OK 3, 2, 1… go!
So, from September 2015 according to new regulations
all A level physics students will be required to carry out a practical to find a value for the
acceleration due to gravity using a freefall method.
I don't know if that'll work. Sorry about the delivery, but hey…
Students will know that the acceleration due to gravity is 9.81 m/s²
so they might be frustrated that they're not doing real science for this
practical. I think it's important to stress to them that the main point of
this practical isn't just to find a value for g, it's about exploring data
collection and analysis, which are skills that scientists rely upon for their work
in the real world.
A simple way to find a value for the acceleration due to gravity is to drop a
ball from a fixed height and time how long it takes. You can then use those values
in the equation for motion s = ut + ½at², and rearrange
to find a. Now this method might seem rudimentary but it's a great way of
getting students to think about measurement uncertainty and accuracy. How could they
improve upon taking just one measurement, where do measurement uncertainties
arise and how will they process any data they collect?
So let's have a go.
0.53 seconds and if my calculations are correct that gives a value of g of 10.7m/s²
So Christina, my experiment says that g equals 10.7
OK, not bad but I think you only did the experiment once?
Yeah, what's wrong with that? Every time you do it you're going to get a different result.
Well you're absolutely right. I've done this with a whole class and even though
they're dropping the ball from the same height using the same apparatus
they get quite a spread of data. One way around this is to use this device which is
called a G ball and it automatically measures time taken to drop. It's got a
little button here and when you release it starts the timer and it stops when it hits
the floor. So we can use this to measure g by holding it up against something fixed like
this which holds in the button and then it starts the timer when we release it
OK, 0.56 seconds which if my maths is right gives us a g value of 9.6m/s²
That's quite impressive but both these devices measure time to the
same degree of precision, they're essentially the same stop clock.
That's right,
to a hundredth of a second. But the great thing about this is that we can do it
lots of times very quickly and we can narrow that spread of data.
And that's what makes this method more precise. So I guess students might suggest that you
use this to take a whole bunch of readings from the same height and take
an average and use that average to calculate g.
Yes, and they probably would. But it's always much better to take lots of data and then analyze that data,
eliminate any anomalies, and then take an average. But in all of this we're assuming
that g is constant, we've used the suvat equations, the equations of
uniform motion which means constant acceleration. So to check if that's valid
we should really drop the ball from lots of different heights and then plot
a graph to see if g is constant. So if we plot a graph of s
against t²
If g is constant then we should get a straight line with a gradient of ½g
OK why don't we try that
ok that's 0.56
…and it didn't work that time because I didn't turn it on.
…and point 55
point five four
Point five five, very consistent.
Is that straight?
I don't know what I'm talking about.
Point five two.
It'd be a good one for students working in pairs on this.
Point 53 again.
I've just realised I've done that awful boy thing of being the one who's doing the stuff.
You're absolutely right, come on.
Right, you can write them down
It's one meter this time, right at the join.
0.48.
OK, so this one's clearly anomalous.
OK, shall we plot?
1.5 metres is point 31.
1.4 metres is point 30.
OK, so there's…
quite a spread on there. But we did it in a great hurry.
OK, that's not the best graph I've seen, and it doesn't look like the straight line we were hoping for.
But you can see the spread in the data.
Yes, and you could do it lots of times very quickly and get a lot more data.
One of the advantages of this method is you can see the quality of your data.
Unfortunately, the quality of ours isn't great.
No, but what I love about doing this experiment with my
students is that it's really quick and easy to do and it actually makes an
affordable way of doing this as a whole class practical since all A-level students
have to do this practical for themselves now.
Not our finest moment.
I've come all the way up to Newcastle to use a legendary piece of apparatus:
The data logger.
This is a light gate and when I drop a ball through it, it starts a timer.
the other light gate stops it, and I get a recording of the time taken to fall
this distance to the nearest ten thousandth of a second.
That's a whole significant figure or two more than a standard stop clock.
Like the g ball, it removes the uncertainties that arise from trying to start and stop a timer by hand.
This method is recommended by at least one of the exam boards,
but I think there are a couple of problems with it.
The first is the most obvious:
Few schools are likely to have enough sets of this stuff to allow students to do it as a whole class practical.
I think the second problem is more serious.
In this arrangement the ball is already falling by the time it gets to the first light gate.
That means are starting velocity is not zero, so in order to plot a straight
line graph we need to do a different rearrangement of our equation s = ut + ½at²
We end up having to plot 2s over t against t
to give us a graph which has a y intercept of 2u
and a gradiant of g.
Now, this sort of equation wrangling and data processing is
absolutely something that A level students ought to be able to do, but I think
introducing it with this practical, early on in the course, is an unnecessary
distraction from the things we really want them to be thinking about.
I think you can do this as a demonstration after students have done the practical using
another method, and I've got one more to show you
Hi, Ronan. I've just been using the data loggers and you know as a physics
teacher it's always good to have a reason to dust off kit that might otherwise not be used,
but I have to say I really don't like the
complications it introduces for the data analysis for this practical.
You've got quite a nice way around that.
Sure. I'm going to be using this millisecond timer to time
the fall of this steel ball from an electromagnet here
down to a switch at the base which is going to stop the clock.
Let's take you through it.
First of all, open the switch at the base…
…and then if you press the green button that will switch on the electromagnet. Hold that.
…and that will hold the ball up, and if you just tap the red button that will release the ball
and start the timer.
So, 0.333 of a second
If my calculations are right, that should give me g = 9.72.
That's very impressive, and I really love that this gives us a higher degree of precision than the g ball
and eliminates the problem of the non-zero starting velocity,
but if I'm not mistaken you can buy a kit like this commercially?
Yeah, this is the standard equipment that you can see in many physics textbooks,
standard circuit diagrams, and I tried various of the commercially
available kits, and apart from the fact that they're pretty expensive, all the ones I've tried
have got problems with releasing the ball cleanly
You've managed to overcome that?
So, with the kit I've designed the ball is only held up with a minimum force, so as soon as
you stop the electromagnet it begins to fall straight away.
I've done this as a demonstration using a C-core and…
Sure, we've all done this in our teaching, we can put together a
piece of kit and have a scaler timer with a C-core: it's pretty fiddly to set up and I
don't know about you but I have found it hasn't been terribly reliable results.
So this equipment has been designed so that not only can the students see the
circuit very straightforwardly, but it's very easy to set up,
releases the ball reliably and the students are able to get data from it
independently. So you could have a whole class set of this equipment and that
would then allow you to do the core practical.
Whatever approach you use with your students, they'll be able to compare their value with a known value for g,
and that's not a luxury scientists and engineers usually have.
Sure, in this practical we know the answer we're supposed to get. But that doesn't mean it
can't be interesting or useful for students. Scientists and engineers are
constantly pushing their techniques and their instruments to the limit to
extract reliable data, and those who manage to do that can publish original work.
And those scientists who publish unreliable data will be proved wrong by other scientists.
That's how science works, and that's what this practical is really about.