Monday, December 12, 2011

Physics

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Aim

The aim of my experiment is to measure the earth's gravitational field strength, which is also the acceleration due to gravity. This involves mass, which is the amount of matter an object contains and weight which is the force of gravity pulling down on a object with a mass. Mass is measured in Kg and weight is measured in Newton's. Gravity is the weakest of the four fundamental forces, yet it is the dominant force in the universe for shaping the large scale structure of galaxies, stars, etc.

The earth's gravitational field strength is calculated by the weight (N) / Mass (Kg), therefore the earth's gravitational field strength (g) is measured in (N/Kg). As an object is in free-fall it accelerates at the rate of g. The gravitational field strength is measured by doing an experiment with a trolley rolling down a tilted runway with the force of g causing it to accelerate down the slope.


Hypothesis

Isaac Newton firstly discovered gravity when an apple fell on his head. He then discovered that every object has a mass and that two masses attract each other. This attraction has a gravitational field strength, Newton wanted to calculate the gravitational field strength of the earth. There is a pendulum that involves g and calculates T the time the pendulum will swing for.

Definitions

Gravity Force , Fgrav

The force of gravity is the force at which the earth, moon, or other massively large object attracts another object towards itself. By definition, this is the weight of the object. All objects upon earth experience a force of gravity which is directed downward towards the center of the earth. The force of gravity on earth is always equal to the weight of the object as found by the equation

Fgrav = m g

where g = 1.8 m/s (on Earth)

and m = mass (in kg)


Normal Force

The normal force is the support force exerted upon an object which is in contact with another stable object. For example, if a book is resting upon a surface, then the surface is exerting an upward force upon the book in order to support the weight of the book. On occasions, a normal force is exerted horizontally between two objects which are in contact with each other.


Friction Force

The friction force is the force exerted by a surface as an object moves across it or makes an effort to move across it. The friction force opposes the motion of the object. For example, if a book moves across the surface of a desk, then the desk exerts a friction force in the opposite direction of its motion. Friction results from the two surfaces being pressed together closely, causing intermolecular attractive forces between molecules of different surfaces. As such, friction depends upon the nature of the two surfaces and upon the degree to which they are pressed together.


Implementation

I will use the following apparatus in my experiment to find “g”

A wooden trolley- the trolley will be able to roll down the runway with a negligible amount of friction acting upon it as it rolls down.

A wooden runway- the runway is wide and long enough to enable the trolley to have a sufficient length run and also be wide enough so the trolley won't touch the edges.

A light gate and picket fence- the picket fence will pass through the light gate and the velocity at which the picket fence passed through the light gate can be measured.


A CBL data logger- this will be connected to the light gate , the data measured by the light gate such as the velocity and time at which the picket fence passed through the light gate can then be displayed as a graph on the data logger.

Blue-tack- this was used to hold the picket fence securely to the top of the trolley, this is so that when a trolley does a run, the picket fence will pass through the light gate and therefore measure the velocity and time of the trolley.

Books- the only resource that was available to elevate one end of the runway to slope the runway was books, so I used different amounts of these to alter the height of elevation and therefore altering the angle of the runways slope.

A metre rule- this was used to measure the height of elevation on one end of the runway and the length of the runway.

A set square- this was used to make sure the picket fence was perpendicular to the trolley and the light gate was perpendicular to the picket fence on the trolley.

A clamp stand- this was used to hold the light gate up above the runway so it could allow the picket fence to pass through it.

The apparatus were set up as shown in Diagram one. The runway would first be put at a very small slope to start off the experiment. The picket fence was checked and adjusted to make sure it was inline with the trolley and not at an angle to the trolley. I then checked and adjusted the light gate to make sure the picket fence could pass through the light gate without colliding with it and that it was perpendicular to the light gate. Every time a run was done the apparatus was re-checked to make sure the apparatus was still accurate.

Each time the angle of slope was increased, the position of the light gate would have to be raised so the picket fence would not hit it. The angle of the light gate would also have to be changed so it is still perpendicular to the picket fence. Each run I would note down the results from the data logger. Three runs were taken for each runway angle and the averages of those three were put into the results. The books were used to increase the angle of the runway.

