine the point
at which the ball first triggers the Photogate Timer—this
is the point at which the LED on top of the photogate
first turns ON—and mark it with a pencil on the side of
the channel. Then determine the point at which the ball
last triggers the timer, and mark this point also. Measure
the distance between these marks and record this dis-
tance as ΔΔ
ΔΔ
Δd. Determine the mid-point of this interval,
and mark it in pencil on the side of the channel.
eSet the Photogate Timer to GATE mode and press the
RESET button.
fMove the ball to a point 5 cm along the track above your mid-point. Hold it at this
position using a ruler or block of wood. Release the ball so that it moves along the
ramp and through the photogate. Record the distance travelled (from the starting point
to the midpoint) and the time (t1) in Table 2.1.
gRepeat the trial 3 times so you have a total of four measured times, then take the aver-
age of your measured times. Record your results in the table.
hMove the ball to positions 10, 15, 20…40 cm from the midpoint, and repeat steps 3-5.
Data and Calculations
cFor each distance from the midpoint of the photogate, calculate the final velocity of the
ball by dividing Δd by your average time.
dConstruct a velocity versus distance graph, with distance on the horizontal axis.
Ball Ramp
Fig- Mark with a pencil
on side of channel. Meter Stick
Figure 2.2: Measuring ΔΔ
ΔΔ
Δd
LED goes OFF
LED comes ON
Photogate
Timer

8
Photogate Timer 012-06379B
®
eIf the graph doesn't turn out to be a straight line (as it shouldn't), manipulate the data math-
ematically and replot it until you obtain a straight line graph. For example, try plotting dis-
tance as a function of
v, v2, 1/v, etc. From your graph, what is the mathematical relation-
ship between the velocity of an object on an inclined plane and the distance from its starting
point that it has travelled along the plane?
Questions
cThe standard equations for motion with a constant acceleration (starting from rest) include:
x = 1/2 at2and v = at. Eliminate t from these equations to determine the relationship between
x and v. Using your result and your graph, can you determine the acceleration of the ball as it
rolled down the plane?
dFrom your answer to question 1, write the equation of motion for the accelerating ball, giving
its position as a function time. Why do you think equations of motion are most often ex-
pressed as a function of time instead of simply relating position to velocity and acceleration?
Distance inside photogate =
ΔΔ
ΔΔ
Δd:
Distance
Travelled t 1t2 t3
Final
Velocity
Average
Time
t4
Table 2.1 Data and Calculations

012-06379B Photogate Timer
9
®
Experiment 3: Speed of a Projectile
Figure 3.1: Equipment Setup
Ramp
Mark with pencil
Photogate
LED comes ON LED goes OFF
Figure 3.2: Measuring ΔΔ
ΔΔ
Δd
Accessory
Photogate
Ramp
Ball
EQUIPMENT NEEDED:
-Photogate Timer, with Accessory Photogate
-Ball and ramp -Meter stick
-Plumb bob -Carbon paper
Introduction
Projectile motion adds a new dimension, literally, to experiments in linear accelera-
tion. Once a projectile is in motion, its acceleration is constant and in one direction
only—down. But unless the projectile is fired straight up or down, it will have an
initial velocity with a component perpendicular to the direction of acceleration. This
component of its velocity, since it is perpendicular to the applied force of gravity,
remains unchanged. Projectile motion is therefore a superposition of two relatively
simple types of motion: constant acceleration in one direction, and constant velocity
in an orthogonal direction.
In this experiment you will determine the initial velocity of a projectile directly,
using the Photogate Timer, and compare that with a value calculated by examining
the motion of the projectile.
Procedure
cSet up the apparatus as in figure 3.1, so the
ball rolls down the ramp onto the table, then
passes through the photogate, interrupting
the beam.
dTape a piece of paper to the table, under the
Accessory Photogate. Use the ramp to push
the ball slowly through the Accessory
Photogate, as shown in Figure 3.2. Deter-
mine the point at which the ball first triggers
the Photogate Timer—this is the first point at
which the LED turns ON—and mark it on
the paper. Then determine the point at which
the ball last triggers the timer, and mark this
point also. Measure the distance between
these marks and record this distance as ΔΔ
ΔΔ
Δd.
Replace the ramp as in Figure 3.1.
eUse a plumb bob to determine the point
directly below where the ball will leave the
edge of the table after rolling down the ramp.
Measure the distance from the floor to the
top of the table at the point where the ball
leaves the table and record this value as dy.
fTo measure the position where the ball will
strike the floor after rolling down the ramp,
tape a piece of plain paper onto the floor with a piece of carbon paper on top. The
impact of the ball will leave a clear mark for measuring purposes.
Ramp

