Centripetal Force Lab

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Centripetal Force Lab

Name: Taylor Penna Date: March, 5 2012 Teacher: Mrs. Gallagher Course Code: SPH 4U

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Intro: Centripetal force is a force in a circular motion at a constant speed with a constant radius. Centripetal force is equal to the force of gravity. The force of gravity is the mass times the gravitational field strength. The centripetal force is equal to the force of gravity because there are no other forces acting on the object besides gravity. Centripetal and gravity are both fictitious forces.

Centripetal Force Equations:

                    Frequency:

    Period:

   Acceleration due to gravity:

   Purpose: The purpose of this lab was to determine that relationship between centripetal force, the radius, period and the frequency.

Hypothesis: It was predicted that as centripetal force increased the time and period would decrease. It was also predicted that as the radius increases the frequency and centripetal force would decrease.

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Procedure: Part A 1. The rubber stopper was tied to the end of a string about 1.5 m long. The string was passed through the tube. 2. Three small standard masses were tied to the end of the string. 3. The string was pilled so that the rubber stopper was about 1.0 m from the top of the tube. 4. With the string pulled taut, the paper clip was placed 3.0 cm below the tube. 5. While holding the mass, the stopper was swung in a circle over one person's head so that the paper clip remained about 3.0 cm about their head. 6. One the swinging was proficient the stop watch was used to time ten rotations. 7. Two more masses were added and step 6 was repeated. 8. The procedure was continued for four more masses. 9. The gravitational force for each mass used was calculated. In this experiment, gravitational force was equal to centripetal force. 10. All data was recorded in Table 1. 11. The graph of centripetal force versus period was plotted 12. The relationship between centripetal force and period was determined. 13. A graph of centripetal versus frequency was plotted. 14. The relationship between centripetal force and frequency was determined.

Part B 1. 5 masses were attached to the end of a string. 2. The string was adjusted to have a radius of 0.750m

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3. The stopper from part a was swung in a circle 10 for rotations 4. Repeated for the radii 1.00,0.90m, 0.60m 5. All data was recorded in table 2 6. A graph of centripetal force versus frequency square was plotted. The points on the graph were not connected but a line was drawn from the origin to the points 7. A vertical line was drawn on the graph. The line crossed all four of the above lines. The centripetal force for a constant frequency square value was read 8. A table was created relating the centripetal force to the radius 9. A graph of centripetal force versus radius for a constant frequency squared value was plotted. The centripetal force was the dependent variable 10. The relationship between centripetal force and the radius was determined.

Materials: 

Rubber stopper

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Masses (Washers)

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1 small paper clip

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2.0m of find thread

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Plastic tube

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Meter stick 

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Stop Watch

Observations: *Refer to graphs on page Table 1 Masses (Kg) 0.0207kg 0.0317kg 0.04476kg

Centripetal Force (N)

  

# of rotations

10 10 10

Time (s)

11.3s 10.4s 9.4s

Period (s)

1.13s 1.04s 0.94s

Frequency (Hz) 0.885Hz 0.962Hz 1.06Hz

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0.05856kg 0.07314kg 0.08321kg

0.574N  0.717N  0.816N 

10 10 10

8.2s 7.3s 6.6s

0.82s 0.73s 0.66s

1.22Hz 1.37Hz 1.51Hz

Table 2 Radius

Time

0.60m 0.75m 0.90m 1.00m

7.68s 8.94s 9.18s 10.25s

Frequency 1.302Hz 1.119Hz 1.089Hz 0.976Hz

2

Frequency 1.695Hz 1.252Hz 1.186Hz 0.952Hz

Centripetal Force versus the Radius

Centripetal Force (N) 350N 350N 350N 350N

   

Sample Calculations: Finding the centripetal force in table 1.

         Finding the Frequency in Table 1

              0.885Hz Finding the Period in Table 1

Radius (m) 0.60m 0.75m 0.90m 1.00m

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           Finding the centripetal force for the 3

rd

table.

        350N Finding a proportionality statement for 1a:

            ( )                                         

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Proportionality Statement between Centripetal force and Frequency Centripetal Force

Multiplier

   0.574N  0.717N  0.816N 

1.56 2.14 2.82 3.53 4.02

Frequency

0.885Hz 0.962Hz 1.06Hz 1.22Hz 1.37Hz 1.51Hz

Multiplier

1.09 1.20 1.38 1.55 1.71

Proportional

1.43 1.78 2.04 2.28 2.35

0.35 0.26 0.24 0.07

Finding Centripetal Force in 2a:

           Sources of Error: Most of the sources of error in this lab were due to human error. The main problem was it was hard to keep the stopper spinning at a constant speed. Also, the time could not be properly determined because of 2 factors. One factor was that the time was started and stopped by the naked eye. Another factor was that the spinner could not keep an exact constant speed. A way to fix this problem is to have a robot spin the stopper. Speed could be change on the robot to find the correct speed at which the radius of the circle was constant. To remove the problem of  recording time by the naked eye, the robot could count the number of rations while recording the time.

Assigned Questions: Determine the relationship between centripetal force and frequency. Centripetal force is equal to the square of frequency. Larger values of frequency lead to larger values of centripetal forces.

     Determine the relationship between centripetal force and radius.

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The relationship between centripetal force and the radius is



   . Larger values of the radius

give a smaller value of the Centripetal force. Smaller values give a larger value of centripetal force if for both situations the mass and velocity is the same. 1. Write a proportionality statement for the equation describing the relationship between centripetal force and: a) Frequency b) Period c) Radius Proportionality statement between Centripetal and Frequency is:

2. From your results what centripetal force would be required to rotate the rubber stopper in a horizontal circle of a radius of 1.5m with a frequency of 8.0Hz? The centripetal force that would be required to rotate the rubber stopper in a horizontal circle motion is 17N.

Conclusion: The frequency, period and radius are all proportional to each other.

References: http://blog.cencophysics.com/2010/02/centripetal-force/