Equipment
- Elastic chord – Gold-Zech elastic
- Plasticine
- Scales accurate to 0.01g
- Meter rulers accurate to 1mm
- Permanent marker
- Flat surface (desk)
- G. Clamp
- Clamp
Method
- Weigh Lego bungee model.
- Decide a range of masses to test of which the mass of the figure is somewhere in the middle.
- Weigh out plasticine into the range of masses making all into a ball.
- Set up apparatus as shown above.
- Using the first mass let it hang on the chord. Measure from the top of the plasticine ball, at eye level, the new length of the chord.
- Repeat the last step twice more to get repeat readings in order to get more accurate readings and to avoid anomalies.
- Record the results in a table.
- Repeat from step 5 with the rest of the masses.
Range of masses of plasticine
I decided to use masses from 0.5g up to 8g at o.5g integrals.
Accuracy
With a marker pen I marked a 1cm length at the bottom of the chord; this was so that I used the same amount of chord each time for the attachment of the masses.
I took two repeat readings and found the average of these to give one, more accurate reading, this will get rid of any anomalies and proves accuracy if all the readings are the same for a certain mass.
Sensitivity
Using 0.5g intervals will make my experiment more sensitive than using just 1g intervals, there will be more points on the graph making any curves smoother and meaning any readings taken from them will be more accurate. I am also a ruler accurate to 0.001m and scales accurate to 0.01g to give more precise readings.
Safety
I was very careful when carry out my experiment, I was sure to securely attach the clamp to the table using the G-clamp so there was no chance of it falling off and doing anyone any damage.
I also kept my workspace tidy at all times to avoid anyone slipping on anything which may have fallen on the ground. The elastic was very thin and broke quite easily, this could fly up and hit someone in the eye so I was sure to wear goggles at all times.
Results
Length of elastic, x = 0.5m The gravity of the earth is taken to be 9.8ms-2.
From this data I could plot a force extension graph.
I then calculated the area under the part of the graph for each mass to get the elastic energy for each unit of force. This elastic energy can then be plotted against extension on the same axis as the graph of g=mg(l+x) and hence the extension at which the jumper will come to rest can be found.
Originally the data only went up to 8.000g as I felt this would be an appropriate range of readings with the mass of the Lego figure being in the middle of this range. It turns out that this was not a large enough range as the weights were not being dropped but just allowed to hang in the preliminary experiment. I decided to increase my range to 13.500 to allow for the extra extension of the elastic when the Lego figure is dropped.
If this graph was linear I would be able to use a calculus to calculate the area under the graph, however it is not linear and so I must split the graph up into a series of triangles and rectangles and then find the area of these.
I could then plot an energy-extension graph. I was also able to plot
g=mg (l+x)
This is the gravitational energy lost by the jumper and when plotted, this graph should be linear.
I could plot these on the same axis the point where the two graphs intersect is the extension at which the jumper comes to rest.
Unfortunately my Eel-extension graph did not turn out as expected in a nice smooth curve but was instead all over the place and would not intersect g=mg(l+x) at all. To correct this I plotted the cumulative elastic energy against extension giving me the desired curve.
Predicting the launch height
In theory the point at which to two graphs meet should show the extension at which the jumper comes to rest. I must find the extension where the lines intersect, this can be done from reading off the graph. X=0.61m
To get the appropriate height of the jump for the Lego figure I must add the unstretched length of the chord to the extension where the lines intersect.
h=l+x
h=0.5+0.61
h=1.11m
Jumping from this height would mean the jumper would just skim the floor. The aim is to come within a safe distance of the floor so to get a safe- adjusted height I must add 0.08m to my launch height.
Safe height=1.11+0.08
Safe height=1.19m
Analysis
According to my graph the point at which the two lines cross and hence the extension at which my Lego figure comes to rest is 0.61m. Assuming the jumper starts from rest, the launch height for the jumper just to hit the floor will be 0.5+0.61=1.11m.
My graph shows no anomalies and both my lines are very smooth showing that the experiment has been carried out to a high degree of accuracy, however they are not plotted quite far enough for me to take a completely accurate reading from the graph of where the two lines intersect. In order to take the reading at all I have had to carry on my lines of best fit further than the points on the graph.
When the predicted launch height was tested (not including the 0.08m safety measure) the figure just hit the ground. When the safety adjusted height was used the jumper reached the bottom of the jump 0.06m from the ground. This shows that without the safety adjustment the jumper fell 1.13m showing my predicted launch height of 1.11m was fairly accurate being only 0.02m out.
Percentage error = 1.13 – 1.11
1.13
The use of triangles on the force extension graph when it was in fact curved led to small errors, the line was curved both inward and outward however most likely cancelling each other out leading to a fairly accurate total Eel.
Evaluation
Limitations
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The measuring method was not accurate enough, it was difficult to measure the extension of the elastic with the loads as they never fully came to rest, a high speed camera would be a more effective way of measuring the extension if it were not costly and inaccessible in the given circumstances. Using a high speed camera would involve setting up the camera at a fixed position pointing at the ruler on which the extension will be measured again. ‘High Speed Photography is the science of taking pictures of very fast phenomena. In 1948, the (SMPTE) defined high-speed photography as any set of photographs captured by a camera capable of 128 frames per second or greater, and of at least three consecutive frames. High speed photography can be considered to be the opposite of .’ [http://en.wikipedia.org/wiki/High_speed_photography]
One must set the camera to take continuous shots for a period of about 5 seconds. Once the photos have been taken they can be uploaded onto the computer and it will be easy to pin point the absolute length at which the mass was at its lowest.
- When a weight was taken off the chord, the elastic did not return to its original length but was slightly longer affecting the accuracy of the following results as the original length of the chord, x, will have been different each time reducing the extension,
Extension = stretched length – original length,x.
A slightly thicker elastic could have been used to prevent this from happening.
- Measuring was inaccurate as it was difficult to get the different size loads the same shape meaning you were measuring from a different point for each of the masses.
Modifications
- If I were to do the experiment again I would consider the effect of different conditions. For example I would repeat the experiment under different temperatures to investigate the elasticity of the chord when it is colder (winter) and warmer (summer).
- I would take a closer look at the effect of friction, air resistance on the jumper to see if my assumption of it having no major effect on the jumper is true, Internal friction of the chord obviously has some effect on the jumper otherwise they would return to the launch height and bungee jumping would no longer work. Air friction could be made a variable by increasing the weight of the jumper hence making them go faster and increasing air resistance. The internal friction of the chord could be increased by using chords of different thicknesses and elasticity.
- Another way of looking at this experiment would be to look at the horizontal motion of the jumper, if jumping from a building, are they going to crash into the side of once they have jumped?