In this experiment, I am going to find out the relationship between Force and extension using stretchy sweets and then find the stiffness of stretchy sweets using Hookes Law.
STRETCHY SWEETS EXPERIMENT
In this experiment, I am going to find out the relationship between Force and extension using stretchy sweets and then find the stiffness of stretchy sweets using Hookes Law.
Hookes Law states that extension in a material is proportional to the force applied provided the proportional limit is not exceeded.
To do this, I will use a fixed length of stretchy sweets and suspend different mass of metals on it. Then I will find the extension on the sweet for each suspended metal of known mass. I will carry out first a trial experiment to find out the behaviour of this sweet under different load and to see if it returns to its original length after unloading it.
There are several factors that may affect the extension of the stretchy sweet. Some of them are:
* The material of the stretchy sweet
* The cross sectional area of the sweet
* The length of the stretchy sweet
* The temperature in the lab
In doing this, I have to keep the material of the sweet constant by using the same type of sweet each time. The cross sectional area of the stretchy sweets will be kept constant by using stretchy sweets with the same diameter. The temperature will be kept constant by performing the experiment in the lab at room temperature, because an increase or decrease in temperature will cause the stretchy sweet to either expand or contract thereby affecting the extension of the sweet when a load is applied to it. For a fair test, I will use the same length of stretchy sweets each time I repeat the experiment and I will also ensure that the length of stretchy sweet that I use is long enough, because longer sweets gives larger and more measurable extensions.
PREDICTION
I think that as the load applied to the stretchy sweet is increased, so will the extension and the rate at which it increases will be proportional to the applied load (i.e. F?e) provided the elastic limit is not exceeded.
This is because of the structure and arrangement of molecules in the stretchy sweet. When a load is applied to the sweet the molecules in the sweet straighten out as atoms in the lattice slide over each other, allowing the sweet to become longer. Increasing the applied load will cause a deformation in the arrangement of molecules and so the sweet will break. But as long as there is no deformation in the structure of the sweet, the molecules will then regain their original positions when the load is removed.
By plotting my graph of extension against force/load, it will reveal a region where extension is directly proportional to the force. Then I will find the stiffness of my sweets using the formula F=kx, where F is the force measured in Newton's, x is the extension measured in metres and the constant k is the stiffness measured in Nm-1.
TRIAL
APPARATUS
. Stretchy sweet over 0.50m long
2. Stop clock
3. Clamp stand and a block of polystyrene
4. Set squares
5. A metre rule
6. Micrometer screw gauge
7. Cello tape and Plastacine
8. A weighing balance
9. 10grams X 10 of metals
I will set up my apparatus as shown in the diagram and then record the initial length of the stretchy sweet. Using a cork with a pin attached to it, I will suspend the following objects of mass 20.2g, 25.0g, 30.0g, 40.0g ...
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TRIAL
APPARATUS
. Stretchy sweet over 0.50m long
2. Stop clock
3. Clamp stand and a block of polystyrene
4. Set squares
5. A metre rule
6. Micrometer screw gauge
7. Cello tape and Plastacine
8. A weighing balance
9. 10grams X 10 of metals
I will set up my apparatus as shown in the diagram and then record the initial length of the stretchy sweet. Using a cork with a pin attached to it, I will suspend the following objects of mass 20.2g, 25.0g, 30.0g, 40.0g and 45.0g. Start the stop clock and remove the load (F), which is equal to (mass*gravitational force) after 1 minute. I will record the new length of the stretchy sweet and then calculate the extension for each load by subtracting the initial length from the new length. Record my results on a table and then plot my graph of extension against force and to see how this material behaves before performing my experiment.
