1206320934 2006 Physics Assessment Task

Student: Wafa Al-Shamare Assessment Task 1 Using a Pendulum to Determine G

Using a Pendulum to determine G

Introduction:

The properties of a pendulum have amazed scientists for centuries. The pendulum was originally discovered by Ibn Yunus al-Masri in the 10th Century. In the 15th Century, the Italian physicist noted that the period of a pendulum is almost independent of amplitude. It is suggested that he may havebeen the first to propose that pendulums be used in clocks, however, the first fully operational pendulum clock was patented by Christiaan Huygens in 1656. This was a breakthrough in the art of timekeeping.

Aim: To determine the rate of acceleration due to gravity by tracing the oscillatory motion of a pendulum.

Theory:

If a weight is attached to a string and hung from a fixed point, the weight will swingback and forth in motion that is approximately simple harmonic. The period of the pendulum is the time taken to complete a full single back and forth swing. This, however depends on two variables; the length of the string and the rate of acceleration due to gravity. The formula for the period is as shown below:

Where: T- is period (s) i.e. time for 1 oscillation l - Is length (m) of the pendulum

g-is acceleration (m/s2 )due to gravity

Hypothesis: As the length of the string increases, the period of the swing also increases, this is a hypothesis that I will be testing.

Equipment:

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ClampBoss HeadRetort StandString 1- meterStopwatchMass Carrier Metre RulerMass 50gHalf circular Protractor

Method:

1. Set up the equipment as shown in the diagram below.

2. Collect a mass carrier and tie it strongly to a string.

3. Hold the mass carrier by the string, allow the other members of the group to measure 0.9m of the string starting from the base of the mass carrier.

4. Record the length of the pendulum.

5. Attach the end of the string to the clamp tightly and ensure that you have obtained a length of 0.9m from the top to the bottom of the string.

6. Vicinity must be ensured to be free of any obstructions to the present swinging pendulum. Ensure that everyone is stationed at a safe certain distance in order not to be a risk of injury from the pendulum motion.

7. Place an excess weight on the retort stand to stop it from absorbing the motion energy of the pendulum vibrating.

8. Gently move the pendulum from equilibrium to some point either side. Using a protractor, carefully measure the angle of deviation from the vertical

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String

Counter Weight

Clamp

Retort Stand

Mass carrier and Mass

Note: Ө <15º to avoid angular

Boss Head

The affect of the length of the pendulum on the period (T ) of acceleration

0

1

2

3

4

5

0.7m 0.75m 0.8m 0.85 m 0.9m

Length (m)

Peri

od (T

)

T2


9. Carefully release the mass, and also activate the stop watch at the same time.

10. Stop timing after the pendulum has moved through 10 complete oscillations and record your results.

11. Repeat the same process for 5 trials in total, each trial the string must be shortened by 0.1m of its length in the preceding trial. Ensure that the deviation angle is controlled for constancy through all trials

12. Present all collected data in a tabular form

13. Represent this same information graphically, plotting T2 as a function of l

14. Using a series of algebraic manipulations and calculations, determine a value for gravitational acceleration from both collected figures, and the graph drawn for confirmation.

Variables:

Control: the mass, the 300 deviation, retort stand and height of the retort stand

Independent: length of the stringDependent: time for each 10 oscillation

Results: note: Deviation of 300 was used for each trial

Trial Time for 10 oscillations (s)

T2 (s2) Length l (m)

g (ms-

2)1 20 2 0.900 8.8822 19 1.9 0.850 9.2953 18 1.8 0.800 9.7484 17 1.7 0.750 10.2455 16 1.6 0.700 10.795

Average: 9.793

The table above shows my results of the five Pendulum trials. The formula of g = 42/ T2 was used to find the value of ‘g’ by averaging all 5 trials, this was found to be 9.793m/s-2.

Due care was taken to eliminate the effect of other variables in each of these trials. As such all other factors involved remained constant apart from the mentioned variable.

