General Physics Lab Department of PHYSICS YONSEI University

Lab Manual (Lite)

Circular Motion Ver.20180320

Circular Motion and Centripetal Force

Setup 1. Equipment Setup

NOTICE This LITE version of manual contains only experimental procedures for easier reading on your smartphone. For more information and full instructions of the experiment, see the FULL version of manual.

Setup

CAUTION To avoid possible injury from the rotating arm hitting the body, keep at least 1m distance from the rotating arm when running the motor. To avoid damaging the apparatus, keep all cords away from the rotating arm. To avoid damaging any other equipment or facilities near

the apparatus, especially your LCD monitor, keep the apparatus away from them.

CAUTION Do not tighten the swivel too hard. It could cause the sensor to fail.

NOTE ① Thread the wire from the swivel hook through the pul-ley as shown below.

② Hook the free mass to the end of the wire. ③ Hold the fixed mass firmly using the mass holder.

Setup 2. Software Setup (1) Run Capstone software.

(2) Add a Photogate. Click the input port which you plugged the Photogate into and select [Photogate] from the list.

(3) Create and configure a timer. To measure the period of the circular motion, click [Timer Setup] in the [Tools] palette and follow the steps below. ① Create a timer. Choose [Build your own timer].

② Select the timing device for the timer. Check [Photogate, Ch1] and then click [Next].

③ Arrange the sequence of timing events. When the rod of the fixed mass holder passes the Photo-gate, the Photogate beam is blocked and a “Blocked” signal is generated. The time interval between the signals equals the period 𝑇𝑇 of the motion, the time for one revolution. (You will use this measurement to calculate the speed of the mass in step (5).) Click [▼] and then select [Blocked].

NOTE To adjust the rotational radius of a free mass, lower or

raise the height of the upper (horizontal) support rod.

Click [▼] again and select [Blocked] one more time. Now you have two [Blocked] events as below. Click [Next] for the next step.

④ Specify the timer’s name. Enter the name of the timer (“period” is recommended) and

click [Finish].

(5) Configure calculator. In a period 𝑇𝑇, the mass travels a distance equal to the cir-

cumference 2π𝑅𝑅 of the circle, so its speed is

𝑣𝑣 =2𝜋𝜋𝑅𝑅𝑇𝑇 (5)

The period 𝑇𝑇 will be measured through the process defined in step (4). Now you define 𝑣𝑣 and 𝑅𝑅 using [Calculator].

Define the speed 𝑣𝑣 of the mass. Enter the equation of 𝑣𝑣 in the first row of the [Calculator].

To define the equation 𝑣𝑣 = 2𝜋𝜋𝑅𝑅/𝑇𝑇, type “v=2*pi*R/” and “[“. Make sure that you enter a left-bracket “[“ instead of “T” be-cause you will insert “measured” data for 𝑇𝑇. (Unlike numerals or math functions, “measured” data are given in brackets “[“ and “]”.) When you type “[“, a pop-up list appears as below.

Select [period(s)], which you named in step (4). When you select it, the equation is completed as shown below.

When you press the enter key, two cells are automatically typed. One is for the unit of the parameter of the first equation, and the other is for the variable R which you do not define yet.

Enter the unit of the speed 𝑣𝑣.

Enter the value and unit of R. You have to enter a correct value for R whenever you vary the radius 𝑅𝑅 of the circular path of the mass.

(6) Configure the Force Sensor. The interface automatically recognizes the Force Sensor. If the sensor is not in the panel, click the input port which you plugged the sensor into. A drop down menu of sensors will appear. Select [Force Sensor, High Resolution] from the list and the sensor’s icon will be added to the panel.

Click the Force Sensor icon in the [Hardware Setup] panel

and then click the properties button (☼) in the lower right cor-ner.

In the [Properties] window, check [Change Sign].

The sign of the outputs of the Force sensor is initially posi-tive for the pressing force and negative for the pulling force. In this experiment, you will measure the pulling force so you have to change the sign of the outputs.

(7) Configure the signal generator. Do not add any sensor for [OUTPUTS 1].

Click [Signal Generator] in the [Tools] palette, and select [850 Output 1].

Change the [Waveform] of the generator to [DC].

