Sensor

Instruction Manual andExperiment Guide for thePASCO scientific ModelCI-6519 & CI-6557

012-04963D2/95

© 1992 PASCO scientific $10.00

STUDENT FORCE SENSOR

MAXIMUM FORCE: 20N

PASCO

STUDENT FORCE SENSOR(FOR USE WITH PASCO COMPUTER INTERFACES)

012-04963D Student Force Sensor

Section PageCopyright, Warranty, and Equipment Return.................................................. ii

Introduction ..................................................................................................... 1

Operation and Calibration ............................................................................... 1

Experiments

Experiment 1: Measuring Impulse and Change of Momentum during a Collision ........................ 5

Experiment 2: Centripetal Force .............................................................. 9

Experiment 3: Measuring the Vaporization Heat of Liquid Nitrogen ........................................................... 13

Experiment 4: Fluid Drag Forces ............................................................ 17

Experiment 5: Dual Harmonic Oscillators ............................................. 19

Experiment 6: Simple Harmonic Motion ............................................... 21

Experiment 7: Falling Chain ................................................................... 24

Experiment 8: Falling Cantilevered Beam .............................................. 24

Specifications.................................................................................................. 25

i

Table of Contents

Student Force Sensor 012-04963D

Please—Feel free to duplicate this manualsubject to the copyright restrictions below.

Copyright, Warranty and Equipment Return

Copyright Notice

The PASCO scientific Model CI-6519&CI-6557Student Force Sensor manual is copyrighted and allrights reserved. However, permission is granted tonon-profit educational institutions for reproduction ofany part of this manual providing the reproductionsare used only for their laboratories and are not sold forprofit. Reproduction under any other circumstances,without the written consent of PASCO scientific, isprohibited.

Limited Warranty

PASCO scientific warrants this product to be freefrom defects in materials and workmanship for aperiod of one year from the date of shipment to thecustomer. PASCO will repair or replace, at its option,any part of the product which is deemed to be defec-tive in material or workmanship. This warranty doesnot cover damage to the product caused by abuse orimproper use. Determination of whether a productfailure is the result of a manufacturing defect orimproper use by the customer shall be made solely byPASCO scientific. Responsibility for the return ofequipment for warranty repair belongs to the cus-tomer. Equipment must be properly packed to preventdamage and shipped postage or freight prepaid.(Damage caused by improper packing of the equip-ment for return shipment will not be covered by thewarranty.) Shipping costs for returning the equipment,after repair, will be paid by PASCO scientific.

ii

Credits

This manual authored by: Dave Griffith

This manual edited by: Eric Ayars

Equipment Return

Should the product have to be returned to PASCOscientific for any reason, notify PASCO scientific byletter, phone, or fax BEFORE returning the product.Upon notification, the return authorization andshipping instructions will be promptly issued.

When returning equipment for repair, the unitsmust be packed properly. Carriers will not acceptresponsibility for damage caused by improperpacking. To be certain the unit will not bedamaged in shipment, observe the following rules:

➀ The packing carton must be strong enough for theitem shipped.

➁ Make certain there are at least two inches ofpacking material between any point on theapparatus and the inside walls of the carton.

➂ Make certain that the packing material cannot shiftin the box or become compressed, allowing theinstrument come in contact with the packingcarton.

Address: PASCO scientific10101 Foothills Blvd.Roseville, CA 95747-7100

Phone: (916) 786-3800FAX: (916) 786-3292email: [email protected]: www.pasco.com

ä NOTE: NO EQUIPMENT WILL BEACCEPTED FOR RETURN WITHOUT ANAUTHORIZATION FROM PASCO.


1

Operation and Calibration

Introduction

The PASCO Models CI-6519 & CI-6557 Student ForceSensor are designed to be used with PASCO ScienceWorkshop™ interface for Macintosh® or Windows®, orSeries 6500 interface for DOS or Windows.

The Student Force Sensor is an electronic balance capableof monitoring rapidly changing forces as well as slowlychanging, or constant forces. Because of this, it is veryversatile and can be used in many different experimentalprocedures. The Student Force Sensor has a four straingauge bridge mounted on a cantilevered beam of tem-pered steel. A stable excitation voltage source from thecomputer interface powers the bridge, whose output isamplified by a precision low noise differential amplifier.The sensor can be adjusted for different sensitivities(volts per unit of force). The default sensitivity is about 1volt per 9.8 Newtons (or 1 kilogram). You can increasethe sensitivity to about 2 volts per 9.8 Newtons, or 2millivolts per 0.0098 Newtons (1 gram).

➤ NOTE: The Student Force Sensor is a versa-tile measurement tool (see the Experiments listedin the Table of Contents). Other equipmentneeded is standard in many school laboratories.(Some creativity on the part of the user may berequired.)