If there was an occurrence that would cause a incorrect result such as the trolley hitting the side of the runway, I would do the run again and ignore the results I got from the run that hit the side of the runway, as the increase in friction from the trolley hitting the side would cause the velocity of the trolley to significantly decrease. I also made sure that the picket fence was fully cutting the light gate beam each run so the reading on the data logger would be accurate. The apparatus I use was the same through out the whole experiment to keep things like the mass and friction of the trolley upon the runway.

The factor of safety is very important in every experiment. Unsafe experiments tend to be inaccurate so fully meeting all of the safety requirements increases the accuracy of the experiment. In this particular experiment I found there to be a few safety factors that needed to be taken into consideration as well as the safety rules of the laboratory. The first safety factor I found was the angle of the runway. I decided that the angle of the runway should be kept fairly small because I wanted to limit the speed of the trolley as it rolled down the runway so it wouldn't travel to fast. This is important because at the bottom end of the runway the trolley had to be caught by hand, if it was travelling to fast the person stopping it may be injured.

The runway had rails along the side so the trolley would not fall over the edge of the runway and break, the trolley was also caught at the end of the runway so it would not hit the floor and break. The light gate was securely fastened to the clamp stand and the picket fence was attached to the top of the trolley so it wouldn't fly off and hit somebody while it speeded down the runway. The runway also had rubber grips at the bottom end of the runway, this was so it would grip onto the table and wouldn't slide off the table and hit somebody.

The reliability and accuracy of the experiment is very important because inaccurate data will cause the results and the graph to be incorrect. To increase the reliability and accuracy of the experiment I checked and adjusted the apparatus every time the trolley did a run so the apparatus were always set up properly and therefore always give the correct reading. The measurements of the runway such as its width and length were measured to the nearest centimetre using the metre ruler.

The CBL data logger measured the velocity of the trolley to four decimal places and the time at which it passed to three decimal places. The CBL data logger was used with the light gate and picket fence to measure the velocity and time instead of a traditional ticker timer. Although the ticker timer is accurate, it presents a higher possibility for error when measuring the distance between the dots on the ticker tape, plus the accuracy of the measurements could not be as accurate as that of the CBL data logger. The measurement of the angle of the runway was also measured using trigonometry instead of using an angle measurer , as I can measure the height and length of the runway more accurately than the angle of the runway.


Results

These tables are the results from my experiment. The figures they contain are the average of the three runs I did for each angle. The first table shows the length and height of the runway and also how they were used to calculate the angle of the runway. The second table shows the initial velocity, final velocity, initial time, final time and how they were used to calculate the acceleration of the trolley.


Table One

Experiment Number Length of Runway,

L in metres Height of Slope,

H in metres Angle of Runway, ᠋ = Tan (L/H), in degrees


Table Two

Experiment Number Initial Velocity, u in metres per second Final Velocity, v in metres per second Initial Time, ti in seconds Final Time, tf in seconds Acceleration, (v-u) / (tf-ti)


The results were put into the graph to show the strength of the earth's gravitational field. These are shown in Graph one where the y axis is the acceleration, x axis is the


sin the intercept is (-F / m) and the gradient of the line on the graph is “g”, the earth's gravitational field strength. The line on the graph is not a line of best fit because all the results I obtained form a perfect positive correlation. I think is because I took three experiments at every height and then derived an average from the three which gave an accurate and reliable results.


Conclusion

I have concluded from my results that the gravitational field strength of the earth is .8 N/Kg. This is only accurate to two significant figures because of the limitations of quality and accuracy of the experiment. If I were to use more accurate equipment I would probably be able to show that the gravitational field strength of the earth , though human error in implementation and calculation of the results.

 To find “g” I had to find the gradient of the line on the graph, the line on the graph was not a line of best fit, but a line which goes through all the points on the graph which means there are no odd results that may throw off the reading of g partially. There is a full positive correlation, which shows that the experiment was carried out accurately each time the experiment was done and a reading was taken.

My results show and prove that my prediction and scientific knowledge were accurate. I have proved Newton's theories on gravity using a different experiment to the one he did. Newton's experiment didn't need many accurate measurements that required electronic measuring equipment. The strength of g may have been better measured using a simpler experiment that didn't require machines to find measurements as this has less equipment to rely on and less factors that could go wrong. Newton using the pendulum found that g is 1.81 N/Kg so if I had to do the experiment again I would use the pendulum experiment.