10
Photogate Timer 012-06379B
®
gSet the Photogate Timer to GATE mode. Now move the ball to a starting point somewhere
on the ramp. Mark this starting position with a pencil so you will be able to repeat the run,
starting the ball each time from the same point. Hold the ball at this position using a ruler or
block of wood. Press the RESET button. Release the ball so that it moves along the ramp
and through the photogate. Record the time in Table 3.1.
hRepeat the trial at least four more times with the same starting point, and record your times in
the table.
iMeasure the distance from the point directly below the ramp to each of the landing spots of
your ball. Record these distances in the data table.
Data and Calculations
cTake the average of your measured times and of your measured distances. Record these aver-
ages in the data table. Also record the average distance as dxin the space provided to the right
of the table.
Table 3.1
Data from Photogate Timer
Trial Time Distance
1
2
3
4
5
Averages
v0(avg)
ΔΔ
ΔΔ
Δd=
Vertical height, dy=
Average horizontal distance, dx=
Horizontal velocity, v0=
Percentage difference =
dDivide ΔΔ
ΔΔ
Δdby your average time to determine v0,the velocity of the ball just before it left the
table.
eNow determine the horizontal velocity of the sphere using the equations for projectile motion
and your measured values for dxand dy:
dx= v0t; dy= 1/2 at2;
where aequals the acceleration caused by gravity (9.8 m/s2or 980 cm/s2).
fCompare your two values for v0. Report the two values and the percentage difference.
Optional
If you have time, choose a value for dxand a value for dy. For what value of v0will the ball
travel the distance dxas it falls the distance dy? Adjust the height and angle of the ramp and the
starting point until you produce the predicted value of v0. Now run the experiment to see if
your calculated values for dxand dyare correct.

012-06379B Photogate Timer
11
®
Experiment 4: Newton’s Second Law
EQUIPMENT NEEDED:
-Photogate timer with Accessory Photogate (or two Photogate Timers)
-Air TrackSystem with one glider -Masses
-Pulley -Pulley Mounting Clamp
-Universal Table Clamp
Introduction
There’s nothing obvious about the relationships governing the motions of objects. In
fact, it took around 4,000 years of civilization and the genius of Isaac Newton to figure
out the basic laws. Fortunately for the rest of us, hindsight is a powerful research tool.
In this experiment you will experimentally determine Newton’s second law by examin-
ing the motion of an air track glider under the influence of a constant force. The con-
stant force will be supplied by the weight of a hanging mass that will be used to pull the
glider. By varying the mass of the hanging weight and of the glider, and measuring the
acceleration of the glider, you’ll be able to determine Newton’s second law.
Procedure
cSet up the air track as shown in Figure
4.1. Level the air track very carefully by
adjusting the air track leveling feet. A
glider should sit on the track without
accelerating in either direction. There
may be some small movement of the
glider due to unequal air flow beneath the
glider, but it should not accelerate
steadily in either direction.
dMeasure the effective length of the glider, and record your value as Lin Table 4.1.
eMount the hook into the bottom hole of the cart. To counterbalance its weight, add a
piece of similar weight on the opposite end as shown on Fig. 4.1.
fAdd 50-60 grams of mass to the glider using 10 or 20 gram masses. Be sure the masses
are distributed symmetrically so the glider is balanced. Determine the total mass of your
glider with the added masses and record the total as min Table 4.1.
gPlace a mass of approximately 5-10 grams on the weight hanger. Record the total mass
(hanger plus added mass) as ma.
hSet your Photogate Timer to GATE mode.
iChoose a starting point x0for the glider, near the end of the track. Mark this point with a
pencil so that you can always start the glider from this same point.
jPress the RESET button.
kHold the glider steady at x0, then release it. Note t1, the time it took for the glider to pass
through the first photogate, and t2, the time it took for the glider to pass through the
second photogate. Repeat this measurement four times. Take the average of your mea-
sured t1's and t2's and record these averages as t1and t2in Table 4.1. panel
lSet the Photogate Timer to PULSE mode.
11
Press the RESET button.
Accessory
Photogate
Hook
Photogate
Timer
ma
String Pulley
Mounting
Rod
Counter
Balance
Glider
x0
Figure 4.1: Equipment Setup
Tableclamp

