0:02 hello i'm mrs wilkins and welcome to
0:03 marsbury science
0:05 today we're going to look at an a-level
0:07 physics-required practical how to
0:08 determine the young modulus of a
0:11 material and specifically a copper wire
0:13 the young modulus is a really important
0:15 property in engineering as it tells us
0:17 how easily a material will stretch or
0:19 deform the young modulus is defined as
0:22 the ratio of tensile stress to tensile
0:25 strain where stress is the force applied
0:27 per unit area and the strain is the
0:30 extension relative to original length
0:32 the young modulus is given the letter e
0:35 and this is equal to f l
0:38 over a delta l this is the setup that
0:41 we're going to use today we have taken a
0:43 fairly long piece of copper wire it is
0:45 over two meters because the extensions
0:47 are so small you do want fairly long
0:50 original length this is just one example
0:53 of a setup you can also hang some wires
0:56 sometimes steel is the best vertically
0:57 suspended from a beam but it depends if
0:59 your school laboratory has that sort of
1:01 infrastructure that enables you to do it
1:03 so this is the best option for us in
1:05 this investigation there are two safety
1:08 precautions to consider the first is
1:11 that if the wire breaks and it may well
1:14 do it could snap across the surface of
1:17 the eye causing damage so it is really
1:19 important to wear eye protection in the
1:22 form of safety goggles this second is
1:24 that if the wire snaps of course the
1:26 slot masses will force the ground
1:28 be careful not to have your foot or a
1:31 knee underneath the slot masses and
1:33 perhaps also place a carpet or a tray of
1:35 sand underneath the slot masses to
1:38 protect the floor when they fall so the
1:40 fourth applied is the tension that we
1:42 apply to the wire as you can see we have
1:44 clamped the wire at the far end of the
1:46 bench and then we've run the wire over a
1:49 pulley and attached it to a vernier
1:50 scale at the end of the vernier scale we
1:54 have the hanger and we are going to
1:56 attach slot masses in increments of 100
1:59 grams and that will provide the tension
2:01 which is mg you will notice that we
2:03 actually have two wires attached and
2:05 this is because it's important to have a
2:08 test wire that we apply the tension
2:11 force to and also a comparison wire this
2:13 allows us to give us a reference point
2:15 and also if there are any changes in the
2:17 ambient atmosphere for example if the
2:19 wire extends due to temperature it will
2:21 happen to both and we can find the
2:23 relative extension of the test wire the
2:25 next step is to find the diameter of the
2:27 wire and for this the best equipment is
2:29 a micrometer and this will give us a
2:30 resolution to a hundredth of a
2:33 millimeter the wire may not be perfectly
2:35 uniform throughout and so it's a good
2:36 idea to take the diameter measure the
2:39 diameter at three separate points and
2:41 then calculate the mean i'm going to
2:42 take it here you
2:43 you
2:45 turn the small dial until you hear the
2:47 first click
2:48 and i can see the reading
2:51 to be
2:54 0.28 millimeters i then measured the
2:56 diameter in the middle of the wire and
2:58 at the far end of the wire
3:00 the first two readings were the same the
3:02 diameter was 0.28 millimeters but the
3:05 third was 0.27 millimeters however when
3:07 i calculated the mean you still have to
3:10 give the final result to two significant
3:12 figures and so it still averages out
3:14 2.28 millimeters cross sectional area
3:17 equals pi d squared over four the next
3:19 measurement we require is the original
3:22 length of the wire and for this we used
3:24 a series of meter rules and found the
3:27 original length to be 2.46 meters we
3:29 have of course already applied a small
3:31 tension to the wire to ensure that the
3:33 wire is taught when we took the readings
3:35 of diameter and original length and this
3:37 was supplied by the hangers already
3:39 attached to the vernier scale
3:42 however before we add the additional 100
3:44 grams we have to make sure that our
3:47 vernier scale is perfectly zeroed so if
3:49 we go back to our original equation e
3:52 equals f l over a delta l we've
3:53 accounted for the force we've measured
3:55 the original length we've calculated the
3:57 cross-sectional area by measuring the
3:59 diameter so now we can start to measure
4:02 the extension under an applied force by
4:06 attaching the slot masses and we will
4:07 measure the extension on the vernier
4:10 scale so i'm going to start by adding my
4:12 first 100 grams because this is our
4:14 reference point of zero as i mentioned
4:17 before the extensions are very small and
4:19 so far i have not seen a significant
4:21 extension so i'm going to add another
4:24 100 grams i've taken a few readings now
4:28 and i can see that adding 500 grams is
4:32 now ascended by 1.4 millimeters if
4:33 you're not sure how to read vernier
4:34 scales remember that there are two
4:37 scales the first reading you see where
4:40 the zero on the sliding scale where it's
4:42 between on the fixed scale so i can see
4:44 it's between one and two millimeters so
4:46 i know it's one point something
4:49 millimeters i then get the next decimal
4:52 point by seeing which is the first line
4:54 that lines up with a line on the fixed
4:57 scale and i can see here that the fourth
5:00 line lines up with the fixed scale and
5:02 therefore i can say it's 1.4 millimeters
5:04 in this investigation although we're
5:06 interested in extension in meters our
5:08 vernier scale gives us an extension in
5:10 millimeters so don't forget to convert
5:12 it to meters when plotting your graph
5:15 when you have a full set of data we can
5:17 now plot the graph there are various
5:18 ways of plotting the graph and you could
5:20 plot the stress versus the strain but
5:22 this is quite a complicated way of doing
5:25 it it's more standard to plot the force
5:27 against extension however plotting a
5:29 force when you have to times the mass by
5:32 g 9.81 the values aren't particularly
5:34 easy to plot on a graph so we're going
5:37 to stick with the mass and the extension
5:39 our preferred method is to plot the mass
5:42 on the y-axis and the extension on the
5:44 x-axis because this gives us quite a
5:47 typical stress-strain curve that you'd
5:50 be familiar with if you plot the
5:52 extension on the y-axis and the mass on
5:54 the x-axis which you may also see it
5:56 does of course give you the inverse for
5:59 the gradient plotting it this way our
6:01 gradient gives us the mass divided by
6:04 delta l we can then say that the young
6:07 modulus e is equal to the gradient
6:10 times g times the original length
6:12 divided by the cross-sectional area
6:14 when measuring the gradient it's really
6:16 important that you take the gradient
6:19 from the linear part of the graph
6:21 your graph may show a linear part and
6:23 then it may curve off in which case
6:25 that's great because you've shown that
6:28 the wire behaves elastically and then
6:30 starts to behave plastically
6:32 however for determining young modulus
6:34 it's really important to only take the
6:37 gradient in the linear part and not
6:39 include the part after it's gone beyond
6:41 the limit of proportionality it's also
6:43 important on your graph to plot the mass
6:46 in kilograms our gradient is 357
6:51 kilograms per meter times that by g 9.81
6:52 times it by our original length which
6:55 was 2.46 meters and divided by our
6:58 cross-sectional area which was 6.2 times
7:00 10 to the minus 8 meter squared and we
7:03 get a value for the young's modulus e of
7:07 1.39 x 10 to the 11 pascals
7:11 or 139 giga pascals we can compare this
7:13 to the known value of the young modulus
7:15 of copper which is
7:18 gigapascals we can now take a percentage
7:20 error in our value compared to the
7:22 theoretical value which gives us a