Adjustment and Calibration

When the Student Force Sensor is in a horizontal positionwith the beam on the left hand side, the sensitivityadjustment trim potentiometer (SENSITIVITY) and thezero adjustment trim potentiometer (ZERO ADJUST) areindicated by the label. You will need a standard screw-driver with a narrow blade to turn the sensitivity and zeroadjust “trim pots”. Please note that the sensitivity andzero adjust “trim pots” will turn only three-quarters of afull turn. Do not force the trim pot to turn more thanthree-quarters of a full turn. Also, the slot of the trim potcan be easily damaged if too much force is applied with ascrewdriver. (Use a plastic screwdriver if possible.)

➤ NOTE: It is not always necessary to changethe ZERO ADJUST and SENSITIVITY trimpots of the Student Force Sensor. You can usethe software that comes with your interface to“zero” and calibrate the sensor. For example, setthe voltage produced by the sensor when it hasNO force on its beam as being equal to “zeroNewtons”. Then add a known mass (e.g., 1kilogram) to the beam. Set the new voltageproduced by the sensor as being equal to “9.8Newtons”. You can “zero” and calibrate thesensor without turning the trim pots.

Figure 1 Student Force Sensor connected to the Series 6500 Interface

CI-6510 SIGNAL INTERFACE

scientific

DIGITAL CHANNELSANALOG CHANNELS


MAXIMUM FORCE: 20NModel CI-6519

PASCO


2

The steps below describe the procedure for changing theZERO ADJUST and SENSITIVITY of the Student ForceSensor.

Adjustment and Calibration Using ScienceWorkshop for Macintosh or Windows:

➀ Connect the DIN plug of the Student Force Sensor toan Analog Channel of the interface. Start the ScienceWorkshop program. In the Experiment Setup window,click-and-drag the analog sensor plug icon to the iconof the channel for the Student Force Sensor. A list ofAnalog Sensors will appear. Select “Force Sensor”from the list. An icon for the Student Force Sensorwill appear in the Experiment Setup window beneaththe channel icon. Double click on the Student ForceSensor icon to open the Analog Sensor Setup dialogbox.

➁ If possible, orient the Student Force Sensor in the po-sition needed for the experiment. Use a narrow bladescrewdriver to gently turn the SENSITIVITY trim potclockwise to near maximum. Then use the screwdriverto gently turn the ZERO ADJUST trim pot until thevoltage shown in the Analog Sensor Setup dialog boxas “Current channel reading:” is nearly zero. Click onthe “Take Reading” button for the “Low Value:”.Then enter “0.000” as the “Low Value”.

➂ Next, attach a known mass (e.g., 1 kilogram) to thehook on the Student Force Sensor beam. (If the Stu-dent Force Sensor is oriented vertically, you can use astring and pulley. Connect one end of the string the tohook and suspend the mass from the other end overthe pulley.) Gently adjust the SENSITIVITY counter-clockwise until the voltage shown in the dialog box as

“Current channel reading:” is a desirable value. Forexample, if the mass is 1 kilogram (9.8 Newtons), ad-just the SENSITIVITY trim pot until the output volt-age shows about 1 volt. This gives a sensitivity of 1millivolt per 1 gram (0.0098 Newtons). Click on the“Take Reading” button for the “High Value:”. Thenenter the appropriate force (such as “9.8” if you used a1 kilogram mass) for the “High Value”.

➤ NOTE: The maximum recommended sensitivityis 2 volts per 1 kilogram (9.8 Newtons), or 1millivolts per 0.5 gram (0.0049 Newtons).

➃ After adjusting the SENSITIVITY of the StudentForce Sensor, click “OK” to return to the ExperimentSetup window. (You can save the calibration file aspart of the Science Workshop document by selecting“Save As” from the File menu. Give the document anappropriate filename such as “Student Force Sensor”.)

In the experiments that follow you will need to use a“force constant” as a conversion factor. The force con-stant “k” is given by the following:

k = amount of force/amount of voltage

In the examples given previously, the amount of force is9.8 Newtons, and the amount of voltage is 1 volt. There-fore, for these examples, k = 9.8 N/V.

Under some circumstances you may want to zero theoutput of the Student Force Sensor when there is aload on the beam. This is similar to “taring” (orzeroing) a balance that is used to measure the mass ofa sample that is added to a container that is resting onthe balance. With the load on the beam of the Student


3

Force Sensor, adjust the ZERO ADJUST trim pot tozero the output. When this is done, the calibrationprocedure may need to be repeated because the sensi-tivity and zero adjust interact slightly.

If the Student Force Sensor is to be used in a differentorientation than when it was calibrated, you may want tofollow the procedures described previously.

➤ REMEMBER: You can use the software thatcomes with the PASCO Computer interfaces to “zero”the Student Force Sensor without adjusting the ZEROADJUST or SENSITIVITY trim pots.

