PHYS 2425 – Engineering Physics I

Centripetal Force with the Pendulum

 

Leader: _________________________          Recorder: __________________________

Skeptic: _________________________         Encourager: ________________________

 

Materials

LabPro

Laptop

Dual Range Force Probe

Pendulum standard and clamp

String

 

Introduction

      In this activity we will explore the relationship between force and velocity for an object constrained to move along the arc of a circle.  The system we will study will be a pendulum.  The mass hanging from a pendulum – usually called the bob – swings along a circular arc.  We know that for something to swing along an arc, there must be a net centripetal force give by .  In this lab, we will explore the relationship between the tension force in a pendulum and the tangential speed.

 

Set-up

      A schematic of a pendulum is shown in the figure below.  We will use the Vernier force probe as the mass in this experiment.  Make sure the switch is in the 10 N position and that the hook is attached to the probe.  Attach the probe to a string hanging from the pendulum support by the hook and connect the probe to CH 1 of the LabPro. Make sure the ULI is plugged in and connected to the computer.  Open LoggerPro and then open the experiment file by following the path "Probes & Sensors" =>"Force Sensors"=>"Dual-Range Force Sensor"=>"10N Dual Range"

Preliminary Questions

Q1.  Draw a free body diagram for the mass when it is suspended at an angle q.

 

 

 

 

 

 

 

Q2.  Which of the forces indicated in your free body diagram does the force probe measure? (Hint:  What is attached to the force probe?)

 

 

 

Q3.  As the bob swings back and forth, do you expect the tension in the string to remain constant?  Why or why not?

 

 

 

Q4.  At what point in the motion of the bob will the tension force be maximum?  Explain.

 

 

 

Q5.  At the point at which the tension force is maximum, find an expression for the tension.

 

 

 

 

We want to explore the relationship between the force and the velocity. We will not measure the velocity directly, but instead will determine it from other measured values. 

 

Q6.  Use conservation of energy to find an expression for the speed of the bob at its lowest point if it is released from rest.  Your expression should be in terms of the length of the pendulum, g, and the release angle.

 

 

 

 

 

 

Q7.  We would like to explore the relationship between force and velocity, so write down a procedure so that you can vary the speed of the pendulum and measure the magnitude of the force.  In your procedure be sure to specify which parameters in the problem you will vary and which you will keep constant.  Type your procedure in Word.  Print and attach it to the report.  Note you may find that you need to modify your procedure.  So print and attach your procedure once it is final.

 

Data Acquisition

1.  Zero the force probe

      We are interested in the force at the bottom of the pendulum's swing.  However, we are only interested in the piece that contributes to the circular motion.  From question 5, we should have obtained at the bottom of the swing the following expression for the tension FMS = FME  + mv2/r.  We can subtract out the weight of the probe by zeroing the force probe while it is suspended at the bottom of the arc.  With the force probe hanging vertically and still, click on the Zero button and then click on the OK button to zero the probe.  (If there is no Zero button, the you can use CTL-0 or go to the Experiment Menu and choose Zero…)

 

 

2.  Examine the force data

Start the pendulum swinging and click on the collect button.  On the axes below sketch what the graph of force vs. time looks like.

 

 

3.  Indicate on the sketch when the probe is at the bottom of the arc.

 

 

4.  Create a data table to record the force and other variables you need to implement the procedure you described in question Q7.  Assume you will collect 5 different data points.

 

 

 

 

 

 

 

 

 

 

 

5.  Carry out the procedure you describe in question 7 for five different data points and fill in your data table.

 

Data Analysis

Q1.  If you have not already done so, determine the speed at the bottom of the arc for each of your trials.  Add the speed to your data table.

 

 

Q2.  Use Excel or LoggerPro to make a graph of Force vs. Velocity.  What type of curve would you expect to obtain?  Explain. Show your graph to your instructor.  Print and attach a copy of the graph to your report.

 

 

Q3.  Often in science we like to show relationships as straight lines.  How could you graph the force and velocity data so that you obtain a straight line?

 

 

Q4.  Construct the graph.  Do your data appear to lie on a straight line?  Show your graph to your instructor.  Print and attach a copy of the graph to your report.

 

 

 

Q5.  Which of the graphs that you constructed do you believe more convincingly demonstrate the quadratic relationship between force and velocity for circular motion.  Explain.