For the sake of a more accurate measurement , this experiment will be separated into two parts . In the first part , we will add the slotted mass to the load gradually until the copper wire breaks , the purpose of this is to locate when will the wire start plastic deformation or in other words , to find the elastic limit . Then in the second part , we will add the slotted weight of smaller mass to the load gradually and measure the variation between the mass and the extension within this elastic limit to find the Young modulus .
Young modulus (E) = = = = = = () () = S
Procedures :
Part 1
- Set up the apparatus on the bench top as shown in figure a . Fix an adhesive label on to the copper wire to act as a marker .
- Measure the original length L of the wire between the wooden block and the marker .
- Load the wire in steps with load m and record the extension e produced . Continue loading until the wire breaks .
Part 2
- Repeat the experiment with a new piece of copper wire , but loading the wire up to its elastic limit only .
- Measure the length L of the wire between the wooden block and the marker . With the micrometer screw gauge , take several readings of the diameter d of the wire , taking two readings at right angles at several points along the wire .
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Increase the load m by successive additions of 0.05 kg and read the extension e1 after each addition.
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When the load has reached about the value near the elastic limit , unload the wire by 0.05 kg at a time and again read the extension e2 .
Precautions :
- Wear safety goggles to protect your eyes in case of any accidents .
- The wire must be hold tightly with the wooden blocks by the G-clamp .
- Avoid making any kinks as it will make the wire break easier .
- Remember to put a cushion under the load in order to prevent any destructive collision with the floor.
- Make sure the wire will not break at the end connected to the load .
Measurement and data evaluation :
Part 1
Original length of wire , L = 1.630 m
From the graph of mass against e , the elastic limit is at m = 0.6 kg approximately .
Elastic limit stress = = = = = 0.145 GPa
Percentage strain the wire can withstand before the elastic limit is exceeded
= X 100% = X 100% = 0.383 %
Percentage breaking strain = X 100% = X 100% = 8.96 %
Part 2
Original length(nature length) of wire , L = 1.531 m
Mean diameter of wire , d = = 0.0002275 m
From the graph above ,
Slope of the line , S = 121.46 kgm-1
Young modulus of the copper wire , Y = S = X 121.46
= 4.48 X 1010 Pa = 44.8 GPa
Error estimation :
= + + 2 x
= + + 2 x
E (Y) = 5.42 GPa ∴ Y = 44.8 ± 5.42 GPa
Percentage of random error = x 100% = 12.1 %
Compared with the value in Wikipedia , 117 GPa (under standard condition) ,
Percentage of systematic error = x 100 % = –61.7 %
Error analysis :
From the above results , we can see that there is a 12.1 % random error in finding the Young modulus of copper . One of the reasons for such errors is the non–uniformity in cross sectional area . When a wire is stretched by a force , the length of course will increase , but at the same time the cross sectional area of the wire will also vary . This little variation will affect the calculation of Young modulus by a pretty substantial degree . Besides , there could have been parallax error which occurs when the eye is not placed directly opposite a scale which a reading is being taken . Moreover , reading errors is another error when guess work is involved in taking a reading from a scale when the reading lies between the lines.
Concerning the large systematic error , the main reason for it is the impreciseness of equipments . Since the extension is so small (about 0.01mm), using a meter rule(minimum scale is only 1mm) to measure it is absolutely unacceptable as many minor data will be omitted . In addition , the length of wire in part 1 and part 2 is different , this will end up in not being a fair test . As the elastic limit depends little on the length of the wire , the wire in part 2 may undergo plastic deformation earlier that we may have ignored .
Conclusions :
Comparing the shape of the graphs , it is obviously that the result is close to the theory . Although the random error is almost 12% , it is still acceptable as human errors must exist inevitably. However , the systematic error in this experiment is quite large due to the inaccuracy of equipments , therefore better design or improvements are required .
Possible Improvements :
- Repeat the experiment for several times to get a more precise average reading .
- Use a longer copper wire to lower the percentage error in measurement .
- A thinner copper wire is also recommended as it can make the extension larger for better resolution .
- Use a large Vernier Caliper instead of meter rule so that the extension of the wire can be measured more accurately . If it is possible , it is also suggested to use a electronic Vernier Caliper as well .
- Add weights at smaller intervals instead of 50g jumps .This would help in making the graphs more accurate, therefore allowing us to read off the graph more accurately and getting better readings.
THE END