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It can be seen from the above graph that the correlation between the length and the period is not a direct correlation. As such, it was required that I square the duration of the period to produce a straight line, as shown above: it can be concluded that as the decreases by 0.05m the period also decreases.

Analysis:

Discussion:

The acceleration due to gravity in this investigation was found to be 9.793 m/s-2. These values were 00.0714% off the accepted value of 9.8m/s-2.

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To find g: 1. Divide recorded times by 10, giving T2. Rearrange the formula for pendulum motion as

follows,

T = 2π√ (l/g) à T/2π = √ (l/g)T2/4π2 = l/ggT2/4π2 = lg = 4π2l/T2

3. Substitute known quantities, T and l and solve for g4. Repeat for each trial5. Calculate an average value for g by dividing the sum

of the results for each trial by the number of trials

Run


In this experiment I have started with 0.9m and used a decreasing pattern of 0.05m in between each trial in order to increase the accuracy of measurements and in turn minimise error. Inaccurate results are obtained when shorter lengths are used in the pendulum method, due to the fact that they have shorter periods.

The controlled variable was the mass carrier which was kept the same for each preceding trial. The use of a control is to obtain a fair test between each trial, in order to collect the average results in determining the value of ‘g’.

Since measurements of period were taken with a stopwatch by a timekeeper, the shorter the periods would have been more difficult for the timekeeper to make accurate judgments or when to start and stop. I have reduced the source of error by using longer strings in my investigation.

The dependent variable in this investigation was the period of 10 oscillations. For a pendulum in simple harmonic motion with a small deviation angle of 300, the period of oscillation depended only upon the pendulum length and the acceleration due to gravity. The reason for timing 10 oscillations, rather than one, was to eliminate the errors in judgment associated with scrambles during short time frames.

This means that it will take slower to complete 10 oscillations, therefore the timekeeper was able to better anticipate the point of closure and, hence, take a more accurate reading of time.

The value for gravitational acceleration calculated in this experiment differed slightly from the theoretical value of 9.80ms-2. One possible reason for this deviation lies in the levels of accuracy of the measuring instruments used.

My experiment was reliable due to the constant 300 deviation for each trial and The location and height of the retort stand was always kept in the same position on the lab bench to preserve reliability. All variables were kept constant for each preceding trial except for the length of the string.

My results show that as the length of the string decreases the time taken to complete 10 oscillations also decrease.

The experiment has obtained very close results according to the theoretical value of ‘g’, this is due to the accuracy of my experiment. The length of the string was precise and it was measured before and after it has been tightened. The counter weight on the retort stand had a mass that stopped it from

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absorbing the motion energy of the pendulum vibrating, therefore enhancing the accuracy of my results.

Safety precautions:

Do not use a large excessive amount of weight on the retort stand, hence make sure that all participants are wearing closed shoes incase of falling objects such as mass carrier or the excessive weight.

Keep the swinging pendulum clear of other people; ensure that everyone present are at a safe certain distance.

Conclusion:

The value for the acceleration due to gravity was determined to be 9.793m/s-2 in which it was very close to the theoretical value. In conclusion my results have also proven my hypothesis to be correct.

Using a ticker timer to determine G

Introduction:

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A ticker-timer is a device that vibrates up and down, stamping a mark on paper 50 times per second. The timer is connected to alternating current (A.C.), which means that the time between each dot is always constant, (0.05 seconds). Depending on the motion of a paper tape being dragged through the timer, the dots can be close together or far apart. The further apart the dots are, the faster the tape is travelling. This device then allows us to measure and record the motion of an object. Look at the Tape 1 below.

Start Tape 1 Finish

. . . . . . . . . The dots are seen to be equally spaced. This tells us it is travelling at a constant speed.

Start Tape 2Finish

. . . . . . . . . . . . . . . On Tape 2 the dots are initially far apart, and the distance between them decreases. The object here must be decelerating or slowing down, that is speed decreasing.

Start Tape 3 Finish

. . . . . . . . . . . . . On Tape 3, the dots are initially close together, but the distance between them increases steadily. The object here must be accelerating or getting faster or speed increasing.