Set the [DC Voltage] to 4V.

Click [Auto] button to automatically activate the generator.

(8) Create displays. You need 4 displays.

Data Table (𝑡𝑡-𝐹𝐹-𝑣𝑣) Graph 1 (𝐹𝐹-𝑡𝑡) Graph 2 (𝐹𝐹-𝑣𝑣) Digital Meter (𝑣𝑣)

Click and drag [Table], [Graph], or [Digits] icon from the [Displays] palette into the workbook page.

NOTE Output options of [Signal Generator]:

[On] : The signal generator always output the signal.

[Off] : The signal generator is not activated. [Auto] : The signal generator automatically outputs the

signal when you start recording, and automatically stops when you stop recording.

① Configure [Table] display. [Table] display initially has two columns. To insert one more

column, click [Insert empty column] icon.

Click <Select Measurement> of each column and select Time(s), Force(N), and v(m/s). Time(s) is a fundamental measurement which shows the elapsed time from when the measurement starts.

You can see the table as below.

② Configure [Graph] displays.

Click <Select Measurement> to define the variables of each

axis.

Make a 𝐹𝐹-𝑡𝑡 graph. Select Time(s) for the 𝑥𝑥 -axis and

Force(N) for the 𝑦𝑦-axis.

In the same way, make a 𝐹𝐹-𝑣𝑣 graph. Select v(m/s) for the 𝑥𝑥-axis and Force(N) for the 𝑦𝑦-axis

③ Configure [Digits] display. Drag [Digits] from the [Displays] palette into the workbook

page, and select v(m/s).

Move and resize the individual displays for easy view.

(9) Adjust the sample rate of the measurement. Select [10.00 Hz ] (collecting data every 0.1 second) for the

sensor in the [Controls] palette.

(10) Start/Stop recording data. Click the [Record] button at the left end of the [Controls] pal-

ette to begin recording data. It will toggle to [Stop]. Click [Stop] to stop data collection.

You can delete any data run using [Delete Last Run] or drop-down menu in the [Controls] palette.

Procedure

NOTE Mass set Information

Free Masses Fixed Masses

Use Measuring Force Balancing

Shape

with Hook

with Center Hole

How to use Hook it to the wire. Secure it to the rotating

arm using a mass holder.

Mass Measure the mass using an electronic balance.

Do not have to measure the mass.

Material Color Mass range (g)

Plastic White 11.50~12.50

Aluminum Light Gray 23.50~24.50

Al + Brass Gray / Yellow 43.00~44.00

Stainless Steel Dark Gray 66.50~67.50

Measure the mass of free masses using the electronic

balance on the lecture table at the front of the lab.

Free Masses Mass (g)

Plastic

Aluminum

Aluminum + Brass

Stainless Steel

NOTE Prior to recording each data run, press the [Zero] button

on the Force Sensor to zero the sensor.

Experiment 1. 𝑭𝑭 − 𝒗𝒗 In this experiment, you will vary the speed 𝑣𝑣 by changing the voltage to the electric motor as the centripetal force is continuously measured by the Force Sensor. The radius 𝑅𝑅 and mass 𝑚𝑚 are held contant as the speed is increased. (1) Follow the equipment setup instruction. [Setup 1. Equipment Setup]

(2) Follow the software setup instruction.

[Setup 2. Software Setup] (3) Set the radius and the mass. ① Mount a set of masses (heavier set recommended).

② Adjust the radius (9cm is recommended) of the free mass. To vary the radius, adjust the height of the Force Sensor, keeping the wire tight. ③ Place the fixed mass at the same radius as the free mass to ensure balancing the arm as it rotates. ④ Be sure to enter the correct value for 𝑅𝑅 in the calculator. If the radius of the circular path of the mass is 9cm, enter 𝑅𝑅 = 0.09(m).

(4) Set the speed. Speed is varied by changing the voltage supplied to the electric motor. This will be displayed on [Digits] display. Apply 4, 5, 6, 7, and 8V DC to the motor. Set [DC Voltage] of [Signal Generator] at 4V.

(5) Measure the force. Click the [Record] button at the left end of the [Controls] palette to begin recording data.

