E106: Uniform Circular Motion

E106: UNIFORM CIRCULAR MOTIONMASALUNGA, Kimberly T.

OBJECTIVECentripetal forceis a force on an object directed to the center of a circular path that keeps the object on the path. Its value is based on three factors: 1) the velocity of the object as it follows the circular path; 2) the object's is distance from the center of the path; and 3) the mass of the object. (education-portal.com)

The purposes of this experiment are:1. To determine effect of the change in radius of the rotating body to the result of the period of rotation, frequency and centripetal force.2. To determine effect of the change in weight of the rotating body to the result of the period of rotation, frequency and centripetal force.3. To determine effect of the change in weight in the weight hanger to the mass of the rotating body.

MATERIALS AND METHODS

The materials used for this experiment are one set of rotating platform, one clamp-on pulley, set of weights, weight hanger and a stop watch.The rotating platform is the apparatus to be used in the experiment to find the centripetal force of the rotating body.The set of weights are used to make necessary weight adjustments in the experiment.Stop watch is used in the experiment to get the time of revolution of the platform.

Figure 1: Materials used in the experiment.

Procedure:

A. Determination of Centripetal Force (with constant mass and variable radius of rotation)1. The rotating platform was placed to a surface that is 0 degrees so that it will be accurate. 2. The radius was set to 16 cm by adjusting the side post to the desired radius.3. A mass of 10 grams (or any mass) was put in the weight hanger.4. The spring bracket was adjusted up or down to make sure that the spring is in vertical orientation. 5. The indicator bracket was adjusted to where the orange indicator is. It was in adjusted with an eye level position to make sure it is at the same level.6. The mass in the weight hanger was removed.7. The apparatus was gently rotated. The orange indicator was at the center of the indicator bracket to keep its desired radius.8. A stop watch was used to record the time of the 10 revolutions of the apparatus. The time obtained was divided into ten and was recorded in the data table.

Figure 2: Group mates were conducting the experiment part 1.

9. For the next trial, the side post was moved to 17 cm and for the other trial, one cm was added. Steps 3 to 8 were repeated.10. The centripetal force was computed by using the formula, Fc = m42f2r.11. Percentage difference was calculated using the formula, .

B. Determination of Centripetal Force (with constant radius and variable mass of rotating body)1. The radius was set to 17 cm (or any desired radius), it was used for the entire experiment B.2. The mass of the rotating body was recorded in the data table. 3. The spring bracket was adjusted up or down to make sure that the spring is in vertical orientation. 4. The indicator bracket was adjusted to where the orange indicator is. It was in adjusted with an eye level position to make sure it is at the same level.5. The mass in the weight hanger was removed.6. The apparatus was gently rotated. The orange indicator was at the center of the indicator bracket to keep its desired radius.7. A stop watch was used to record the time of the 10 revolutions of the apparatus. The time obtained was divided into ten and was recorded in the data table. 8. Two more trials were made by changing the mass of the rotating body then steps 3 to 7 were repeated.9. The centripetal force was computed by using the formula, Fc = m42f2r. 10. Percentage difference was calculated using the formula, .

C. Determination of mass of rotating body (with variable force)1. A mass of 10 grams was put on the weight hanger. 2. The radius was set to 17 cm (or any desired radius), it was used for the entire experiment C.3. The spring bracket was adjusted up or down to make sure that the spring is in vertical orientation. 4. The indicator bracket was adjusted to where the orange indicator is. It was in adjusted with an eye level position to make sure it is at the same level.5. The mass in the weight hanger was removed.6. The apparatus was gently rotated. The orange indicator was at the center of the indicator bracket to keep its desired radius.7. A stop watch was used to record the time of the 10 revolutions of the apparatus. The time obtained was divided into ten and was recorded in the data table. 8. Four more trials were made by hanging the mass in the weight hanger.

Figure 3: Group mate was changing the mass in the weight hanger.

9. The mass of the rotating body was computed using the formula, m= . 10. Percentage difference was calculated using the formula, .

OBSERVATIONS AND RESULTS

Table 1. Determination of Centripetal Force (variable radius of rotation)

Mass of rotating body, m= 207.7 g

(Mass hanging+ mass of pan) x 980 cm/s2 = 14 700 dynesActual value of centripetal force

TRIALRadius of rotation, rPeriod of rotation, TFrequency of rotation, fCentripetal Force (experimental value), Fc

1

16 cm1.7325 s0.5772 rev/s13, 912.9703 dynes

217 cm1.9315 s0.51773 rev/s11, 893.3954 dynes

318 cm1.8180 s0.5501 rev/s14, 214.4843 dynes

419 cm1.7440 s0.5734 rev/s16, 304.4818 dynes

520 cm1.9620 s

0.5097 rev/s

13, 560.5827 dynes

Centripetal Force (Average)13, 977.1829 dynes

Percent Difference5.0411%

In this part of the experiment the mass of the rotating body and the mass in the weight hanger are constant. Only the radius is changing, the initial radius was set at 16 cm then in every trial one cm was added. The period of rotation is obtained by dividing the time in the stop watch by 10 while frequency is the inverse of period. Centripetal force was computed using the formula in the procedure.