Adjustment and Calibration Using DataMonitor for MS-DOS:

➀ Connect the DIN plug of the Student Force Sensor toan Analog Channel of the interface. Start the DataMonitor program. Select O-Other Optionsfrom the Main Menu. Pick I-Select Chan-nels from the Other Options menu. Use the arrowkeys and Space Bar to “turn off” the channels that arenot being used (e.g., turn off B and C if the StudentForce Sensor is connected to Channel A). Press [EN-TER] and then return to the Main Menu. Select Z-Calibration from the Main Menu. Pick R-Read Voltage from the Calibration Menu.

➁ If possible, orient the Student Force Sensor in the po-sition needed for the experiment. Use a narrow bladescrewdriver to gently turn the SENSITIVITY trim potclockwise to near maximum. Then use the screwdriverto gently turn the ZERO ADJUST trim pot until thevoltage on the computer monitor is nearly zero.

➂ Next, attach a known mass (e.g., 1 kilogram) to thehook on the Student Force Sensor beam. (If the Stu-dent Force Sensor is oriented vertically, you can use astring and pulley. Connect one end of the string the tohook and suspend the mass from the other end overthe pulley.) Gently adjust the SENSITIVITY counter-clockwise until the output voltage is a desirable value.For example, if the mass is 1 kilogram (9.8 Newtons),adjust the output voltage to 1 volt. This gives a sensi-tivity of 1 millivolt per 1 gram (0.0098 Newtons).

➤ NOTE: The maximum recommended sensitivityis 2 volts per 1 kilogram (9.8 Newtons), or 1millivolts per 0.5 gram (0.0049 Newtons).

➃ After adjusting the SENSITIVITY of the StudentForce Sensor, press [ENTER] to return to the Cali-bration menu and select Z-Calibrate Input .Select the channel for the Student Force Sensor fromthe Calibrate Input menu. Follow the instructions onthe Calibrate Input screen to calibrate the StudentForce Sensor. (You may want to save the calibrationfile for future use. Select S-Save CurrentCalibration from the Calibration menu.)

SENSITIVITYZERO ADJUST(DC OFFSET)

Hook Beam


4

Copy-Ready Experiments

The following experiments are written in worksheet form.Feel free to photocopy them for use in your lab.

➤ NOTES:

– The first paragraph in each experiment lists all the equipment needed to performthe experiment. Be sure to read this equipment list first, as the requirements varywith each experiment.

– All experiments using a PASCO Computer Interface are described in detail foruse with the Series 6500 and Data Monitor for MS-DOS.If you are using the Science Workshop interface please refer to the corresponding experiment in theExperiments Library for Science Workshop.


5

Experiment 1: Measuring Impulse and Change ofMomentum during a Collision

EQUIPMENT NEEDED:

- Air track or Model SE-9478A Impulse Collision Apparatus- Student Force Sensor- Series 6500 Computer Interface- Data Monitor program- Accessory Photogate (ME-9204A)- scale or balance for measuring mass- Universal Clamp- rod for mounting the Student Force Sensor to the clamp(The PASCO Force Transducer to Airtrack Mounting Kit contains bumpers for an air trackglider and a universal clamp.)

Introduction

Newton’s 2nd laws states that force equals the rate of change of momentum.

F = ∆mv∆t

From this it can be shown that impulse (force x time interval) equals the change of momentum.

F x ∆t = ∆mv

For a changing force, the integral of the impulse equals the change of momentum.

∫F dt = ∆mv

The object of this experiment is to determine the change of momentum of an air track glider orthe cylinder of the impulse collision apparatus during a collision and compare it to the integral ofF dt (or impulse) of the force acting on it.

Procedure

In this experiment you will use theStudent Force Sensor to measure theimpulse of a glider on an air track (seeFigure 1.1) or a swinging cylinder ofthe impulse collision apparatus (seeFigure 1.2) during a collision. Aphotogate is used to trigger the oscillo-scope “sweep” in the Data Monitorprogram. The Data Monitor programalso records the times that the photogateis blocked before and after the collision.The momentum immediately before andafter the impact with the Student ForceSensor can be calculated.

X x x x x xx xx x x x

X x x x x xx x

x x x x

MA

XIM

UM

FO

RC

E: 20N

StudentForce

Sensor

Computer

Airtrack

Accessory Photogate(ME-9204A)

Glider Clamp (fromME-9356)

Figure 1.1 Equipment Setup with Airtrack


6

Air Track Setup

➀ Set up experiment as shown in Figure 1.1. A small glider with medium velocity or larger gliderswith appropriately lower velocity should be used so that the maximum impact force is approxi-mately 15 - 20 N. Carefully measure the mass of the glider.

➁ The glider should have foam fastened to the bumper to minimize vibration of the transducerbeam at its natural resonant frequency. The bumper extension should be attached in the lowerattachment hole on the glider.

➂ Carefully position the transducer so its glider rebounds smoothly by centering the transducerimpact point on the foam-covered bumper. The bumper extension is needed so the glider willstill be over the air holes at the instant of impact. Although only one bumper is used in theexperiment, it is important to attach one at each end of the glider to maintain balance.