Aim:

To determine the rate of acceleration due to gravity by using a ticker timer.

Theory:

When an object falls ‘freely’ it accelerates vertically downwards. An equation to describe this is;

S = ut + ½ at2

Where: S = displacement

u = initial velocity

a = acceleration

t = time or period

Hypothesis:

The heavier the mass the increase rate of acceleration obtained. This is a hypothesis in which I will be testing.

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Equipment:

White paper tapeTicker timerConnecting wiresRetort standMass (50g, 75g, 100g)Power packMasking tapeClampStop watchBoss headCarbon paperMetre ruler

Method:


2. Measure one metre of a white paper tape, ensuring that the measurements are kept constant for the preceding trials.

3. Switch the power on, and ensure that another member of the group releases the paper tape at the same time, therefore allowing the attached weight to pull it through the ticker timer vertically.

4. Repeat this process three times by using 3 different masses (50g, 75g and 100g)

5. Examine the tape to ensure that the dots are spaced so as to indicate uniformly accelerated motion.

6. Select 3 strips from each trial, ensuring that each strip consists of 4 dots in a row from the start clearly showing accelerated motion. Record the average of the 3 strips from each trial, then record the average of all 3 trials to determine the acceleration due to gravity.

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7. Present data in a tabular form as well as draw a graph of average velocity versus time and calculate the slope of this graph. Remember that average velocity over a time interval occurs at the middle of that time interval. The value of the slope is your experimental value of acceleration due to gravity.

Variables:

Control: length of the white paper tape, the location and the height of the retort stand

Independent: the mass carrier (50g, 75g and 100g)Dependent: the distance between 4 dots

Results:

Note: that the time interval between 2 dots are 0.05 s, this is because the frequency is 20Hz, therefore 1/20 = 0.05 s. however the measurements below are taken between 4 dots only.

1. Mass 50g:

Strip 1: 0.07m strip 2: 0.102m strip 3: 0.114m

S = ut + ½ at2 S = ut + ½ at2 S = ut + ½ at2

0.07 = ½ at2 0.102 = ½ at2 0.114 = ½ at2

0.07 = ½ a (0.15)2 0.102 = ½ a (0.15)2 0.114 = ½ a (0.15)2

0.07 / 0.5 = 0.14m 0.102 / 0.5 = 0.204m 0.114 / 0.5 = 0.228m

... 0.14 = a (0.15)2 ... 0.204 = a (0.15)2 ... 0.228 = a (0.15)2

a = 0.14 / (0.15)2 a = 0.204 / (0.15)2 a = 0.228 / (0.15)2

a = 6.222 m/s-2 a = 9.06m/s-2 a = 10.133 m/s-2

Average: 6.2 + 9.07 + 10.13 = 8.5 m/s-2

2. Mass 75g:


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0.101 = ½ at2 0.124 = ½ at2 0.152 = ½ at2

0.101 = ½ a (0.15)2 0.124 = ½ a (0.15)2 0.152 = ½ a (0.15)2

... 0.101 / 0.5 = 0.202m ... 0.124 / 0.5 = 0.248m ... 0.152 / 0.5 = 0.304

0.202 = a (0.15)2 0.248 = a (0.15)2 0.304 = a (0.15)2

a = 0.202 / (0.15)2 a = 0.248 / (0.15)2 a = 0.304 / (0.15)2

a = 8.97 m/s-2 a = 11.02 m/s-2 a = 13.51 m/s-2

Average: 8.97 + 11.02 + 13.51 = 11.167 m/s-2

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3. Mass 100g:



0.108 = ½ at2 0.133 = ½ at2 0.167 = ½ at2

0.108 = ½ a (0.15)2 0.133 = ½ a (0.15)2 0.167 = ½ a (0.15)2

... 0.108 / 0.5 = 0.216m ... 0.133 / 0.5 = 0.266m ... 0.167 / 0.5 = 0.334m

0.216 = a (0.15)2 0.266 = a (0.15)2 0.334 = a (0.15)2

a = 0.216 / (0.15)2 a = 0.266 / (0.15)2 a = 0.334 / (0.15)2

a = 9.6 m/s-2 a = 11.822 m/s-2 a = 14.844 m/s-2

Average: 9.6 + 11.82 + 14.84 = 12.1m/s-2

Total ‘g’ for ticker timer: 12.1 + 11.167 + 8.5 = 10.59 m/s-2

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by using the formulae S = ut + at2 for every strip and taking the average for each trial, and finally averaging my total results I have obtained acceleration due to gravity as shown above.