As well as the gradient of the line being the gravitational strength, the intercept of the line is equal to the negative friction divided by the mass of trolley. As shown on the graph the intercept is 0.1. I can also conclude from my results that there are many uncontrollable factors that affect the experiment when trying to measure the earth's gravitational field strength. Such as the variations that appear close to the earth's surface, though these won't affect Newton's calculation when put to two significant figures. When measured to significant figures we may not always get 1.81 N/Kg, but this is usually ignored because g is usually rounded down to one significant figure which is 10.00 N/Kg.

In my scientific knowledge it is stated that g is also the acceleration due to gravity so the calculation of g could be acquired simpler if I could measure an object in free-fall and then measure its time and displacement through the following derived equation

S = ut + ½ at^ ,

Initial velocity is zero so, S = 0 + ½ gt^

Therefore g = S / t^.

Though for this to be accurate the only force acting on the object must be gravity and the air resistance must be negligible. The results also show that the force of gravity has not changed over time since Newton first carried out the experiments.

Evaluation

I believe that the experiment that I used to find the earth's gravitational field strength was suitable and was able to accurately show “g”. The measurements that needed to be taken were more complex such as the velocity, were measured by a CBL data logger which is a hand held computer connected up to the light gate. There were no anomalous results as t reset the apparatus every time I did the experiment, this meant every time the experiment was done the apparatus was checked and re-adjusted.

This is important because when the height of elevation of one end of the runway was changed the light gate would have to be re-adjusted to make sure it was perpendicular with the picket fence on the trolley. There are limitations to the accuracy and results of my experiment because of certain factors to do with the apparatus and also fundamental factors that were uncontrollable.

One of these factors was the runway being curved due to its own weight, although not significantly causing an error in the results, it still does contribute to the overall result not being accurate to three significant. Another factor is the speed at which the trolley passes the light gate at as friction increases with speed. The light gate may not have been one hundred percent perpendicular to the picket fence causing a small in accuracy in the results. This is shown in Diagram 4.

The wheels on the trolley may have caused some runs to be slow and some to run normally which would severely affect the acceleration when calculated in the results. The measurements were accurately done though some ideas to improve them have come to mind, such as using a plumb line to measure the height of elevation of one end of the runway. This would mean the height is measured completely straight and accurately whereas I may have measured it at an angle which would cause the height to be measured greater than it really was.


The runway should have also been made of a stronger material that would not bend or curve affecting the run of the trolley. I did try to make the measuring as accurate as possible by using the CBL data logger which was connected to the light gate to measure the time and velocity of the picket fence on the trolley, the distance between the start of the run and the light gate was kept constants the only factor that would affect the velocity of the trolley was the angle of the runway.

The light gate was put perpendicular to the picket fence each time the trolley did a run. To obtain fair and reliable results, I did the experiment at each runway angle three times and then took an average result and used it as my final result to be put into the graph. As the three results for each angle were extremely similar there were no odd results that would have thrown the average off. The angle of the runway was not measured using an angle measurer, instead I used trigonometry which meant the measurement of the angle was much more accurate as I only needed the measure the height of the elevated side of the runway and the length of the runway.

Overall I feel that the experiment was suitable as it did allow me to find “g” accurate to two significant figures so the limitations of the apparatus and error causing factors were not too great as the effect they had was minimal. If I had to do the experiment again I would use the trap door experiment as shown in Diagram 6. I would only need to find the displacement and time of an object in free-fall. This experiment would provide both and very accurately. The experiment would also be a lot simpler, I believe that the simpler the experiment the more accurate it will be and the lower the chance of human error.

The clock would measure the time and all I would have to do is measure the displacement and then putting these two measurements in the formula, g = S/t^, would provide me with the earth's gravitational field strength. I could also have used the original pendulum experiment that Isaac Newton used but I found that it would be even harder to measure than the original experiment, meaning it is likely to be very inaccurate when I try to calculate the results.

I also believe that the results were off because the trolley wasn't in free-fall, it had a considerable amount of friction and air resistance acting against it. The steel ball from the trap door experiment would be in free-fall as there would be no friction acting against it and the air resistance would be a lot less than that acting on the trolley.




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