As the rotating arm rotates, the displays show the speed of the mass and the force acting on the sensor. Wait a second for stable rotation. (6) Repeat measurement. Repeat measurement for 4, 5, 6, 7, and 8V DC.

(7) Stop data collection. Click the [Stop] button to stop data collection.

NOTE You can use [Pin] tool for easy view of the displays

.

NOTE Collected data are stored in memory and appear in all

displays. The data runs are listed in the legend for each display. (You can delete any run by clicking [Delete Last Run] or drop-down menu in the [Controls] panel.)

(8) Analyze the data. Click [Show coordinates…] to read off data points.

(9) Repeat experiments. Repeat measurement more than 3 times for each voltage and calculate the average value to reduce the possibility of experimental error. (10) Record your results.

Mass Radius Speed Force (Theo.)

Force (Result)

𝑚𝑚 𝑅𝑅 𝑣𝑣 𝑚𝑚𝑣𝑣2

𝑅𝑅 𝐹𝐹

(kg) (m) (m/s) (kg ⋅ m 𝑠𝑠2⁄ ) (N)

(11) Plot 𝐹𝐹-𝑣𝑣2 graph. Plot 𝐹𝐹-𝑣𝑣2 graph and verify the centripetal force is propor-

tional to the square of the speed. Use the method of least squares if required. (Refer to the appendix of [Free Fall] ex-perimental manual.)

CAUTION It is strongly recommended that you save the data file

with a different file name if you need to change the value 𝑅𝑅 in the calculator. Changing 𝑅𝑅 makes all pre-measured speed 𝑣𝑣 recalculated with the new value 𝑅𝑅.

NOTE If 𝐹𝐹-𝑡𝑡 graph vibrates as below,

① Make sure all the rotating parts are aligned.

(Continued)

Experiment 2. 𝑭𝑭 −𝒎𝒎 In this experiment, the radius 𝑅𝑅 and the speed 𝑣𝑣 are held contant as the mass 𝑚𝑚 is varied. By replacing the mass set, the mass of the system becomes increased. (1) Follow the equipment setup instruction. [Setup 1. Equipment Setup]

(2) Follow the software setup instruction.

[Setup 2. Software Setup] (3) Set the radius and the speed. ① Set [DC Voltage] of [Signal Generator] at 7V.

② Adjust the radius (9cm is recommended) of the free mass. ③ Place the fixed mass at the same radius as the free mass. ④ Enter 𝑅𝑅 = 0.09(m) for the radius in the calculator.

(4) Set the mass. Use the lightest mass set. (5) Measure the centripetal force. Click the [Record] button at the left end of the [Controls] pal-

ette to begin recording data.

As the rotating arm rotates, the displays show the speed of the mass and the force acting on the sensor. Wait a second for stable rotation. Record the speed. This value will be used to fine-tune the voltage in the step (7). Repeat measurement more than 3 times for each mass and

calculate the average value to reduce the possibility of exper-imental error. (6) Stop data collection. Click the [Stop] button to stop data collection.

② It could occur due to mechanical problems of the swivel ball bearing. In this case, search the data for the time interval of interest and calculate the average value of the force to find the experimental value.

(7) Replace the mass set. For all mass sets, repeat the steps (5) and (6). Make sure the speed is equal to that of step (5). The speed could be slightly different for each mass set even if the volt-age remains constant, i.e. you need to fine-tune the voltage for the each mass set. (8) Analyze the result. Click the icon below to select the data run of interest.

Click [Show coordinates…] to read off data points.

(9) Record your results.

Mass Radius Speed Force (Theo.)

Force (Result)

𝑚𝑚 𝑅𝑅 𝑣𝑣 𝑚𝑚𝑣𝑣2

𝑅𝑅 𝐹𝐹

(kg) (m) (m/s) (kg ⋅ m 𝑠𝑠2⁄ ) (N)

(10) Plot 𝐹𝐹-𝑚𝑚 graph. Plot 𝐹𝐹-𝑚𝑚 graph and verify the centripetal force is propor-

tional to the mass. Use the method of least squares if re-quired. (Refer to the appendix of [Free Fall] experimental manual.)