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Discussion:

The acceleration due to gravity in this investigation was found to be 10.59m/s-2. These values were 7.46% off the accepted value of 9.8m/s-2. In this experiment I have started with a mass of 50g and used an increasing pattern of 25g in each trial, this includes 50g, 75g and 100g for three trials. The masses used were the independent variable in the experiment.

Different masses were used in order to measure the affect the weight has due to the value of ‘g’ as well as obtaining an average to determine the value of ‘g’.

The controlled variables were the length of the white paper tape, the location and position of the retort stand; these controls were used to ensure a fair test is being applied to all three trials and also to obtain accuracy of the current investigation. The control of the length of the white paper shows the affect that each mass had on the acceleration due to gravity. My results show that as you increase the mass the rate of acceleration also increases, which in turn proves my hypothesis to be correct.

The investigation was reliable because it was repeated 3 times with 3 different masses and an average was taken to determine the value of ‘g’. However, my investigation could have been more reliable by repeating the experiment 4 times with different masses ranging from 25g, 50g, 75g and 100g and also repeating each trial 3 times for accuracy, this method will increase the accuracy of measurements and in turn minimise error.

Inaccurate results are obtained when shorter lengths are used in the white tape due to the fact that they have shorter periods. I have used white tape of 1 metre to ensure validity and accuracy of the experiment. This investigation was valid because all variables were kept constant in the preceding trials. The experiment was valid because it is consistent with the result of other experiments, although the ticker timer experiment is rarely done, the experiment with other ticker timer shows that as the mass increases the faster the acceleration.

The formula above works on the assumption that acceleration due to gravity is constant. However, it is known that gravitation acceleration changes with such factors as altitude, crustal density and position on the Earth’s surface. For this reason, no change in white tape length was made without adjusting the boss head and clamp so as to keep the distance between the mass carrier and the ground constant for all trials. Also,

A possible source of error, and a possible cause for the difference between the value of g calculated in this experiment and the theoretical value, lies in the variations in gravitational acceleration that relate to geographical position. Depending on the thickness and density of the Earth’s crust, proximity to the Earth’s poles and the magnitude of centrifuge forces at any one

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point on the Earth’s surface, the value for g calculated in this experiment could have deviated by as much as 0.79ms-2 due to factors beyond direct control.

Other factors that have possibly contributed to the errors in measurement of the value of ‘g’ include the apparatus used, this may be the cause of a weak or worn component of the boss head, clamp, mass carrier and retort stand. Solutions to this source of errors include replacing the equipment before each new trial and carefully examining and replacing other apparatus where, and when, necessary.

Safety precautions:

make sure that every participant are standing at a safe certain distant away from falling masses, hence ensure that everyone present are wearing closed wear footPlace a soft object directly underneath the ticker timer in which the masses will fall towards in order to absorb the masses’ kinetic energy and prevent the masses from bouncing away to other participants.

Conclusion:

The value for the acceleration due to gravity was determined to be 10.59m/s-2 as I have investigated the ticker timer method. In conclusion my results have also proven my hypothesis to be correct.

Using a water drop method to determine G

Introduction:

The water drop method is another experiment to determine the value of ‘g’. during this investigation the water drop experiences a ‘free fall’. A free-falling object is an object which is falling under the sole influence of gravity. Thus, any object which is moving and being acted upon only by the force of gravity is said to be "in a state of free fall." This definition of free fall leads to two important characteristics about a free-falling object:

Free-falling objects do not encounter air resistance. All free-falling objects (on Earth) accelerate downwards at a rate of approximately 10 m/s/s (to be exact, 9.8 m/s/s).

