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Instruction Manual

No. 012-08904A

Goniometer

PS-2138, PS-2137

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Summary of Contents for Pasport PS-2137

Page 1: ...Instruction Manual No 012 08904A Goniometer PS 2138 PS 2137 ...

Page 2: ...nts Introduction 3 Probe Mounting 4 Sensor Setup 5 Suggested Activities 6 Experiment 9 Experiment Teachers Notes and Sample Data 19 Other Sample Data 23 Safety 25 Specifications 25 Technical Support 25 Copyright 25 Limited Warranty 25 ...

Page 3: ...rms and legs as experimental apparatus The Goniometer in conjunction with a PASPORT interface measures and records the angle angular velocity and angular acceleration of an elbow knee or hip The sensor can be used with a single Goniometer Equipment Included Part Number Probe PS 2138 Mounting straps two small one large PS 2547 Angle Sensor included in PS 2137 only PS 2139 Probe Angle Sensor Require...

Page 4: ...ing straps can be used in two ways The easier method is to place the straps on the limbs then stick the probe to the outside of the straps For more secure attachment tuck the probe arms inside the overlapping portions of the straps When mounting the Goniometer probe the wide and narrow arms of the probe are interchangeable the only difference will be the sign of the data collected Attach the wide ...

Page 5: ...tal Align the probe s hinge with the hip joint Attach one arm of the probe to the thigh parallel to the tibia Have the subject stand on both feet attach the other probe arm vertically to the waist strap Move the hip joint through its full range of forward and backward rotation to check for proper alignment Sensor Setup Connect one or two Goniometer Probes to the Angle Sensor Connect the Angle Sens...

Page 6: ...otion Explain what you observe Collect angle data of the hips during walking fast walking and running How does the angle of forward rotation compare to the angle of backward rotation Compare the left and right hips Are they symmetrical Compare the range of movement and period of oscillation for walking fast walking and running What patterns do you observe Compare data from different students walki...

Page 7: ...ubject standing on the opposite foot on a low surface Leg with knee bent at right angle freely dangling about the hip Do angle angular velocity and angular acceleration approximate simple harmonic motion Determine the period frequency and amplitude of the oscillations What is the relationship between the phases of angle angular velocity and angular acceleration How does bending the knee affect the...

Page 8: ...Goniometer Suggested Activities 8 ...

Page 9: ...forearm rotates Setup 1 Connect the Goniometer to the interface 2 Mount the Goniometer on your elbow so that a flexion of the joint is measured as a positive angular displacement as pictured below 3 Stand next to the white board with your arm relaxed at your side Let your elbow and the back of your hand touch the board Equipment Part Number Goniometer Probe PS 2138 Angle Sensor PS 2139 PASPORT int...

Page 10: ... the pen Distance from elbow to pen Procedure 1 Fully extend your elbow and place the pen tip on the board 2 Start data collection 3 Draw an arc on the board by flexing your elbow Move only your forearm and hand while keeping your elbow at the marked location on the board 4 Stop data collection It is important not to twist your hand in order to allow your arm to rotate in a plane parallel to the b...

Page 11: ...o the pen θ s r According to this theoretical relationship and your measured values of θ and r how far did your hand travel s theoretical 3 Measure the length of the arc that you drew and record it below Tape a piece of string to the board exactly over the arc Mark the endpoints of the arc on the string then un tape the string lay it straight on a table and measure the distance between the marks s...

Page 12: ...ocity ω of your forearm equals the change in angle θ divided by the change in time t ω θ t In Part 1 you discovered that the relationship between arc length and angle is s r θ thus s r θ Predict You will use the Motion Sensor to measure the tangential velocity of your hand and the Goniometer to measure the angular velocity of your forearm Based on the above equations write an equation predicting w...

Page 13: ...from the sensor 3 Stop data collection Analysis In this analysis use units of m s for velocity and rad s for angular velocity 1 Look at graphs of Velocity vs Time and Angular Velocity vs Time together How are the two graphs related 2 Create a graph of Velocity vs Angular Velocity Qualitatively describe the graph 3 Apply a linear fit to the graph What is the slope of the best fit line Include units...