➃ Position the accessory photogate so that the glider moves completely through the photogatebeam before it hits the transducer.

➄ Connect the plug of the accessory photogate to the #1 digital channel on the Series 6500. Con-nect the DIN plug of the force sensor cable to the A analog channel. Calibrate the Student ForceSensor using the Data Monitor program.

SE-9478A Impulse Collision Apparatus Setup

➀ Use a piece of tape be make anopaque flag between the two pegson the bottom of the cylinder.Measure the mass of the cylinder ofthe collision apparatus. The cylin-der has soft foam on the front tominimize the effect of the forcetransducer’s natural resonantfrequency.

➁ Set up the Impulse CollisionApparatus with the Student ForceSensor as in Figure 1.2.

➂ Carefully position the transducer sothe foam bumper on the cylinder iscentered on the impact point duringthe collision to produce a smoothrebound.

➃ Position the photogate so that the trailing edge of the flag on the bottom of the cylinder goescompletely through the photogate beam just before the impact. Connect the plug of theaccessory photogate to the #1 digital channel on the Series 6500. Connect the DIN plug ofthe force sensor cable to the A analog channel. Calibrate the Student Force Sensor using theData Monitor program.

ComputerStudent Force

Sensor

Accessory Photogate(ME-9204A)

Impulse CollisionApparatus (SE-9478A)

X x x x x xx xx x x x

X x x x x xx x

x x x x

SE

NS

ITIV

ITY

ZE

RO

AD

JUS

T(D

C O

FF

SE

T)

-+

Figure 1.2 Equipment Setupwith Impulse Collision Apparatus


7

Measure Impulse and Velocity

➀ To measure impulse during the collision and velocity before and after impact, use the CollisionTimer option in the Triggering menu of the Oscilloscope mode of Data Monitor. As the glider(or cylinder flag) passes through the gate before and after the collision, the times will be recordedon the display of the oscilloscope screen.

➁ By using the length and mass measurements of the glider, the velocity and momentum beforeand after impact can be calculated. The change in momentum is given by:

∆momentum = final momentum - initial momentum = mvf - mvi

where subscripts f and i refer to final and initial conditions respectively. Since the two momentaare oppositely directed vector quantities, the magnitude of the change is the sum:

∆momentum = mvf + mvi

➂ Select the Oscilloscope mode in the Data Monitor program. Turn offthe unused channels. Select “No Triggering” from the Triggeringmenu. Let the glider or cylinder collide with the transducer a fewtimes so you can adjust the oscilloscope sensitivity and sweep speedso the trace looks like figure 1.3. (Don’t worry if the beginning of thecurve doesn’t appear on the screen. You may want to use the “SingleSweep” option during this step.)

➃ After sensitivity and sweep speed are set, select “Collision Timer”from the Triggering menu. Set the delay for a few milliseconds andlet the glider or cylinder collide with the transducer a few more times.Adjust the delay time or change the position of the photogate until theentire trace of the collision appears on the oscilloscope screen.

➄ When all adjustments are made, record data using “Collision Timer”with the oscilloscope mode. Be sure to record the before and after times (time #1 and time #2).Use these times and the length of the glider or flag to calculate the speed before and after impact.Then calculate the change in momentum of the glider or cylinder.

➅ Exit from the oscilloscope (S-Exit, Storing Data ). Use “Plot Graph” to make a plotof voltage versus time. Then select “Integrate” from the Graph Follow-up Menu to find theintegral of voltage versus time during the impact. Use the right and left arrow keys to positionthe vertical cursor bar to the beginning and then the end of the collision (see the dotted line onFigure 4). Record the value of the integral (measured in volt-seconds).

➆ Convert the integral value from volt-seconds to Newton-seconds using the conversion factordetermined during the calibration procedure.

⑧ Compare the change in momentum to the amount of impulse.

Figure 1.3 Oscilloscope Trace


8

Data

Length of flag = __________________m, Mass =____________________kg.

Time before =____________________sec, Time after=________________sec

Speed before =__________________m/sec, Speed after =______________m/sec

Momentum before = ______________kg m/s, Momentum after =__________kg m/s

Change of momentum = __________________kg m/sec.

Force Calibration (assuming a 1 kg calibration mass)

Zero force, Vo = volts 9.8 Newtons, V2 = ______ volts

Force constant (conversion factor), k = ______________ N/V (Newtons per volt)

Integral of voltage vs time = _______________V s (volt seconds)

Impulse = k x integral of voltage vs time = ______________ N s (Newtons seconds)


9

Experiment 2: Centripetal Force

EQUIPMENT NEEDED:

– Student Force Sensor – tall rod with support base (a square rod is ideal)– Series 6500 Computer Interface – right angle clamps– Data Monitor software – mounting rods– Photogate timer (such ME-9215A) – masses (slotted)– solenoid magnet – glass bushing– low current power supply – string– switch– cylindrical pendulum masses (made of ferrous metal)

➤ NOTE: The pendulum can be made of steel electrical conduit of various lengths filled withlead metal.