Aim:

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To determine the value for the acceleration due to gravity by manual timing.

Theory:

When an object falls freely it accelerates vertically downwards. An equation to describe this is; S = D / T in which a = vf – vi / t

Hypothesis:

The shorter the height of the nipple to the ground the faster the rate of acceleration experienced during the free fall of the water drop.

Equipment:

Burette Retort standMetre rulerStop watch Counter weightWater250mL BeakerBoss headClamp

Method:


Burette filled with 50mL of water

Retort stand

Counter weight

250mL empty beaker

2. Place a retort stand at the edge of the laboratory bench and place a counter weight to support the retort stand.

3. Measure one metre height of the burette by using a metre ruler; ensure that another member of the group adjusts the burette to the retort stand. Measure the height of the nipple to the ground again to ensure precise measurements are made. Record this value in the results.

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4. Place a 250mL beaker on the floor, making sure that it is placed directly facing the nipple of the burette.

5. Add 50mL of water to the burette by using a beaker.

6. Gently open the tape of the burette to release water drops, ensure that you place your finger on the nipple to prevent water from being released.

7. Release your finger after you and the timekeeper are ready to measure 10 water drops.

8. Repeat this trial 5 times from the same height to ensure reliability and then repeat the same process with a different trial of 0.9m height.

9. Record your results and present data in a tabular form.

Variables:

Control: the amount of 10 water drops, the length and position of the retort stand.Independent: the height of the nipple of the burette to the ground.Dependent: the time taken for 10 drops to reach the ground from two different heights.

Results:Height of 1m

Trial Time for 10 drops (s) Residual (mL)1 7.35 32 7.89 43 8.15 34 9.04 45 9.93 4

average 8.47 3.6

Height of 0.9m

Trial Time for 10 drops (s) Residual (mL)1 7.63 42 7.35 43 7.50 44 7.63 35 7.59 3

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average 7.54 3.6

The tables show the time taken for 10 water drops to reach the ground. Both trials of different heights were repeated 5 times and the average was then collected to find the value of ‘g’.

Measurements:

Height of 1m height of 0.9m

S = D / T S = D / T

S = 100 / 0.847 S = 100 / 0.754

S = 118.064m/s-2 S = 132.63m/s-2

... S = 118.064 / 10 ... S = 132.63 / 10

= 11.80m/s-2 = 13.26m/s-2

a = v1 – v2 / t a = v1 – v2 / t

a = 11.80 – 0 / 0.847 a = 13.26 – 0 / 0.754

... a = 13.9 m/s-2 ... a = 17.586m/s-2

Total value for ‘g’ = 13.9 + 17.586 / 2 = 15.743 m/s-2

Discussion:

The acceleration due to gravity in this investigation was found to be 15.743 m/s-2. These values were 35.75% off the accepted value of 9.8m/s-2.

The value of ‘g’ in my investigation was not precise due to many errors experienced and that fact that the investigation was not reliable enough.

In this experiment I have started with a height of 1m and used a decreasing pattern of 0.1m in the next trial in order to increase the accuracy of measurements and in turn minimise error. Inaccurate results are obtained when shorter lengths are used in this method, due to the fact that they have shorter periods, therefore not measuring the value of ‘g’ accurately.

This investigation is valid due to the fact that it obtain a controlled variable was the amount of 10 drops which was kept constant for the preceding trial of a decreasing height of 0.1m. The use of a control in this investigation was to obtain a fair test between each trial, in order to collect the average results in determining the value of ‘g’. In this investigation I have identified that the shorter the height of the nipple to the ground the faster the rate of acceleration experienced during the free

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fall of the water drop, this has proved my hypothesis to be correct.