Page 14: ...est fit line in terms of vT ω and slope Does the relationship represented by this equation support the prediction that you made earlier 5 What physical quantity is represented by the slope Measure this quantity directly and compare it to the value of slope ...

Page 15: ...angular acceleration α of your forearm equals the change in angular velocity ω divided by the change in time t α ω t In Part 2 you discovered that the relationship between tangential velocity and angular velocity is vT r ω thus vT r ω Predict You will use the Acceleration Sensor to measure the tangential acceleration of your hand and the Goniometer to measure the angular acceleration of your forea...

Page 16: ...the picture 5 Measure the distance r from your elbow to the Acceleration Sensor r 6 Hold your arm so that your forearm will rotate in a horizontal plane as pictured and the X Y plane of the Acceleration Sensor is also horizontal Procedure 1 Extend your elbow 2 Start data collection 3 Quickly flex your elbow wait a moment then quickly extend your elbow 4 Stop data collection The Acceleration Sensor...

Page 17: ...ion vs Angular Acceleration and apply a linear fit What is the slope of the best fit line including units 3 Write the equation of the best fit line in terms of aT α and slope Does the relationship represented by the best fit line support the prediction that you made earlier 4 What physical quantity is represented by the slope Measure this quantity directly and compare it to the value of slope Tang...

Page 18: ...and toward or away from your elbow 8 Create a graph of Centripetal Acceleration vs Angular Velocity The theoretical relationship between Centripetal Acceleration aC and Angular Velocity ω is aC r ω2 where r is a constant Does your data appear to support this relationship Explain your reasoning 9 Create a graph of aC versus ω2 Apply a linear fit According to the slope of the best fit line what is t...

Page 19: ... In this example r 0 38 m 1 Arc Angle θ 1 42 rad 2 s r θ 0 38 m 1 42 rad 0 54 m theoretical 3 s 0 57 m actual 4 In this example the theoretical and actual values of s differ by 5 Part 2 Students should predict vT rω 1 The graphs of Velocity vs Time and Angular Velocity vs Time appear to be directly proportional ...

Page 20: ...bow to the hand In this case the actual value of r is 0 36 m The theoretical value from slope and actual value from direct measurement differ by about 8 Note that the directly measured values of r in Part 1 and Part 2 are slightly different though they are from the same student This is due to the different hand positions used in each part Part 3 Students should predict aT rα 1 The graphs of Angula...

Page 21: ...ope is equal to r In this case the actual value is 0 36 m The theoretical value from slope and actual value from direct measurement differ by about 24 5 The graphs of Angular Velocity vs Time and Centripetal Acceleration vs Time appear to show a proportionality between aC and the magnitude of ω 6 When ω was positive aC was also positive therefor the centripetal acceleration was toward the elbow ...

Page 22: ...f aC versus ω2 the slope of the best fit line is the theoretical value of r in this case 0 232 m 0 008 m 10 The theoretical and actual values of r differ by about 55 In Part 3 your students will probably find that the values of r according to the best fit lines differ significantly from the actual value and that the graphs themselves contain significant scatter or noise Have them compare the diffe...

Page 23: ...ontribute to precision and accuracy of the collected data Other Sample Data Simple Harmonic Motion of the leg rotating about the hip dangling freely and oscillating at its natural frequency with the knee unbent top and bent bottom Note the higher frequency of the leg with bent knee ...

Page 24: ... and amplitude The angle top and angular velocity bottom of the hip while walking The maximum slope of the angle plot is about 1 9 rad s equal to the maximum value of angular velocity Angle data from the knee top and hip bottom of a walking subject acquired using two probes simultaneously Note the phase relationship between the joints ...

Page 25: ...ce Technical Support For assistance with any PASCO product contact PASCO at Address PASCO scientific 10101 Foothills Blvd Roseville CA 95747 7100 Phone 916 786 3800 800 772 8700 Fax 916 786 3292 Web www pasco com Email techsupp pasco com Copyright The PASCO scientific 012 08904A Goniometer Instruction Manual is copyrighted with all rights reserved Permission is granted to non profit educational in...

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