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# Centripetal Force

Extracts from this document...

Introduction

Centripetal Force

Aim:

• To investigate the relationship between the centripetal force action on an object moving in a circle of constant radius and the frequency of revolution.

Hypothesis:

The centripetal force of an object of mass (m) moving at a constant velocity (v) and radius (r) is given by ΣF = = 4π2rmf2. where:

Fc is the centripetal force in N

Fg is the force of gravity in N

r is the radius of the string in m

ms is the mass of the rubber stopper in kg

ml is the mass of the suspended load in kg

g is the gravitation in m s-2

From that equation, I can deduce that if the frequency of object spinning is increased, the centripetal force will increase. Also, in this experiment, the force of gravity acting on the suspended mass should be the one providing the centripetal force. This force is given by: where in this case m is the mass of the suspended load and g is the gravity.

Variables:

 Dependent Independent Controlled The period of the revolution measured by using stopwatch, the frequency and the centripetal force load mass (varied from 10 gr until 50 gr with interval 10 gr each) The small of soft mass (rubber stopper)horizontal string length

Apparatus:

 Name Quantity Accuracy Thin plastic tube about 15 cm long, with no sharp edges 1 ±0.5cm 1.5 of fishing line 1 - Paper clip 1 - Small soft mass (rubber stopper) 1 - Mass carrier and slotted masses (10 g each) As needed - Stop watch 1 ∆t ±0.005s Metre ruler 1 ∆l ± 0.5 cm Electronic Scale 1 ∆m ± 0.005 g

Method:

1. Securely tie one end of the fishing line to a small, soft mass.

(Since this is going to be twirled around your head, make sure the mass isn’t too hard!).

1. Pass the line down through a thin plastic tube and attach a 10 g slotted mass carrier to the end as shown in the diagram. Attach a paper clip to the line to act as a marker for a measured radius of around 1 metre.
2. Add 10 g masses to the mass carrier to make a total mass of 20 g. 1. Twirl the stopper in a horizontal circular path at a speed that pulls the paper clip up to, but not touching, the bottom of the tube.
2. Get a partner to keep an eye on the position of the clip to ensure that the speed of rotation stays quite constant. Practise doing so for a while before trying any measurements.
3. Maintain the speed of revolution and measure the time taken for 10 revolutions of the small mass.
4. Add an extra 10 g to the mass carrier and repeat steps 2 and 3.
5. Add another 10 g to the mass carrier and repeat steps 2 and 3. Keep adding an extra 10 g mass to the mass carrier.

Data Collection:

Radius of the string, r = 0.3 m

Mass of the rubber stopper: m=0.0187 kg

Table 3.1 Result of time taken for 10 revolutions for mass 10 g

 Trial Time Takent(s)∆t = ±0.005 s 1 8.00 2 7.47 3 7.49 4 7.09 5 7.16 6 7.25 7 7.45 8 7.22 9 7.49 10 6.78

Table 3.2 Result of time taken for 10 revolutions for mass 20 g

 Trial Time Takent(s)∆t = ±0.005 s 1 6.47 2 7.47 3 6.91 4 7.44 5 7.00 6 7.32 7 6.35 8 7.50 9 7.79 10 8.47

Table 3.3 Result of Time taken for 10 revolutions for mass 30 g

 Trial Time Takent(s)∆t = ±0.005 s 1 7.16 2 7.25 3 6.79 4 7.72 5 6.40 6 8.04 7 7.84 8 7.41 9 6.32 10 6.53

Table 3.4 Result of time taken for 10 revolutions for mass 40 g

 Trial Time Takent(s)∆t = ±0.005 s 1 7.03 2 7.40 3 6.62 4 6.87 5 7.34 6 7.12 7 6.47 8 6.60 9 5.91 10 7.72

Table 3.5 Result of time taken for 10 revolutions for mass 50 g

 Trial Time Takent(s)∆t = ±0.005 s 1 5.68 2 6.03 3 7.97 4 6.34 5 6.16 6 6.90 7 7.59 8 6.81 9 7.78 10 6.67

Middle

6.78

0.678

1.474926

2.175407

0.481308

0.068510

0.0046937

ΣFc=

4.127976 0.0116417

Average centripetal force: Standard deviation: So, the centripetal force of mass 10 g is: Force of gravity with mass 10 g:   Table 4.2 Data of Centripetal Force for mass 20 g

 Time for10 revolutions (s) Period(T/s) f = 1/T(Hz) f2 Fc(N)  6.47 0.647 1.545595 2.388864 0.528535 0.101778 0.0103587 7.47 0.747 1.338688 1.792086 0.396498 -0.030259 0.0009156 6.91 0.691 1.447178 2.094324 0.463368 0.036611 0.0013404 7.44 0.744 1.344086 1.806567 0.399702 -0.027055 0.0007320 7.00 0.700 1.428571 2.040816 0.451529 0.024772 0.0006136 7.32 0.732 1.366120 1.866284 0.412914 -0.013843 0.0001916 6.35 0.635 1.574803 2.480005 0.548700 0.121943 0.0148701 7.50 0.750 1.333333 1.777778 0.393332 -0.033425 0.0011172 7.79 0.779 1.283697 1.647878 0.364592 -0.062165 0.0038645 8.47 0.847 1.180638 1.393905 0.308401 -0.118356 0.0140082 ΣFc= 4.267571 0.0480119

Average centripetal force: Standard deviation

: So, the centripetal force of mass 20 g is: Force of gravity with mass 20 g:   Table 4.3 Data of Centripetal Force for mass 30 g

 Time for10 revolutions (s) Period(T/s) f = 1/T(Hz) f2 Fc(N)  7.16 0.716 1.396648 1.950626 0.431575 -0.010600 0.0001124 7.25 0.725 1.379310 1.902497 0.420926 -0.021249 0.0004515 6.79 0.679 1.472754 2.169004 0.479891 0.037716 0.0014225 7.72 0.772 1.295337 1.677897 0.371234 -0.070941 0.0050326 6.40 0.640 1.56250 2.441406 0.540160 0.097985 0.0096011 8.04 0.804 1.243781 1.546991 0.342271 -0.099904 0.0099807 7.84 0.784 1.275510 1.626926 0.359957 -0.082218 0.0067598 7.41 0.741 1.349528 1.821225 0.402945 -0.039230 0.0015390 6.32 0.632 1.582278 2.503605 0.553921 0.111746 0.0124872 6.53 0.653 1.531394 2.345166 0.518867 0.076692 0.0058817 ΣFc= 4.421747 0.0532685

Average centripetal force : Standard deviation: So, the centripetal force of mass 30 g is: Conclusion

There will be some improvements in this experiment that I need if I’ll do this experiment again. First of all we need to practice to swing it horizontally, and when we want to record the revolution after 10 swings, we must carefully count the revolution because sometimes our eyes can’t follow the revolution. Secondly, we also need  more careful when swing because sometimes the mass can contact our head or our friends. I also need to keep the string is not moving so that the length can be measured perfectly. To get more accurate results, we can also give an alternative independent variable such as the length of the string. By getting the results from the different mass and different length of string it will make the data more accurate to prove the theory and hypothesis.

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