Introduction

This experiment enables the student to observe and measure centripetal force with the StudentForce Sensor and Series 6500 interface. The speed, radius, and mass parameters are changedindependently, and from the data obtained, one can derive an empirical equation for centripetalforce.

Procedure

➀ Mount the Student Force Sensor to a tall stand so that a pendulum, approximately 90 cm long,can be suspended as shown. If a square support rod is available, maintaining vertical alignmentwill be simpler than with a round rod.

➁ Support a glass bushing (7 or 8 cm longmade from fire-polished thick-wallcapillary tubing with about 1.0 mmbore) directly below the transducer.Raise or lower this bushing to changethe radius of the pendulum. The speed ofthe pendulum at its lowest point will bedetermined with a photogate timer suchas the model ME-9215A. (Major compo-nents of the experimental setup areshown in Figure 2.1.)

➂ Suspend the pendulum by a string from thetransducer beam.

➃ Use an electromagnet made from a lowvoltage relay solenoid with a 10 mmdiameter hemispherical tip to hold thecylinder in a displaced position.

ZERO ADJUST

SENSITIVITY

oscilloscope

labstand

glassbushing

electro-magnet

mass

Photogate Timer(ME-9215A)

Student ForceSensor

Figure 2.1 Equipment Setup


10

➄ Attach the magnet to the midpoint of the pendulum and release it with a switch so the pendulumwill swing without unwanted oscillations. Change the height and position of the magnet to varythe pendulum’s vertical drop and therefore the speed it will reach at the lowest point.

Calibration

Force can be determined by observing the output of the calibrated force transducer with the“Monitor Input” mode of the Data Monitor program.

Calibration is accomplished as follows:

➀ With the pendulum hanging at rest, zero the transducer or tare off the weight of the pendulum.

➁ Next hang additional masses approximately equaling the weight of the pendulum on the pendu-lum and adjust the sensitivity of the transducer until the output is a convenient value.

➂ Repeat the adjustments until they are reproducible with no further adjustments.

A. Centripetal force F c as a function of speed v.

Use a pendulum having a mass of about 200 gm and a length of about 40 cm, measured to thecenter of the mass. Use the “Oscilloscope” mode of the Data Monitor program. Adjust thesensitivity and sweep speed so you can see a trace of voltage versus time for several completeswings of the pendulum. To measure force over several swings, use the “Single Sweep” option,and then leave the Oscilloscope mode (S-Exit, Storing Data ). Use “Plot Graph” or“Display Table of Data”. Examine the data to find the maximum force. Use the Photogate Timerin GATE mode to determine speed of the pendulum at the bottom of its swing. Measure forceand speed for approximately ten data points so the centripetal force will range from very small toat least equal the weight of the pendulum. By graphical analysis or power regression, determinethe functional relationship between fc and v.

B. Centripetal force F c, as a function of radius R.

With a pendulum having a mass of about 200 gm set the release magnet so the vertical drop isabout 15 cm. Make about seven more measurements of centripetal force for different radii withforce ranging from very small to at least equal the weight of the pendulum. Initial height mustalways be adjusted so the speed is held constant. Suggested values of radius are 66, 52, 43, 36,32, 28 and 25 cm. Determine the functional relationship between centripetal force and radius bygraphical analysis or power regression.

C. Centripetal force as a function of mass

Swing four or more cylinders having different masses ranging from about 100gm to 400 gmsuccessively with the same radius and speed. Radius is held constant by leaving the glassbushing fixed and raising or lowering the transducer so that the center of mass always interceptsthe center of the photogate beam. Suggested values of radius R and vertical drop h are such thatR≈4h. For each mass used, it may be necessary to adjust h slightly so that the speed is the samein each case. Determine the functional relationship between centripetal force and mass bygraphical analysis or power regression.


11

Data and Calculations

A. Centripetal Force vs. Speed

mConstant = ____________, RConstant = ____________, Diameter of Pendulum = ________

ƒc time speed ν

__________ __________ ____________________ __________ ____________________ __________ ____________________ __________ ____________________ __________ __________

B. Centripetal Force vs. Radius R


ƒc R ƒc = ƒ (R) = ______________

__________ ____________________ ____________________ ____________________ ____________________ __________

C. Centripetal Force vs. Mass


ƒc m ƒc = ƒ (m) = ______________

__________ ____________________ ____________________ ____________________ ____________________ __________


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Notes:


13

Experiment 3: Measuring the VaporizationHeat of Liquid Nitrogen

EQUIPMENT NEEDED:

– Student Force Sensor – base and support rod (ME-9355)– Series 6500 Computer Interface – styrofoam cup– Data Monitor software – 2 ohm (10 watt) wire-wound resistor– 200 g mass – patch cords– CI-6503 Voltage Sensor – liquid nitrogen– power supply (such as SF-9584) – styrofoam cups (14 ounce)

Introduction

This is an improvement in the method of data taking of the experiment described by P.A.Knutson and G.L. Salinger in THE PHYSICS TEACHER, May 1969, page 288. The basicdifference is the use of the model transducer as an electronic balance so that mass is measured asa function of time rather than time as a function of mass.