12
Photogate Timer 012-06379B
®
mm
at1t2t3v1v2aF a
Glider Length, L =
Table 4.1 Data and Calculations
12
Again, start the glider from x0. This time measure and record t3, the time it takes the glider to
pass between the photogates. Repeat this measurement four more times and record the aver-
age of these measurements as t3in Table 4.1.
13
Vary ma, by moving masses from the glider to the hanger (thus keeping the total mass,
m+ ma, constant.) Record mand maand repeat steps 5 through 11. Try at least four different
values for ma.
14
Now leave maconstant at a previously used value. Vary mby adding or removing mass from
the glider. Repeat steps 5-11. Try at least four different values for m.
Calculations
For each set of experimental conditions:
cUse the length of the glider and your average times to determine v1and v2, the average glider
velocity as it passed through each photogate.
dUse the equation a = (v2- v1)/t3to determine the average acceleration of the glider as it passed
between the two photogates.
eDetermine Fa, the force applied to the glider by the hanging mass.
(Fa= mag; g = 9.8 m/s2= 980 cm/s2)
Analysis
cDraw a graph showing average acceleration as a function of applied force, Fa,.
dDraw a second graph showing average acceleration as a function of the glider mass with Ma
being held constant.
eExamine your graphs carefully. Are they straight lines? Use your graphs to determine the
relationship between applied force, mass, and average acceleration for the air track glider.
fDiscuss your results. In this experiment, you measured only the average acceleration of the
glider between the two photogates. Do you have reason to believe that your results also hold
true for the instantaneous acceleration? Explain. What further experiments might help extend
your results to include instantaneous acceleration?

012-06379B Photogate Timer
13
®
EQUIPMENT NEEDED:
-Photogate timer with Accessory Photogate -Air Track System with one glider.
Introduction
In this experiment, you will use Newton’s Second Law (F = ma) to measure
the force exerted on an object by the Earth’s gravitational field. Ideally, you
would simply measure the acceleration of a freely falling object, measure its
mass, and compute the force. However, the acceleration of a freely falling
object is difficult to measure accurately. Accuracy can be greatly increased
by measuring the much smaller acceleration of an object as it slides down an
inclined plane. Figure 5.1 shows a diagram of the experiment. The gravita-
tional force Fgcan be resolved into two components, one acting perpendicu-
lar and one acting parallel to the motion of the glider. Only the component
acting along the direction of motion can accelerate the glider. The other
component is balanced by the force from the air cushion of the track acting in
the opposite direction. From the diagram, F = Fgsin θθ
θθ
θ, where Fgis the total
gravitational force and Fis the component that accelerates the glider. By
measuring the acceleration of the glider, Fcan be determined and Fgcan be
calculated.
Procedure
cSet up the air track as shown in Figure 5.2.
Remove the block and level the air track very
carefully.
dMeasure d, the distance between the air track
support legs. Record this distance in the
space on the following page.
ePlace a block of thickness hunder the support
leg of the track. Measure and record hon the
following page. (For best results, measure h
with calipers.)
fMeasure and record D, the distance the glider moves on the air track from where it triggers the first
photogate, to where it triggers the second photogate. (Move the glider and watch the LED on top of
the photogate. When the LED lights up, the photogate has been triggered.)
gMeasure and record L, the effective length of the glider. (Move the glider slowly through a photo-
gate and measure the distance it travels from where the LED first lights up to where it just goes off.)
hMeasure and record m, the mass of the glider.
iSet the Photogate Timer to GATE mode and press the RESET button.
jHold the glider steady near the top of the air track, then release it so it glides freely through the
photogates. Record t1, the time during which the glider blocks the first photogate, and t2, the time
during which it blocks the second photogate. Use the memory function to determine each time.
kRepeat the measurement several times and record your data in Table 5.1. You needn’t release the
glider from the same point on the air track for each trial, but it must be gliding freely and smoothly
(minimum wobble) as it passes through the photogates.
Glider
Figure 5.1: Forces Acting
on the Glider
L
d
h{=
Figure 5.2: Equipment Setup
Experiment 5: The Force of Gravity
D
Fg
ϑ
Component of Fg
perpendicular to air track
Force of air cushion
pushing glider away
from air track

14
Photogate Timer 012-06379B
®
lChange the mass of the glider by adding weights and repeat steps 6 through 8. Do this for at
least five different masses, recording the mass (m) for each set of measurements. (If you have
time, you may also want to try changing the height of the block used to tilt the track.)
Data and Calculations
Table 5.1 Data and Calculations
mt
1t2v1v2aa avg Fg
d = D = θ=
h = L =
cCalculate θθ
θθ
θ, the angle of incline for the air track, using the equation θθ
θθ
θ= tan-1(h/d).
dFor each set of time measurements, divide Lby t1and t2to determine v1and v2, the velocities
of the glider as it passed through the two photogates.
eFor each set of time measurements, calculate a, the acceleration of the glider, using the equa-
tion
v2
2- v1 2= 2a(x2-x1) = 2aD.
fFor each value of mass that you used, take the average of your calculated accelerations to
determine aavg.
gFor each of your average accelerations, calculate the force acting on the glider along its line of
motion (F = maavg).
hFor each measured value of F, use the equation F = Fgsin θθ
θθ
θto determine Fg.
iConstruct a graph of Fgversus m, with mas the independent variable (x-axis).
Analysis
Does your graph show a linear relationship between Fgand m? Does the graph go through the
origin? Is the gravitational force acting on the mass proportional to the mass? If so, the gravi-
tational force can be expressed by the equation Fg= mg, where gis a constant. If this is the
case, measure the slope of your graph to determine the value of g.
g=
Questions
cIn this experiment, it was assumed that the acceleration of the glider was constant. Was this a
reasonable assumption to make? How would you test this?
dThe equation v2
2- v1 2= 2a(x2-x1)was used to calculate the acceleration. Under what condi-
tions is this equation valid? Are those conditions met in this experiment? (You should be able
to find a derivation for this equation in your textbook.)
eCould you use the relationsip Fg= mg to determine the force acting between the Earth and the
Moon? Explain.

