Galileo's Experiment with an Inclined Plane

[Lukeblackhill]

Morning mates,

I've peformed Galileo's experiment with inclined planes, using a ramp of 88cm (divided in 4 parts of 22cm), inclined by a height on the right-edge of 4cm. I've measured the following,

1/4 of the ramp (22cm): 1.75s (error of 0.1s)
1/2 of the ramp (44cm): 2.70s (error of 0.1s)
3/4 of the ramp (66cm): 3.25s (error of 01.s)
4/4 of the ramp (88c): 3.80s (error of 01.s)

How can I interpret such results in order to arrive to the conclusion that d(t) is proportional to t²?

Thanks!
Cheers,

 

[sophiecentaur]

To measure ‘dt’ you need a step that’s something like a real d or delta. But you could try to fit a curve to your data (best quadratic fit or by eye)

 

[anorlunda]

Do you know how to fit a curve as @sophiecentaur suggested?

 

[sophiecentaur]

Do you know how to fit a curve as @sophiecentaur suggested?

You don't need to do a quadratic fit if those data points fit well to a hand drawn curve and you can draw a tangent at the various points to find the slope (which is the speed, Δd/Δt) Not as 'good' but it would give a set of speeds which should increase in equal steps for equal time increases. (Quick and dirty method with very little brain ache)

 

[nasu]

You can plot d versus t² and see how well the points fit a straight line.
Compare the slope of the line with a/2 where a is the acceleration for the motion on the incline.