Procedure

➀ Set equipment up as shown in Figure 3.1. Connect the DIN plug of the transducer to AnalogChannel A of the Series 6500 interface.

➁ Calibrate the transducer by suspending aknown mass of about 200 grams on thebeam. Select Channel A and use the“Monitor Input” mode of the Data Monitorprogram to monitor the transducer outputas you alternately adjust the zero balanceand sensitivity until the sensitivity is 1 mv/gm. (The input can be calibrated in massunits. This will allow you to record mass asa function of time using the GRAPH INREAL TIME MODE.)

➂ Suspend a styrofoam cup (14 oz size isideal) from the transducer. A second cupinside the other will improve insulation.

➃ Connect the 2 ohm, 10 W wire-woundresistor to the power supply. Connect theCI-6503 Voltage Sensor in parallel withthe resistor. Connect its DIN plug toAnalog Channel B of the Series 6500.Make sure that the resistor is supported soit hangs near the bottom of the cup withouttouching it. I

CI-6510 SIGNAL INTERFACEFOR USE WITH PASCO SERIES 6500 SENSORS

1 2 3 4

ANALOG CHANNELSA ▲ B ■ C ●

ON

GAIN = 1,10,100ISOLATED

GAIN = 1ISOLATED

GAIN = 1REF TO GND

INTERFACESYSTEM

PASCO

6500SERIES

DIGITAL CHANNELS

SENSITIVITYZERO ADJUST(DC OFFSET)

- +

current and voltageconnections

power supply

styrofoam cup withliquid nitrogen

Series 6500Interface

labstand


Student Force Sensor


14

➄ Add liquid nitrogen to the cup. Adjust the current and voltage for a power of 40 Watts deliveredto the heating resistor. (Select Channel B and use “Monitor Input” to measure the power supplyvoltage.)

➅ Now, with power off, record the transducer output voltage every 30 seconds for about four orfive minutes. (You can use the GRAPH IN REAL TIME MODE. At the end of the data collec-tion period a complete data table can be printed out.)

➆ Next turn the heater power on and record the transducer output voltage every 15 seconds forthree or four minutes.

➇ Then turn power off and record output voltages every 30 seconds for four or five minutes.

Data and Calculations

Plot mass vs time and determine the slopes for the best straight line of each of the three data sets.The slope will be the rate of evaporation of liquid nitrogen. Subtract the average of the twoslopes when power was off from the slope when power was on. This will be the net rate of lossof liquid nitrogen caused by the energy supplied to the heater. The heat of vaporization, H

v, is

given by:

Hv = power to heater (current x voltage)/net rate of evaporation

➤ NOTE: Since only the slopes or evaporation rates of the three data sets are used, the clockmay be started at time zero for each period, so there is no problem if some time is “lost”between periods.

With the Series 6500, the input can be calibrated in mass units and mass recorded as a functionof time in the GRAPH IN REAL TIME MODE, or Strip Chart Recorder. The GRAPH INREAL TIME MODE is ideal. This eliminates the need for a data table since a complete datatable can be printed out.


15

Power Off ITime (s) υ m Time (s) υ m Time (s) υ m

0

30

60

90

120

150

180

210

240

270

0

15

30

45

60

75

90

105

120

135

0

30

60

90

120

150

180

210

240

270

Current I = __________________ Voltage V = __________________

Data Table 1: Heat of Vaporization

Slope I _____________ Slope II _____________ Slope III _____________

Average of Slope I and Slope III =Slope I + Slope III

2= ambient rate of evaporation

Power in

net rate of evaporationH

v of liquid N

2 = = =

j

gm

Power Off IIIPower On II

V x I j/sec

Slope II gm/sec

-Average Slope gm/sec


16

Notes:


17

EQUIPMENT NEEDED: (SEE FIGURE 4.1)

– Wind tunnel (could be made with any good blower followedby a sheet metal or plastic pipe 25-30 cm diameter filled withplastic soda straws or other thin walled tubes to producesmooth air flow).

– Voltmeter– Various shaped objects or models made of material at least as

dense as the fluid, including vehicle shapes made of balsawood or toys.

– A 1/16” - 1/8” thick by 1/2” wide metal bar 25-30 cm longwith a 90° twist about 10 cm from one end is clamped to thetransducer beam to support the object in the air stream.

Purpose

With accessories that are easy to create the force transducer can beused to measure drag forces due to air or liquid flowing overdifferent shaped objects.

