Gravity exerts a force on every object which is
proportional to its mass. The amount by which it is proportional is the value g or the acceleration
due to gravity. On the surface of the earth g is 9.8 meters per second per second
and this is the rate that an object will accelerate when it's in freefall.
Now the value of g will vary a little bit depending on where you are, mostly to do with altitude and the value of
9.8 is an average and it has actually been measured quite precisely,
but today we're going to throw precision out the window and attempt to measure g using human hair.
First let's talk about pendulums. A simple pendulum
consists of a metal sphere on a long thin string. One period of
oscillation will be the time it takes for this mass to go from, say here,
through one complete cycle and back to where it started. We can work out the period T from this formula here
2 pi times the square root of L, which is the length of our pendulum, over g, which is our acceleration due to gravity.
Note that the period doesn't depend at all upon the mass and just know that this formula was derived using an
approximation that sin(theta) is equal to theta
So it's only valid for small angles say less than about 15 degrees.
We can rearrange this formula for g if we know our length and our period.
Experimentally if you have a longer length
then you're going to have a longer period which may reduce the significance of errors when you're trying to time the period,
so what better to use as a length of the pendulum than some of my hair?
I am going to attach a mass to the end to provide some tension force that will allow it to oscillate.
I don't personally drink but I found this nice bottle opener, which I think will be appropriate. Now the big assumption here
is that my hair doesn't weigh very much
compared to the mass i'm going to put on the end.
I'm assuming that the center of mass of the pendulum is still going to be in this metal spot on the end
and I'm also assuming that my hair stays a constant length throughout which may not be true in practice
but I'm hoping we'll be an OK approximation here. To get my hair as close to massless as possible
I haven't included all of it for the pendulum just
a small amount and I'm going to measure the length of the pendulum as the distance from the top of my hair tie
down to where I think the center of mass of this metal part is.
I got some help measuring the length and found it to be 90 centimeters with an uncertainty of two centimeters.
Then I released the hair at an angle and timed five oscillations.
This makes it easier to measure one period by dividing the time by five afterwards.
I repeated this part of the experiment twice more and got an average period of 1.9 seconds with an uncertainty of 5
milliseconds.
Putting my values into the formula for g
I get g equal to 9.8 plus or minus 0.7 meters per second squared and
that's actually pretty good especially
since this is far from a high-tech science lab. Some of the possible sources of error include measuring the distance to the center of mass,
assuming that my hair is massless and also assuming that it travels out a perfect 2d shape when in reality
I think it travels out a bit of an ellipse.
There's also some
uncertainty in the measurement of the period of oscillation. If you wanted to make this experiment a bit more accurate you could try using
various different values of L for the length of the pendulum and then finding a line of best fit to find our value of g
but this was pretty alright for some quick backyard physics. Now, this video is sponsored by brilliant.org
So if you would like to have some fun with science, you can go to brilliant.org/tibees and sign up for free.
They have a course on gravitational physics
so that might be a great place to learn a little bit more about the subject discussed here. The
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so I'd recommend brilliant as a fun way to
learn more about some of the concepts that I've discussed here.
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