The reason the validity of conclusions may have suffered, could have been the intervention of humans in both the data collection, and the data analysis process. Both systematic and accidental errors, as well as parallax error may be experienced, arising from human involvement would have had a negative impact on the reliability of gathered data, the accurate analysis of that data, and the validity of the drawn conclusion. using an artificial intelligence in the form of robots and/or computers in the areas of data collection and analysis (for example, having the line graph produced on Microsoft Excel instead of by hand) would have rectified this error source and improved the reliability of the investigation as a whole.

The experiment would have been more reliable if I have used 5 trials instead of 2, therefore using 5 different heights ranging from 1m and having a decreasing pattern of 0.05m to 0.75m, ensuring that each trial is repeated 3 times to obtain an average. This method would ensure accuracy and reliability in order to obtain a precise value of ‘g’.

My results showed an increasing pattern of the rate of acceleration experienced each time I repeat the same process; this may be the cause of the decreasing amount of water in the burette which has reflected upon my results to differ. This may also have been a discrepancy approach to my results, therefore to ensure reliability fill in water to the burette up to 50mL every time you repeat an experiment.

Safety precautions:

Make sure that every participant are standing at a safe certain distant away from falling masses, hence ensure that everyone present are wearing closed wear footThe counter weight must not consist of a large mass, but heavy enough to keep the retort stand from moving.Make sure that paper towels are in handy for uses encase of spilling water.

Conclusion:

The value for the acceleration due to gravity was determined to be 15.743m/s-2 as I have investigated the water drop method. In conclusion my results have also proven my hypothesis to be correct.

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My Judgment

All three procedures were performed to determine the value of ‘g’. However, not all of them obtained accurate results and/or a precise theoretical value of 9.8m/s-2.

In my opinion, the Pendulum was the outmost reliable method of all three due to obtaining a value of 9.793m/s-2 which was 0.0714% off the theoretical accepted value of 9.8m/s-2.

My decreasing pattern of 0.05m in between each trial has increased the accuracy of measurements and in turn minimised the error. Inaccurate results are obtained when shorter lengths are used in the pendulum method, due to the fact that they have shorter periods. Therefore I have used longer lengths to ensure accuracy and validity in this investigation.

The controlled variable was the mass carrier which was kept the same for each preceding trial. The use of a control is to obtain a fair test between each trial, in order to collect the average results in determining the value of ‘g’. I have kept all variables constant and precise as well as making the same members in the group to perform the same job in the preceding trials.

It was reliable because the experiment was repeated 5 times with 5 different lengths of the string. The use of 10 oscillations instead of 1 or 2 was to reduce errors, this means that it will take slower to complete 10 oscillations, therefore the timekeeper was able to better anticipate the point of closure and, hence, take a more accurate reading of time.

In conclusion the pendulum was the most reliable method because of its obtained ‘g’ value of 9.793m/s-2 comparing to the

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ticker timer which obtained 10.59m/s-2 and the water drop method which obtained an outrageous value of 15.473m/s-2

Q. Describe 3 applications of gravitational Force?

1. The first application of the gravitational force is keeping the satellites in place.

2. Another application includes water pipes and damps and how they are designed in a declining structure allowing gravitational force to drag it down to the required destination.

3. Finally, faeces do not flow up hill.

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Bibliography

The Writing Centre, University of Wisconsin-Madison,http://www.wisc.edu/writing/Handbook/ScienceReport.html

R Nave, http://hyperphysics.phy-astr.gsu.edu/hbase/pend.html

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Why does the meter beat the second? http://www.roma1.infn.it/~dagos/history/sm/sm.html

Wikipedia contributors. Pendulum [Internet]. Wikipedia, the free encyclopedia;

Available from: http://en.wikipedia.org/wiki/PendulumWikipedia contributors. Galileo Galilei [Internet]. Wikipedia, the free encyclopedia;

Available from: http://en.wikipedia.org/wiki/Galileo_Galilei

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http://www.roma1.infn.it/~dagos/history/sm/sm.html

http://www.roma1.infn.it/~dagos/history/sm/sm.html

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1206320934 2006 Physics Assessment Task