Calibration

Calibrate the force transducer by placing known masses on thecenter of the objects with the Transducer mounted horizontally.With a 25 cm extension, sensitivity is about 0.007 gmf/mv.

MA

XIM

UM

FO

RC

E: 2

0N

Clamp

Metal bar

90° Twist

Tunnel(Air or liquid

flow)

Pins

Fluid Flow →

Model

Experiment 4: Fluid Drag Forces

Student ForceSensor



18

Notes:


19

EQUIPMENT NEEDED: (SEE FIGURE 5.1)

– 10 cm long flat bar built to specifications shown in Figure 8 inset.– Student Force Sensor – Spring– 2 hooked masses – C-Clamp– Base and support rod – Right angle clamp

Purpose

To observe the Net Force acting on a pair of harmonic oscillators.

Procedure

➀ Clamp the flat bar near the end of the force sensing beam and perpendicular to it (see Figure 8).The ends of the bar should be adapted to support two springs, each having a spring constant ofabout 5 - 7 Nt/m.

➁ Hang a 100 gm mass on one spring and about 70 gm on the other.

➂ Connect the output of the force transducer to the Series 6500 interface in the oscilloscope mode.Transducer should be set to high sensitivity and zeroed with the weights hanging at rest.

➃ Now start the masses oscillating vertically and record the output with the computer, trace rate1000 ms/div. and appropriate sensitivity.


MAXIMUM FORCE: 20NModel CI-6519

PASCO

3 cm 3.5 cm

10 cmFlat Bar

Spring

100g Mass

70g Mass

Spring

Right angleclamp


Experiment 5: Dual Harmonic Oscillators

C-Clamp

Student ForceSensor


20

FO

RC

E Dual

Simple

Harmonic

Oscillators

TIME (milliseconds)


21

Experiment 6: Simple Harmonic Motion

EQUIPMENT NEEDED:

– Student Force Sensor – Photogate timer (optional)– Series 6500 interface –Data Monitor software– Spring – Power supply– Masses – Meter stick– Tall beaker with water – Damping unit– Electromagnet – Power supply

Purpose

To study damped and undamped harmonic motion using a mass and spring system.

Theory

Harmonic motion, the most familiar type of vibration, is illustrated b y the motion of a pendulumor a mass hanging by a spring. Such an object moves back and forth along a fixed path andreturns to each position and velocity after a definite period of time. This type of motion isproduced by a varying force; hence, the object experiences varying accelerations.

Simple harmonic motion requires a restoring force F acting on an object that is proportional toand acting in the opposite direction from the displacement X of the object.

F = -Kx where K is the force constant of the spring, measured by hanging the spring and addingmasses while the displacement is recorded. If a plot of force versus displacement yields astraight line, the spring is said to obey Hooke’s law.

F = ma = md2x

dt2 = –Kx

d2xdt2 + K

m x =0

x = A cos ω0t + φ

where

ω0 = Km

The effective mass of a spring is 1⁄3 its total mass, therefore m in the above equation is:

m =ms3 + M , where M is the mass suspended from the spring and m

s is the mass of the spring.

In almost all physical situations, friction plays a role. For example, a harmonic oscillator that issubject to a damping force has an amplitude that continually decreases with time. For thedamped harmonic oscillator, the equation of motion is:

md2xdt2 = –kx – bdx

dt

➤ NOTE: Frictional force is proportional to velocity.


22

fr = –bv = – bdxdt

General solution: x = AePt

dxdt

= PAePt = Px

d2xdt2 = P2AePt = P2x

Now substitute these values in the differential equation:

(mP2 + bP + K) x = 0

P = –b ± b2 – 4mK

2 = – b2 + ( b

2 )2

– Km

In our case: K

m > ( b2m)

2,

P = – b

2m ± i Km – ( b

2m)2

,

γ = b2m ,

ω02 = K

m ,

ω = ω02 – γ2,

Solution: P = – γ ± i ω02 – γ2

x = A1e–teit + A2e–te–it

Let

A1 = Aeiφ

2 , A2 = Ae–iφ

2

Then x = Ae–γt 12 ei(ωt + φ) + e–i(ωt + φ)

But cos ωt + φ = 12 ei(ωt + φ) + e–i(ωt + φ)

By this identity x = Ae–γt cos ωt + φ


23

Procedure

➀ Clamp the force transducer on a tall sturdy support rod andsuspend a spring from it.

➁ Use a mass hanger consisting of a 25 cm long, 1/8” diameterrod with a hook at the top, a mass supporting platform consist-ing of a small circular disk soldered on a few centimetersbelow the hook, and two flat rectangular vanes soldered on theside of the rod perpendicular to each other at the bottom toserve as a damper that oscillates in a liquid (see Figure 9).

➂ Record the output of the transducer with the PASCO Series6500 computer interface.

