# Acceleration Due to Gravity

mattmate
I need to prove the folowing statement. Can someone please help me as i am having trouble working out the formula needed to determine a value for acceleration. (This has to be proved as simply as possible, using things easily measured, ie Mass, time etc...

Thanx
matt

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mattmate
Extra Info

The question i need to answer is:
"Gather infomation using a wide variety of sources and carry out a simple first hand investigation to determine a value for acceleration due to gravity. Present this by:
1)Including labeled diagram
2)Showing a sample of simple calculations used
3)Identifying Independant, Dependant and constant variables"

The experiment i chose to perform is to drop a small ball froma height of 2meters. I time this, and then i was hoping to be able to answer the above question via this experiment

Thanx
Matt

Integral
Staff Emeritus
Gold Member
So my initial guess at your question was not correct. What information do you have? Such as what equations have you been given? Please show us a bit of what you have done. It is hard to guess what you know, you must share more information.

Also we do not do your homework for you, show us where you are and what you have done.

mattmate

Sorry, im not actully asking you to do it for me!

Basically, i have dropped a small ball from a height of 2 meters, 20 times. Each Time, i recorded the result in a table that listed the distance of 2 meters, then the time i got.

I chose to perform it 20 times, to find the average due to the human error of me timing.

I also have the mass of the ball.

We have been given no formulas or anything of such.

I was hoping someone would know a simple relationship to get a value of acceleration due to gravity to get a result similar to the accepted value of 9.8m/s2

Thanxs again

HallsofIvy
Homework Helper
The way you have done the experiment,I don't believe you can calculate the acceleration. Certainly, you can calculate average speed, simply by dividing the distance by the time but you can't then calculate acceleration (how fast the speed is changing) without further information. I can think of two things you might try.

1) Repeat the experiment using a different distance. Now that you know the average speed for two different distances (and the associated times) you can, at least, approximate the acceleration.

2) Use the fact (if you are allowed to- you can't get this from your experiment) that the acceleration due to gravity is constant and so the average speed is exactly half the speed at the end of the drop.
Double the average speed you got, and divide by the time. That will give the acceleration.

mattmate
Thanx mate

Thanx Mate, ill try that,

Thanx again
matt

If you assume that the acceleration is constant, then you can obtain,

$$h = \frac{1}{2} gt^2$$
$$g = 2h/t^2$$

But just by using a single height, you can't prove that the acceleration is really constant. As HallsofIvy said, you can obtain more information by varying the height.

If you know how to use a spreadsheet like Excel, the best way to do this is by a power fit to the data: plot all your h vs. t values, and then do a power fit. It assumes your data is of the form

$$h = Ct^\gamma$$

and will tell you what C and &gamma; are (if you tell it to display the equation).
Equating with the above expression, &gamma;=2 and C = g/2, so you can get the acceleration of gravity g from whatever it reports C to be.