Magnetic Oscillation IA Practical IB Diploma

7/28/2019 Magnetic Oscillation IA Practical IB Diploma

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Magnetic Oscillation IA Practical

Andrew Hu [DCP&CE]

Aim:To investigate the relationship between the length of metal wire (l) and the tension ofthe string (T) whilst it oscillates at its fundamental frequency in a magnetic field by finding

the frequency of the mains

Theory suggests that the relationship between length (l) of the metal wire and the tension

(T) is governed by the equation:

l=1

2f

T

m Wheref= frequency of the mains and = mass per unit length of the wire.

Raw DataLength of the string oscillating at Fundamental Frequency (mm) (1mm)

Mass (g) (0.5g) Trial 1 Trial 2 Trial 3 Average

20.0 263 263 264 263

40.0 372 374 374 373

60.0 453 454 455 454

80.0 486 487 489 487

100.0 555 560 565 560

120.0 638 639 648 642

Mass for 50cm of the metal wiring used: 0.15g (.005g)

Note:Error for mass of weights is estimated by taking the manufacturers stated error. Error

for length of metal wiring is estimated by taking the smallest unit of measurement. This is

not divided by two as there is error associated with both ends of the ruler when measuring.

Qualitative observation:Amplitude of the wire varied periodically even with the length of

the wire staying constant.


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Processed Data

Mass per unit length: 0.0003 kgm-1

( 110-5

kg)

Sample calculations for Processed Data

Note: All calculations are made for the first set of data.

Mass Converted from mass in gramsto mass in kilograms by dividing value

by 1000.

M= Mg1000

M =20

1000

M= 0.0200kg

Length of string Converted from

millimeters to meters by dividing value

by 1000.

l=lmm

1000

l=263

1000

l= .263m

Average Calculated by averaging thetrials. lAv =

l1 + l2 + l3

3

lAv =0.263+ 0.263+ 0.264

3

lAv = 0.263m

Uncertainty in Length Calculated by

dividing the difference between the

maximum value and the minimum

value by 2.

luncert =lmax - lmin

2

luncert =0.2640 - 0.2630

2

luncert=

0.0005m

luncert = 0.001m (Rounded because of precision)

Percentage Uncertainty of Length

Calculated by calculating the

percentage of uncertainty to the

length.

l%uncert =luncert

l

100

l%uncert =0.001

0.2633

100

l%uncert = 0.19%

Length Squared Calculated by

squaring the Length.lsquared = l

2

lsquared= (0.2633)2

lsquared = 0.069

Mass (kg)

(.0005kg)

Length of the string (m)

(.0001m)Uncertainty

in length

(m)

Percentage

Uncertainty in

Length (%)

Length

Squared

(m2)

Percentage

Uncertainty in

Length Squared (%)Trial 1 Trial 2 Trial 3 Average

0.0200 0.263 0.263 0.264 0.263 0.001 0.19 0.069 0.38

0.0400 0.372 0.374 0.374 0.373 0.001 0.27 0.139 0.54

0.0600 0.453 0.454 0.455 0.454 0.001 0.22 0.206 0.44

0.0800 0.486 0.487 0.489 0.487 0.002 0.31 0.238 0.62

0.1000 0.555 0.560 0.565 0.560 0.005 0.89 0.314 1.79

0.1200 0.638 0.639 0.648 0.642 0.005 0.78 0.412 1.56


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Percentage uncertainty of Length

Squared Calculated by doubling the

percentage uncertainty of Length

Squared.

l2uncert = (luncert)2

l2uncert = (0.19%)2

l2uncert = 0.38%

Mass per unit length and its associated uncertainty Calculated by doubling the value (as

length is 50cm) and converting it into kgm-1

.


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Presenting Processed Data

Note:Error bars are drawn on the graph but are small and hard to see because of its small

value.

As this experiment is conducted very precisely there should be little systematic error in the

collected data. However the Graph 1 shows that there may be random error associated withthe experiment that have caused oddball data. Thus two sets of calculations will be carried

out in this investigation for two reasons:

- The oddball data in graph 1 can affect the end result for the frequency of the mains.- Defining a relationship between two variables by using only four points is

inaccurate.

Thus Graph 2 has the oddball data removed as compared to Graph 1.

Graph 1

Line of best fit: T2 = 3.237m+0.003000

Line of min fit: T2 = 3.357m+0.002000

Line of max fit: T2 = 3.494m - 0.001000

Uncertainty in trend line gradient

GradientUncert =Gradientmax - Gradientmin

2

GradientUncert =3.494 - 3.357

2

GradientUncert = 0.0685m2kg- 1

Thus Gradient is 3.237 m2kg

-1 0.0685 m

2kg

-1

Graph 2

Line of best fit: T2 = 3.418m+0.001532

Line of min fit: T2 = 3.357m+0.002000

Line of max fit: T2 = 3.494m - 0.001000

Uncertainty in trend line gradient

GradientUncert =Gradientmax - Gradientmin

2

GradientUncert=3.494 - 3.357

2

GradientUncert = 0.0685m2kg- 1

Thus Gradient is 3.418 m2kg

-1 0.0685 m

2kg

-1


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Conclusion

My graphs indicate that the squared length of the wiring that oscillates in the magnetic field

is proportional to the amount of tension on the wire. The equations for the relationships

are:

Graph 1: T2 = 3.237m+0.003000

Graph 2: T2 = 3.418m+0.001532

This can be compared to the equation

l=1

2f

T

m which can be rearranged to l2 =g

4 f2m m with the equation T= mgThus the gradient of the equations equate to

g

4 f2m In order to find the frequency of the mains in New Zealand

grad=g

4 f2m is rearranged to f= g(grad)4 m Graph 1

f=g

(grad)4 m f=

9.79936

(3.237)(4)(0.0003)

f=50.2 Hz (3sf) (1.37 Hz)

(Uncertainty calculated from percentage

uncertainties)

Uncertainty calculated by adding the

percentage uncertainty of the gradient to the

percentage uncertainty of the mass per unit

length, then halved because of the square root

term.

