Coursework - Gravitational Field Strength

[XiaoII]

Homework Statement

Okay so, we weren't given much of a question other than "Prove the Earth's GFS is 9.81 N/KG"
So what I'm asking is, with the data that I have collected, is how I go about doing this?
As it stand we set up an experiment with the ticker tape machine, rolled the little buggy thing (technical I know =/) down the 2.43 Meter board at an initial height of 13.4 Cm.
The ticker timer we had ran at 50 Hz, so that equals to 50 dots per second if I was informed right. Meaning that to work out each 0.1 of a second, I would have to measure the space between every 5 dots. So this is what I did and as shown in the attached results, the first displacement column is from the last section of 5 dots and the column after is the total displacement from the start to the end of the board. (I have NO idea as to why the total displacement does not match the length of the board, there's one for the write up). I believe the cart we rolled down the slope was 300g.

Homework Equations

Right so here's where I manage to get lost, I was given two equations but I don't know WHAT they mean, or HOW to get the data I need for them. So I Guess this is where I need the guidance really.

1)mgSinθ-f=ma
2)gSinθ-f/m=a

I then found out a few more from other class members but we can't agree on which to use where or indeed why.
1)Driving force - friction = mass x acceleration
2)Driving force - friction = mass x gravity sinθ - friction
3)Ma - Mg Sinθ - friction

The Attempt at a Solution

As yet, I don't know where to begin, but I have an idea of working out the angle at which the slope was at so I can replace the Sinθ with an actual value so add some form of logic to the equations. Besides this I'm not entirely sure what I'm supposed to be doing. I apologise for any information missing or anything which is unclear, if you find something that is missing otherwise confusing please post and I'll happily add the information up there. I have another 13 sets of results to complete after this one, so if I could gain some idea as to HOW to analyse them properly and how to work them out, I'd be grateful.

Thanks in advance.

 

[mikelepore]

I was given two equations but I don't know WHAT they mean

1)mgSinθ-f=ma
2)gSinθ-f/m=a

Shouldn't those "minus" signs that you typed be "equal" signs? I would have expected to see:
mg sin theta = f = ma
g sin theta = f/m = a

This is the way I have always done it:

I would neglect friction.

An incline is at an angle theta with respect to the horizontal. An object on the incline has weight mg which is a vector vertically downward. The vector can be resolved into a set of two perpendicular vectors, with your choice of axes. So draw the triangle and see that the weight vector can be resolved into (mg sin theta) parallel to the incline and (mg cos theta) perpendicular to the incline. The object is constrained to move only on the surface of the incline, so you only need the component parallel to the incline. There's your force, F = (mg sin theta). It is F=ma where a = g sin theta. Now you don't need the mass m of the object, because equations of kinematics will relate acceleration to time intervals and distances.

 

[XiaoII]

Ah ah! Thankyou!
Finally someone explained it where I can actually understand it, I can see where I have to go now... well to an extent.

This whole mg business still confuses me because the way I see it I still need a value for it, but not how exactly to get hold of that value. Hmm...I'll have a research round and post what I find.
Never Mind, Worked that bit out at least. xD

Oh, and I wrote those equations as I was given them, minus signs as they were. But it does make sense they should be equal, when you look into it.