PHY 101 Lab 6: Centripetal Force & a Conical Pendulum1

Names of group members: Scribe, Student1, Student2

SUIDs of group: 12345, 67890

Lab instructor (TA): Richard Feynman

Section # or meeting time: ??

In this lab you’ll investigate the forces involved in a conicalpendulum. The photograph shows a stationary pendulumused in the lab. There’s a small metal sphere (the “bob”)attached to a string. The photo was taken from just above thepoint where the pendulum has been hung.

In use, you’ll use your hands to start the bob moving in acircle that matches one of the circles in the template. Thistakes some practice.

Learning goals in this labWhen you’ve finished this lab, we think that you’ll haveincreased your abilities to:

● Explain and use the components of a vector tocharacterize motions and forces.

● Apply Newton’s Second Law and the centripetal force concept to a physical situationinvolving circular motion.

● Use multiple, independent experiments to determine a quantity and assess theassociated uncertainties.

Tools● Ring stand, clamps, and rod● Pendulum bob and string● Circle template (a sheet of paper

with concentric circles of severalradii)

● Meter stick● Force sensor (Vernier, Inc.). The

particular sensor has a switch thatchanges the maximum force that canbe measured. The 10 N setting ispreferred for smaller forces. The 50N setting is used for larger forces.Please avoid applying forces larger than 50 N to the sensor.

1 This laboratory was written and distributed by Eric Schiff, Syracuse University, in October 2021.

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● Desktop computer (internet browser, LoggerPro program). Note: The force sensorshould be “zeroed” before measurements using the LoggerPro software.

● Timer/stopwatch (smartphone or timer app on the desktop computer)

Force Sensor CheckoutIf you haven’t worked with the force sensor setup and its computer connection before, here’s thelink to a slide deck that can help get you started.

The force sensor used in this laboratory is calibrated in “Newtons”. A Newton is the name for theproduct of the fundamental units: (kilograms x meters)/(seconds)2. It corresponds to the productof mass and acceleration.

The sensor is “uniaxial”, which means that it is intended to measure the component of a forcethat is parallel to the axis. The photograph of the force sensor above shows this axis. Forcesapplied at right angles to the sensor axis are not supposed to affect the reading, but may have asmall effect.

Do a quick experiment to:

● Check the calibration of the force sensor● Check that the sensor mainly measures just the one component of force that is parallel

to the axis.

Describe your experiment, its results, and your conclusions. Is the calibration accurate?Is it correct that the sensor measures just the one component of a force that’s parallel toits axis?

(for your group)

Design and execute experiments to determine the forces involvedin a conical pendulumFamiliarization with the motion of a conical pendulumAlign the pendulum so that it is suspended directly above the center of the circle template. Atrest, the pendulum bob should be just above the center dot of the template. Play with thispendulum until you can get it to swing in a circle around this center.

Write a brief explanation of how you achieved this circular motion. Record the radius ofthe circle you’re using as well as the length L of the pendulum. Tip: record exactly how youmeasured L, and explain your reasoning for choosing it.

(add your group’s work here)

Design of experimentsWith your lab group, design at least two independent experiments with the conical pendulumthat yield estimates for forces on the pendulum bob while it is traveling in its circle. Start yourdesign session by (i) making a force diagram for the pendulum bob at one location on its circle

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(ii) separately summing the horizontal and vertical components of the forces. Then figure outsome methods of determining these forces when the pendulum is in motion.

Describe your two experiments and how they will yield information about these forces.Tip: consult with your teaching assistant if this design phase takes your group more than 10minutes.

(add your group’s work here)

Experiment #1Execute your first experiment. Record your procedure and your measurements. Clearly showhow you use your measurements to determine the components of the force on the bob inmotion. Your description should be complete. Note any difficulties and possible errors in theexecution of this experiment. Tip: Check the reproducibility of your force estimate by repeatingyour measurements at least once.

(add your group’s work here)

Experiment #2Execute the second experiment, recording the new procedure, measurements, notes, andresults for the force components. If time permits, repeat the measurements to estimatereproducibility.

(add your group’s work here)

DiscussionCompare the force estimates. Are they consistent with each other? If not, suggest someassumptions you’ve made that could explain the inconsistency. If time permits, design andexecute an experiment to see if you’ve correctly identified a source of inconsistency.

(add your group’s work here)

RubricsHere are the rubrics that your instructor will use in evaluating your group’s lab report. A morecomplete set of rubrics is posted at this web site:https://sites.google.com/site/scientificabilities/rubrics.2

D2 Is able to design a reliableexperiment that solvesthe problem

0 No attempt is made to identify any shortcomings of the experiment

1 The shortcomings are described vaguely and no suggestions forimprovements are made.

2 The rubrics were developed by the Rutgers University Physics and Astronomy Education (PAER) group.They are used in this document with permission.

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2 Not all aspects of the design are considered in terms of shortcomingsor improvements

3 All major shortcomings of the experiment are identified andreasonable suggestions for improvement are made.

D5 Is able to evaluate theresults by means of anindependent method

0 No attempt is made to evaluate the consistency of the result using anindependent method.

1 A second independent method is used to evaluate the results.However there is little or no discussion about the differences in theresults due to the two methods.

2 A second independent method is used to evaluate the results. Theresults of the two methods are compared correctly using experimentaluncertainties. But there is little or no discussion of the possible reasonsfor the differences when the results are different.

3 A second independent method is used to evaluate the results andthe evaluation is correctly done with the experimental uncertainties.The discrepancy between the results of the two methods, and possiblereasons are discussed.

G3 Is able to describe howto minimize experimentaluncertainty and actuallydo it

0 No attempt is made to describe how to minimize experimentaluncertainty and no attempt to minimize is present.

1 A description of how to minimize experimental uncertainty is present,but there is no attempt to actually minimize it.

2 An attempt is made to minimize the uncertainty in the final result ismade but the method is not the most effective.

3 The uncertainty is minimized in an effective way.

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Notes for instructors (andinterested students)The photograph shows an aircraft that’s3

turning as it flies. In order to turn, the aircrafthas been “banked” at an angle ɸ; the axisthrough the wings isn’t parallel to the ground.The radius of the turn is determined by the𝑟air speed of the aircraft and the banking𝑠angle ɸ :r = s2/(gtan( )) .ϕ

g is the gravitational acceleration on earth’s surface. In trigonometry, tan(ɸ) refers to the“tangent” of the angle ɸ. This is the ratio of the lengths of two sides at right angles in a righttriangle. The mathematical analysis that yields this radius is a variation on the analysis of aconical pendulum.

ɸ is about 35 degrees from the photograph. Using a calculator with trigonometric functions,tan(ɸ) is about 0.7 . We think a reasonable value for the airspeed is 40 m/s (about 130kilometers per hour or 80 miles per hour). The turning radius is then 230 meters.

You may have noticed in aircraft rides that the pilot increases the airspeed during turns. This4

compensates for the fact that the vertical component of the lift on the flying aircraft is reducedwhen it turns. The plane would start losing altitude if the pilot left the speed unchanged.

4 https://www.boldmethod.com/learn-to-fly/aerodynamics/the-aerodynamics-of-a-turn-in-an-airplane/

3 The original photograph was taken by Noah Wulf in 2017. It is available at commons.wikimedia.org andis freely licensed. The photograph has been rotated and cropped.

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