Table 2. Determination of Centripetal Force (constant radius and variable mass of rotating body)

Radius of rotation, r= 17 cm

(Mass of hanging + mass of pan) x 980 cm/s2 =14,700 dynes

TRIALMass of rotating body, mPeriod of rotation, TFrequency of rotation, fCentripetal Force (exp. Value), Fc

1207.7 g2.9210 s0.3423 rev/s16,337.3661 dynes

2157.3 g2.5030 s0.3995 rev/s 16,850.6121 dynes

3106.9 g2.3650 s0.4228 rev/s12,826.9698 dynes

Centripetal Force (Average)15,338.3160 dynes


In experiment B, the radius of the rotating body and the mass in the weight hanger are constant while the mass of the rotating body is changing. The period of rotation is obtained by dividing the time in the stop watch by 10 while frequency is the inverse of period. Centripetal force was computed using the formula in the procedure. As the mass of the rotating body is decreasing, the period of rotation is decreasing as well. While as the mass of the rotating body is decreasing, its frequency is increasing.

Table 3. Determination of Mass of the rotating body (constant radius and variable force)

Radius of rotating body, r = 17 cm

Mass of rotating body, m = 207.7 g

TRIAL(Mass hanging +mass of pan) x 980 cm/s2Period of rotation, TFrequency of rotation, fMass of rotating body (exp. value), m

119, 600 dynes2.3490 s0.4257 s161.1437 g

224, 500 dynes2.1790 s0.4589 s173.3293 g

329, 400 dynes1.9620 s0.5097 s168.6307 g

434, 300 dynes1.9560 s0.5112 s195.5344 g

539, 200 dynes1.9900 s0.5025 s231.3042 g

Mass of rotating body (Average)185. 9885 g


In this part of the experiment the mass of the rotating body and the radius are constant. Only the mass in the weight hanger is changing. The period of rotation is obtained by dividing the time in the stop watch by 10 while frequency is the inverse of period. Centripetal force was computed using the formula in the procedure. As the mass in the weight hanger is increasing, the mass of the rotating body is increasing as well.

Sample computations: (For Table 1)

For trial 1:

Fc = m42f2r

Fc = (207.7) (42) (0.5772)2 (16) = 13, 912.97026

(For Table 2)

For trial 1:

Fc = m42f2r

Fc = (207.7) (42) (0.342348)2 (17) = 16, 337.36608

(For Table 3)

For trial 1:

m=

=

=161.144

DISCUSSION & CONCLUSION

I can say that the experiment that I have conducted with my group mates was successful because the data that we have gathered are good. And the percentage difference that we have computed is very small which means that our data is near to the calculated values. For the improvement of this experiment, it is important to follow the procedures correctly and to set the materials properly because wrong set up might cause inaccurate results. It is better to have coordination among the group so that the time of revolution will be accurate.

After conducting the experiment, I can say that radius of the rotating body may affect the time of revolution. The longer the radius the longer the time it takes to make 10 revolutions. The same with the change in mass of the rotating body, it also affects the result of the period of rotation. As the mass of the rotating body is decreasing, the period of rotation is decreasing as well. While as the mass of the rotating body is decreasing, its frequency is increasing. And lastly, as the mass in the weight hanger is increasing, the mass of the rotating body is increasing as well.

The possible errors that might be encountered in the experiments are the wrong set up of the rotating platform. Also, there may be an inaccurate time if the start of the time is not equal to the time the platform rotated. Inaccuracy may also be encountered if the surface where the platform is placed is not at 0 degrees. There may also be errors if the orange indicator is not at the indicator bracket.

ACKNOWLEDGMENT & REFERENCE

I would like to express my deepest gratitude to all those people who have inspired and helped me to finish this lab report. First I would like to thank God for giving me the energy, wisdom and strength to do this. Also, I would like to thank my professor, Ricardo De Leon, for explaining to us what should be done with the experiment. Also I would like to thank him for teaching us how to write this lab report properly. And to Mang Jing and Mang Jerry who never lose patience in lending us the materials and explaining to us the use of the materials. Also, my group mates who helped me conduct the activity successfully. I would like to acknowledge their enthusiasm to finish this experiment with good data and results. I would like to give special recognition to Niel Atienza and Kashieca Roxas for their skills in MS Excel. Also, I would like to thank Reymarie Carbonel for uploading all the photos of our experiment in our facebook group. And lastly, I would like to thank my parents for supporting me in my studies.

SOURCE:

http://education-portal.com/academy/lesson/centripetal-force-definition-formula-examples.html

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E106: Uniform Circular Motion