 Level: International Baccalaureate
 Subject: Physics
 Word count: 2481
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 s2
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) 

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:
 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!).
 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.
 Add 10 g masses to the mass carrier to make a total mass of 20 g.
 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.
 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.
 Maintain the speed of revolution and measure the time taken for 10 revolutions of the small mass.
 Add an extra 10 g to the mass carrier and repeat steps 2 and 3.
 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 Taken t(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 Taken t(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 Taken t(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 Taken t(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 Taken t(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 for 10 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 for 10 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.
This student written piece of work is one of many that can be found in our International Baccalaureate Physics section.
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