Immersing the vane in a liquid damps the motion depending onthe viscosity of the fluid. With the Series 6500 system, make aprint-out of the data for analysis.

Data Analysis

Undamped system

➀ Find K by hanging 5 masses ranging from 100 - 500 g. from the spring. Plot force versusdisplacement and the slope will be the spring constant.

➁ Show for three different masses that

ω = Km where

m =

ms3 + M =

hanging mass + mass of spring3 .

Calculate ω = 2πT , where T is the period measured by the photogate timer.

Damped System

➂ Draw a smooth curve connecting the decay peaks on your plot. The plot decays as e-γ t where

γ = b2m . When t = 1

γ the amplitude has decreased by a factor of e-1, or about 0.368 times the

initial value. Beginning from any time along the x-axis, determine the length of time required forthe amplitude to decrease by e-1. This time is equal to 1/γ . Solve for γ and equate with b/2m todetermine b.

➃ Assign coordinates to the peaks of your decay plot, taking time (t) along the x-axis and displace-ment (y) along the y-axis. Do a linear regression using 1n(y) vs. t, and the slope will be yourdamping constant. (Because y = Ae- γ t and 1n(y) = 1n(A)- γt). Compare your result from part 3with this result.

➄ Show that ω2 = ω0

2 – γ2 = km – ( b

2m)2

by comparing with ω = 2πT .

Measure the period directly from your plot.

➤ NOTE: Use the same spring for all parts of this lab.

MAXIMUM FORCE: 20N

Liquid damping unit

Container,liquid filled

Dampingvanes

Spring


Student ForceSensor


24

Introduction

A classical problem in mechanics is to calculate theforce produced by a falling chain as a function oftime during the fall. This force can be measured withthe force transducer and data acquisition system inoscilloscope mode. Analysis of the data requirescurve fitting and data smoothing to eliminate signalscaused by oscillations of the transducer beam andcatch bucket caused by the falling chain.

MAXIMUM FORCE: 20N


Ball chain, orsmall link chain(approx. 180 cm

long)

Introduction

A classical problem in elementary mechanics is tocalculate the force on one end of a horizontalbeam supported at one end and free to pivot aboutthat end at the very instant the other end is re-leased. This force can be measured with the forcetransducer and data acquisition system in theoscilloscope mode.

Analysis of the data requires data smoothing toeliminate signals caused by oscillations of thesystem when the beam is released.

MAXIMUM FORCE: 20N


End attachedwith string

End threaded torelease

Beam: L ≈ 1 m M ≈ .5 Kg

Student ForceSensor

Right angleclamp

Right angleclamp

Experiment 7: Falling Chain

Styrofoam cup(attached bydouble-sided

tape)

Student ForceSensor

Experiment 8: Falling Cantilevered Beam


25

Specifications

Operating voltage: 5 Volts (CI-6519) or 12V(CI-6557) supplied by thecomputer interface

Current requirement: about 16 milliamperes at maximumsensitivity and about 8 milliam-peres at minimum sensitivity

Output voltage: approximately -3 Volts to + 3Volts (CI-6519) or +6 Volts to-4Volts (CI-6557) at maximumsensitivity

Maximum sensitivity:about 200 millivolts per Newton

Linearity for static applications: less than 1%

Maximum force: approximately 20 N force atinteraction point near the endof the beam

Deflection of end interaction point:

1.8 mm 5 N

3.7 mm 10 N

5.7 mm 15 N

Fundamental mechanical resonance frequency:about 140 Hz

Frequency response: ±1.5 % D.C. to 70 Hz sinusoidaldisplacement

±0.5% D.C. to 30 Hz sinusoidaldisplacement

Tare capability: at least 5 N


26

Notes:


27

Technical Support

Contacting Technical Support

Before you call the PASCO Technical Support staff itwould be helpful to prepare the following information:

• If your problem is computer/software related, note:

Title and Revision Date of software.

Type of Computer (Make, Model, Speed).

Type of external Cables/Peripherals.

• If your problem is with the PASCO apparatus, note:

Title and Model number (usually listed on the label).

Approximate age of apparatus.

A detailed description of the problem/sequence ofevents. (In case you can't call PASCO right away, youwon't lose valuable data.)

If possible, have the apparatus within reach when call-ing. This makes descriptions of individual parts mucheasier.

• If your problem relates to the instruction manual, note:

Part number and Revision (listed by month and year onthe front cover).

Have the manual at hand to discuss your questions.

Feed-Back

If you have any comments about this product or thismanual please let us know. If you have any suggestionson alternate experiments or find a problem in the manualplease tell us. PASCO appreciates any customer feed-back. Your input helps us evaluate and improve ourproduct.

To Reach PASCO

For Technical Support call us at 1-800-772-8700 (toll-free within the U.S.) or (916) 786-3800.

email: [email protected]

Tech support fax: (916) 786-3292

Web: http://www.pasco.com

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