EXPERIMENT
DIAGRAM
METHOD
I will set my apparatus as shown in the diagram above. Using a metre rule, I will measure the length of stretchy sweet (0.40m). Then I will measure the diameter of the stretchy sweet using a micrometer screw-gauge and find the cross sectional using the formula A=1/4?d2. I will then weigh out my given mass to 10g and apply it to my stretchy sweet. Once this is applied, I will start the stop clock and stop it after 1 minute. Then I will take down my new length reading, using my setsquare and will read from my metre rule at eye level. I will then leave the stretchy sweet for about 30seconds while it reshapes itself then I will take my new length reading and repeat the experiment with the following load.
I will then record my results in a table. By plotting a graph of extension on the y-axis against load/force on the x-axis. From the equation F=kx which correspond to the equation of a straight-line y=mx, I will find the stiffness of the stretchy sweet, which is the reciprocal of the gradient of the region of the graph which obeys Hookes Law.
Modification
* I performed suspended my load on the stretchy sweet, by forming a loop instead of inserting a pin to the end of the sweet.
* I used a setsquare to take my readings at eye level.
* I used a cello tape to form a pointer on my sweet so I could take my readings more accurately.
* I repeated my experiment for each load applied.
ACCURACY
To keep this experiment as accurate as possible, I need to ensure that while measuring the length of the stretchy sweet, that I don't compress it while trying to make it straight. I also have to ensure that as I use plastacine to hold my stretchy sweet firmly on the metre rule, I don't compress it as this will change the cross sectional area of that region and may affect the extension when a force is applied.
I also have to ensure that the while taking my measurements that it is read at eye level to avoid parallax error. I will also measure the diameter of the sweet at two different points and take an average of the two, as the diameter along the length of stretchy sweet is not uniform.
SAFETY: - To ensure that the experiment is safe, I will put a block of polystyrene beneath the metre rule to act as cushion to prevent injuries when the load disengages itself. I will handle all heavy load with care as I move them about.
OBSERVING AND RECORDING
I performed the experiment as planned and was able to get the following results.
For the experiment result when I applied different load using stretchy sweet of length 44.5cm and cross sectional area 8.25X 10-7m2.
Mass in g
±0.1
Weight/load in N
Initial length of sweet in m
New length of sweet in m
Extension of sweet in m
Average extension in m
0.0
0.100
0.445
0.449
0.544
0.548
0.089
0.099
0.094
20.5
0.205
0.470
0.490
0.677
0.699
0.207
0.209
0.208
25.5
0.255
0.465
0.499
0.703
0.739
0.238
0.240
0.239
40.5
0.405
0.444
0.617
0.724
0.898
0.280
0.281
0.281
50.8
0.508
0.502
0.550
0.785
0.834
0.283
0.284
0.284
Table of result for force/load and extension
Force/load in N
Extension in m
0.100
0.094
0.205
0.208
0.255
0.239
0.405
0.281
0.508
0.284
For the experiment result using stretchy sweet of length 44.5cm and cross sectional area 2.66X 10-6m2, when I suspended different load.
Mass in g
±0.1
Weight/load in N
Initial length of sweet in m
New length of sweet in m
Extension of sweet in m
Average extension in m
2.0
0.120
0.402
0.404
0.462
0.465
0.060
0.061
0.061
20.0
0.200
0.407
0.420
0.487
0.501
0.080
0.081
0.081
29.4
0.294
0.442
0.460
0.546
0.565
0.104
0.105
0.105
40.0
0.400
0.430
0.452
0.571
0.597
0.141
0.145
0.143
52.0
0.520
0.490
0.505
0.641
0.659
0.151
0.154
0.152
Table of results for force and extension
Force/ load in N
Extension in m
0.120
0.061
0.200
0.081
0.294
0.105
0.400
0.143
0.520
0.152
I observed that in both results that as the force increased, extension also increased and force was directly proportional to extension. This only occurred up to a certain point on my experiment graph, where the limit of proportionality was exceeded and the graph were seen to curve at the point known as the elastic limit of the stretchy sweet. Once this happened, the material no longer obeyed Hooke's law. I also observed that although the same length of stretchy sweet was used in the trial and the main experiment, the stretchy sweet, which had the smallest cross-sectional area, had a greater extension. This is because the stress exerted on the molecules in the stretchy sweet is equal to load / cross sectional area and so the greater the thickness of the stretchy sweet, the smaller the extension.