NOTE Recorded data run has a default name Run#%1,

where %1 is an automatically generated run number. You can change the name of each data run if required. ① Click [Data Summary] in the [Tools] palette ② Select [Show Sensor Data] tap. ③ Right-click on the run name of interest. ④ Select [Rename] from the pop-up list.

CAUTION It is strongly recommended that you save the data file

with a different file name if you need to change the value 𝑅𝑅 in the calculator. Changing 𝑅𝑅 makes all pre-measured speed 𝑣𝑣 recalculated with the new value 𝑅𝑅.

Experiment 3. 𝑭𝑭 − 𝑹𝑹 In this experiment, the mass 𝑚𝑚 and the speed 𝑣𝑣 are held

constant as the radius 𝑅𝑅 is varied. By lowering the Force Sensor, the radius increases. As the radius increases, the fixed mass must be moved to a matching radius to balance the rotating arm. (1) Follow the equipment setup instruction. [Setup 1. Equipment Setup]

(2) Follow the software setup instruction.

[Setup 2. Software Setup] (3) Set the mass. Choose any mass set. (4) Set the speed. (You will finally set the speed in step (6).) The (linear) speed is dependent to the radius of the circular

path of the mass, i.e. whenever you change the radius, you have to adjust the voltage so the speed remains constant. (5) Set the radius. ① Adjust the radius of the free mass to 9cm. ② Place the fixed mass at the same radius as the free mass ③ Enter 𝑅𝑅 = 0.09(m) for the radius in the calculator.

(6) Find the appropriate voltage output. Click the [Record] button to monitor the speed of the mass.

You can monitor the speed of the mass in [Digits] display. Fine-tune the [DC voltage] near 4V so you can find any volt-

age at which the speed shows easy value. This speed 𝑣𝑣 is the target speed of this experiment.

In the later steps, you have to adjust the voltage to rotate the mass under the same linear speed. (As the radius de-creases, the voltage must be increased.) In the pre-experiment, the linear speed was 2.0m/s in the conditions of 𝑅𝑅 = 9cm and 4.0V output. And then 7.2V was supplied to rotate the mass with 2.0m/s in the condition of 𝑅𝑅 = 5cm. (Required voltages depend on your motor status.) You should choose the voltage between 3V and 9V. The motor may not work in a lower voltage than 3V, and could make a noisy vibration in a greater voltage than 9V. (7) Measure the centripetal force. If you have any useless data during monitoring the speed in

the previous step, delete it using [Delete Last Run] or drop-down menu in the [Controls] palette.

In the condition of the voltage as you set in the step (6), begin recording data.

(8) Stop data collection. Click the [Stop] button to stop data collection.

(9) Change the radius. Adjust the radii of the masses to 8 cm. Change 𝑅𝑅 in the [Calculator] to 𝑅𝑅 = 0.08(m).

(10) Repeat measurement. In the condition of 𝑅𝑅 = 8cm, you must adjust the output

voltage so the speed shows the predetermined value in the step (6). Repeat measurement for R = 9, 8, 7, 6, and 5cm. (11) Record your results.

Mass Radius Speed Force (Theo.)

Force (Result)

𝑚𝑚 𝑅𝑅 𝑣𝑣 𝑚𝑚𝑣𝑣2

𝑅𝑅 𝐹𝐹

(kg) (m) (m/s) (kg ⋅ m 𝑠𝑠2⁄ ) (N)

(12) Plot 𝐹𝐹- 1 𝑅𝑅⁄ graph. Plot 𝐹𝐹- 1 𝑅𝑅⁄ graph and verify the centripetal force is propor-tional to the inverse of the radius. Use the method of least squares if required. (Refer to the appendix of [Free Fall] ex-perimental manual.)

Please put your equipment in order as shown below. □ Delete your data files from your lab computer. □ Turn off the Computer and the Interface. □ Do NOT disassemble the equipment. □ Keep the Mass Set, Mass Holder, Wire, and Bubble Level in the compartment box.

CAUTION You MUST save the data file with a different file name

for each data run in this experiment. Changing 𝑅𝑅 makes all pre-measured speed 𝑣𝑣 in the prior step recalculated with the new value 𝑅𝑅.

End of LAB Checklist