012-06379B Photogate Timer
15
®
Experiment 6: Conservation of Momentum
EQUIPMENT NEEDED:
-Air track system with two gliders -Two Photogate Timers.
Introduction
When objects collide, whether locomotives, shopping carts, or your foot and the sidewalk, the
results can be complicated. Yet even in the most chaotic of collisions, as long as there are no ex-
ternal forces acting on the colliding objects, one principle always holds and provides an excellent
tool for understanding the dynamics of the collision. That principle is called the conservation of
momentum. For a two-object collision, momentum conservation is easily stated mathematically
by the equation:
pi= m1v1i + m2v2i = m1v1f + m2v2f = pf;
where m1and m2are the masses of the two objects, v1i and v2i are the initial velocities of the ob-
jects (before the collision), v1f and v2f are the final velocities of the objects, and piand pfare the
combined momentums of the objects, before and after the collision. In this experiment, you will
verify the conservation of momentum in a collision of two airtrack gliders.
Procedure
cSet up the air track and
photogates as shown in
Figure 6.1, using bumpers
on the gliders to provide an
elastic collision. Carefully
level the track.
dMeasure m1and m2, the
masses of the two gliders to be used in the collision. Record your results in Table 6.1.
eMeasure and record L1and L2, the length of the gliders. (e.g., push glider1through photogate1and
measure the distance it travels from where the LED comes on to where it goes off again.)
fSet both Photogate Timers to GATE mode, and press the RESET buttons.
gPlace glider2at rest between the photogates. Give glider1a push toward it. Record four time mea-
surements in Table 6.1 as follows:
t1i = the time that glider1blocks photogate1before the collision.
t2i = the time that glider2blocks photogate2before the collision.
(In this case, there is no t2i since glider2begins at rest.)
t1f = the time that glider1blocks photogate1after the collision.
t2f = the time that glider2blocks photogate2after the collision.
➤ IMPORTANT: The collision must occur after glider1has passed completely through
photogate1and, after the collision, the gliders must be fully separated before either glider
interrupts a photogate.
➤➤
➤➤
➤NOTE: Use the memory function to store the initial times while the final times are being
measured. Immediately after the final times are recorded, the gliders must be stopped to prevent
them from triggering the photogate again due to rebounds.
Photogate1
Glider2
Glider1
Photogate2
m2 m1
Figure 6.1: Equipment Setup

16
Photogate Timer 012-06379B
®
hRepeat the experiment several times, varying the mass of one or both gliders and varying the
initial velocity of glider1.
iTry collisions in which the initial velocity of glider2is not zero. You may need to practice a
bit to coordinate the gliders so the collision takes place completely between the photogates.
Data and Calculations
cFor each time that you measured, calculate the corresponding glider velocity.
(e.g., v1i = ±L1/t1i, where the velocity is positive when the glider moves to the right and nega-
tive when it moves to the left.
dUse your measured values to calculate piand pf, the combined momentum of the gliders be-
fore and after the collision. Record your results in the table.
Questions
L1=L
2=
Table 6.1 Data and Calculations
cWas momentum conserved in each of your collisions? If not, try to explain any discrepancies.
dIf a glider collides with the end of the air track and rebounds, it will have nearly the same mo-
mentum it had before it collided, but in the opposite direction. Is momentum conserved in
such a collision? Explain.
eSuppose the air track was tilted during the experiment. Would momentum be conserved in the
collision? Why or why not?
Optional Equipment
Design and conduct an experiment to investigate conservation of momentum in an inelastic
collision in which the two gliders, instead of bouncing off each other, stick together so that
they move off with identical final velocities. If you are using a PASCO airtrack, replace the
bumpers with the wax and needle. Otherwise, velcro fasteners can be used with most gliders.
m1m2t1i t2i t1f t2f v1i v2i v1f v2f pipf
(m1v1i + m2v2i)(m
1v1f + m2v2f)