Investigation to find a value of g using the oscillations of a spiral spring.
AS / A2 Physics Coursework
Name Nicola Morris Teacher Mrs. Farrow
Date February 2002
Title / Aim
Investigation to find a value of g using the oscillations of a spiral spring.
Diagram
A2b partial
A4c complete + labelled
List of apparatus
Clamp Stand and G clamp
Metre Ruler (0-100 cm) +/- 0.1 cm
Slotted mass and mass hanger (0-1kg added in 0.1kg masses)
Stopwatch =/- 0.01 seconds
Spiral Spring
Fiducial Mark
Blu-tack
Pointer Flag
A2d some
A4d comprehensive
A6d full specification
Variables involved (constant and changing)
There are two types of variable within my experiment - dependant and independent. In the static experiment, the load is independent, kg, and the extension is dependant, m. In the dynamic experiment, there is the time period, seconds, which is dependant, and the load, kg, which is independent.
F=ke, if k is kept constant. If k is kept constant, then my graph will show a straight line through the origin. This shows that F ? extension.
In my dynamic experiment, T 2 = 4? 2 m/k . This shows that again, if k is kept constant, my graph will be a straight line, and T 2 ? mass. To ensure that k is kept constant, I always used the same spring and same masses.
My range of variables was so that, my mass didn't exceed 0.7kg, as from my preliminary experiments, I knew that this wouldn't exceed the elastic limit. I took 7 results for both experiments. The preliminary tests, were to test the spring, and see how far it could stretch before exceeding its elastic limit. I loaded the spring up, with slotted masses. One at a time, until the spring broke. I measured the extension for each load, and plotted a graph from my results. I could see on my graph, that where the line was straight, the spring hadn't exceeded its elastic limit. Where the graph began to curve was where it had exceeded its limit.
A4b one appropriate
A6a one fixed variable
Method
Static Experiment
I set up the equipment as shown in the diagram. I hung the mass hanger onto the spring, with a pointer to give a clear indication of its position against the ruler. The pointer was good because it reduced parallax. I kept the pointer in the same place on the mass hanger, so the measurements of extension were fair each time. When I hung my mass hanger on, I looked at the metre ruler, and found my scale measurement. This was the measurement I ...
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A4b one appropriate
A6a one fixed variable
Method
Static Experiment
I set up the equipment as shown in the diagram. I hung the mass hanger onto the spring, with a pointer to give a clear indication of its position against the ruler. The pointer was good because it reduced parallax. I kept the pointer in the same place on the mass hanger, so the measurements of extension were fair each time. When I hung my mass hanger on, I looked at the metre ruler, and found my scale measurement. This was the measurement I would use to work out all my extension values. The final position of the pointer minus the original position I recorded at the start, would give me the extension. I loaded up the mass hanger with 0.1kg loads at a time. I took each reading, recorded it, and also conducted repeat readings for accuracy, and worked out an average extension for each load. With my results, I then plotted a graph.
Dynamic Experiment
Again, I set up the equipment as shown in the diagram, but this time without the metre ruler. I attached the mass hanger onto the spring, and observing where the bottom of the stationary mass hanger was, I stuck a piece of paper onto the stand behind it. I drew a fiducial mark on the paper, level with the bottom of the mass hanger. Each time I added a mass to the mass hanger, I would observe the bottom of the hanger, and move the fiducial mark level with it. This was to ensure that I was measuring my oscillations from the same point each time. With all my readings I took at least two, occasionally three repeat readings.
When I had my mass hanger with the slotted number of masses on it, I would pull it slightly below the level of the fiducial mark and let it begin oscillating. When it had done a few oscillations, I began timing the time for 50 oscillations to happen. I began counting at zero.
When I had all my results, I found an average time for each load, divided it by 50, to get the time for one oscillation, and then squared it. I graphed these results.
With the gradients from both my dynamic and static experiments, I was able to work out a value of g.
/gradient of static experiment x 10-1 x g = 4?2 x (1/gradient of dynamic experiment)
My value of g should be around 9.81 Nkg -1, if my experiment is very accurate.
A2a outline plan
A4a detailed plan
A6c logical sequence
Safety considerations
* Use of safety glasses, to protect eyes from the possibility of the spring snapping during the preliminary experiment to test the elastic limit.
* Cushioned landing if loads fall, so they don't bounce.
* Keeping feet out of the way, as falling loads may injure the feet.
A2c OK
Intended readings - number and range
I intended to take seven readings for each experiment, as this seemed a reasonable amount of readings to provide a good enough range. I went from 0 - 0.7kg in the static experiment, as above a load of 0.7kg, the elastic limit is exceeded. In the dynamic experiment, I again took seven readings, but only went up to 0.5kg, as I had to pull the spring down to begin the oscillations. This was more likely to exceed the elastic limit, so I chose a lower load. I did still take seven readings, using some increments of 0.05kg.
A6b both OK
Design justification(s) - based on knowledge and understanding
There are many designs in my experiment based on the theory of simple harmonic motion. If the spring obeys the laws of SHM, then the time period will always be constant, despite the varying amplitude. This justifies my reason for letting the spring move for a few oscillations before I began timing. This should not affect my accuracy in anyway, as I am calculating the time period, which remains constant. However, I am assuming the fact that the spring does obey Hooke's Law and does have simple harmonic motion. The oscillations of my spring did decay however, due to air resistance, and the work done in the spring.
I conducted the preliminary experiment to test the spring's elastic limit. Hooke's Law says that the load applied to a spring is proportional to its extension, providing that it doesn't exceed the elastic limit. I knew from this theory and formula that if I exceeded the elastic limit during my experiment, my results would be very inaccurate.
A8a OK
Design justification(s) - based on supporting theory (formulae or calculations)
Static - Hooke's Law F = ke
?s (gradient for static experiment) ?s = 1/k
The static experiment follows Hookes Law, and the rules for SHM:
* The Time Period is always constant, even if the amplitude varies.
* The acceleration is always directed towards the equilibrium position.
* The acceleration is directly proportional to the displacement from the equilibrium position.
T is the time period, ? is the angular velocity
T = 2?/?
= V(mass of oscillating system/ force per unit displacement)
Since a = - k/m x e = -?2 e where ?2 = k/m T=2?/? = 2V(m/k)
Then to achieve the formula for the dynamic experiment, squaring the formula for the time period, we get T 2 = 4?2 x (m/k). These two formulae can be put together to gain g.
A8b OK
Aspects of the plan based on predictions/secondary sources/preliminary work
For my dynamic experiment, I chose to measure t 2 against mass, because I predicted that it would give me a straight line, because of the formula : t2 = 4?2 x (m/k)
Because I know that 4?2 is a constant, and k is the spring constant, I can plot t2 against m, and it will give me a straight line. They are the variables.
I used the preliminary experiment to set my range. I found out from this that I couldn't time oscillations with 0.1kg because they were too quite, and tended to swing from horizontally, which flawed the timings. I also knew not to add more than 0.7kg to the mass hanger, as from my preliminary experiment, anything more exceeded the elastic limit.
I predict that my value for g will be around 9.8. I know that the universal value of g is 9.81 N kg-1 but I know that my value will not be as accurate as this as my equipment will induce errors.
A8c (A2 only) OK
Use of secondary sources or preliminary work
I derived my formulae from Advanced Physics - Materials and Mechanics, T. Duncan.
A8d (A2 only) OK