110- 50.0003

100

+

0.0685

3.237100

2= 2.72%

Graph 2

f=g

(grad)4 m f= 9.79936

(3.418)(4)(0.0003)

f=48.9 Hz (3sf) (1.31 Hz)

(Uncertainty calculated from percentage

uncertainties)

Uncertainty calculated by adding the

percentage uncertainty of the gradient to the

percentage uncertainty of the mass per unit

length, then halved because of the square rootterm.

110- 50.0003

100

+

0.0685

3.418100

2= 2.67%

Note: Value for gravity is taken from the website

(http://www.wolframalpha.com/input/?i=gravity+in+auckland+new+zealand) for the gravity

in Auckland, New Zealand. g= 9.79936ms- 2
http://www.wolframalpha.com/input/?i=gravity+in+auckland+new+zealandhttp://www.wolframalpha.com/input/?i=gravity+in+auckland+new+zealandhttp://www.wolframalpha.com/input/?i=gravity+in+auckland+new+zealandhttp://www.wolframalpha.com/input/?i=gravity+in+auckland+new+zealand


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Percentage difference

Graph 1

%Difference = 50 - 50.250

100

%Difference= 0.4%

Graph 2

%Difference= 50 - 48.950

100

%Difference= 2.2%

Note: Value of frequency of mains is taken from the website

(http://www.kropla.com/electric2.htm) f= 50Hz

The fact that both calculations with and without the omission of the outliers give values that

are within the calculated uncertainties of the mains frequency suggests that the experiment

is accurate even with a leeway with the way the experiment is conducted. The percentage

differences of calculated values for the frequency of the mains are 0.4% and 2.2% which isvery accurate. However it can be seen that there is random error concerned with the

outliers in Graph 1 which may have decreased the gradient and also systematic error of

0.003000 and 0.001532 in T2that has lifted all the results upwards. With the exception of

outliers, the data was extremely close to the graph with small error bars meaning the

experiment was both accurate and precise.

Conclusion

1) A limitation can be the uncertainty in weight or tension as a result of the crocodile clip

and the current providing wire.

As seen in the photograph the wire and the crocodile clip are adding more weight to the

masses that provide tension to the system. Thus the measurements for mass may appear to

be larger than it actually is. This increase in mass may decrease the gradient value and thus

as seen in the equation f=g

(grad)4 m decrease the value for the frequency of the mains.This systematic error can be seen in Graph 2 values of mass may have been shifted to the

left, thus giving a frequency value of 48.9 Hz. This is very significant as the crocodile clip is
http://www.kropla.com/electric2.htmhttp://www.kropla.com/electric2.htmhttp://www.kropla.com/electric2.htmhttp://www.kropla.com/electric2.htm


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considerably heavy being made of metal. This issue can be improved by connecting the thick

wiring to another thin piece of wiring that rests lightly on the oscillating wire reducing the

uncertainty in mass/tension whilst providing a current.

2) A limitation that may have been the origin of the random error as seen in Graph 1 may be

the pulsating of the wire even as the length that is adjusted stays constant. This means thatthe amplitude changes periodically even as the length is not changed. This may have caused

the inaccurate readings of the length where the wire oscillates at the first fundamental

frequency. This is a random error that may decrease or increase the value for the mains

frequency as the gradient is also subject to decrease or increase. This limitation may be

avoided by making sure that the length of wire used is not deformed in any way prior to its

use as we observed that there were parts of the wire that have been bent and become out

of shape. A thicker and less malleable wire can also be used in the experiment to ensure that

the wire is not deformed prior to use. However the experimenter must ensure that the wire

is not too thick as to cause issues in terms of not being able to take measurements due to

small amplitudes that thicker wires tend to oscillate at.

3) The random error that occurred may also be a case of being unable to observe the

amplitude properly because of the fast oscillations of a thin wire. The wire oscillates very

fast and appears as a blur to the observer thus making it difficult to judge whether the wire

is oscillating at the highest amplitude at the fundamental frequency. This is a random error

that may decrease or increase the value for the mains frequency as the gradient is also

subject to decrease or increase.

As seen in the photograph above, it is very hard to see the wire due to the color of the

background and thus can be solved by wedging a piece of white paper between the

magnets. This allows the wire to be seen more clearly thus enabling the experimenter to

make more accurate judgments for length.

4) A further factor that could have affected the experiment is the wooden triangular prism

that was used to determine the length. As it was made of wood, the multiple trials of

adjusting the length of the wire eventually made a small groove where the wire rested on

the prism. Thus in some trials we may have accidentally moved the prism forwards and as a

PulleyTriangular Prism

Clamp


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result caused the wire to bend. This may further become the cause of unwanted

components of force affecting the tension of the wire. This will most likely increase the

tension in the wire and thus decrease the value for the frequency of the mains due to a

decrease in the trend line gradient. This can be avoided by clamping a ruler to the table,

parallel to the wire. This allows the experimenter to slide the prism against the ruler and

thus minimize the amount of unwanted force perpendicular to the wire.

Magnetic Oscillation IA Practical IB Diploma

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