Anomalies: Most of the errors were too small for the scale on my graph to be plotted accurately on it. The anomalous result is highlighted blue on my table this error may have been encountered while the molecules in the stretchy sweet were uncoiling at this point as the load was applied to it. It may also have been caused by a change in the temperature of the lab at the time when the load was applied to the stretchy sweet, as a change in temperature will cause the stretchy sweet to expand or contract.
EVALUATION
I feel that overall my results were quite accurate. The stiffness of the stretchy sweet, found in my experiment was 9.27 X 10-1Nm-1. This was different from the value for stiffness found in my trial experiment. This may have been as a result of the different thickness of the sweet used in the both experiments. This is because a thinner stretchy sweet will stretch more than a thicker one when the same force is applied as a result of the compressive and tensile force that acts on the material making the length longer, and the diameter shorter. It may also have been as a result of the different method used as the method used in the trial experiment, involved the suspension of the load by the insertion of a pin attached to a cork to the end of the stretchy sweet. This indeed will have an effect on the extension of the stretchy sweet because the cross sectional area at that point changes resulting in a change in the applied tensile and compressive force.
OrCONCLUSION
The graph of extension against load was seen to be a straight line until it got to a point known as the elastic limit were it was seen to curve. An increase in load did result to an increase in extension as seen in both graphs until the yield point. The stiffness of my stretchy sweet is 9.27 X 10-1Nm-1.
When a load of 0.120N was applied, the extension of the stretchy sweet was 0.061m and when the load was increased to 0.200N, the extension was seen to increase to 0.081m. This was also seen in the trial experiment when a load of 0.100N was suspended on the stretchy sweet the extension was 0.094 and when the load was increased to 0.205N the extension was also seen to increase to 0.208m.
This is because of the structure and arrangement of molecules in the stretchy sweet. When the load was applied to the sweet, the molecules in the sweet uncoiled and straightened out as atoms in the lattice were sliding over each other, allowing the sweet to become longer.
When the elastic limit was exceeded, my graph was seen to curve. At this point, an increase in the load applied resulted in very large extensions. This is because at this point, an increase in the applied force did cause deformation in the arrangement of molecules in the stretchy sweet as a result of layers of atom sliding over each other or movement of dislocations causing imperfections in the structure and arrangement of atoms in the molecules of the stretchy sweet. This causes the stretchy sweet not to regain its original position when the load is removed. As seen on my graph in the trial experiment, when a force of 0.508N was applied, the stretchy sweet had an extension of 0.284m and also on my graph in the experiment when a load of 0.400N was applied, the stretchy sweet had an extension of 0.1434m. The stretchy sweet then began to thin evenly along its length as a result of these dislocations.
The stretchy sweet at this point can be said to be exhibiting plastic behaviour as a small increase in the applied force resulted in very large extensions.
Overall, I don't think my results were accurate and I don't seem to understand what happened in the graph for my trial experiments. There were still errors encountered with my refined method in taking down my extension readings after applying the load and timing for 1 minute, as it was impossible to take off the load and at the same time, take my readings without the sweet recoiling itself again. Holding it with your hand does result in an increase in the force applied to the stretchy sweet. There were also errors encountered when the stretchy sweets sagged as the load was applied to it.
The only way I can make my results more reliable will be to use a different method. I will suspend two strips of the same stretchy sweet from a beam clamped. And on one strip, I will put a millimetre scale while on the other; I will put a vernier scale for reading small extensions. I will also keep the strand with the millimetre scale taut by putting a fixed weight on it. To eliminate any sag of the beam. The reason why I will suspend two strips of the same stretchy sweet is to eliminate error due to temperature changes while performing the experiment.