If a is the acceleration parallel to the slope, and s is the distance travelled along the slope, then you don't need to account for the elevation in your calculations (because the elevation influences the data itself).
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measuring acceleration from slope
I am doing an experiment to find the acceleration from the slope of a graph. The experiment setup is like this, I have a cart which is run in an incline plane with an angle of 5 degrees. And the cart is rolled from 5 different distances. So what I had in mind is to use the equation
s = vot + 1/2at^2, the initial velocity here is 0, so the equation becomes, s = 0.5at^2. The distance is known here and I can measure the time. so therefore I can plot s/t and t here, the slope will be 0.5a, and from that I can find the acceleration. But I am not sure this is the right way as the system is on an incline plane and I might have to use Newton's second law to do this.. any ideas? or is this fine?
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Answers
if you plot s, the distance traveled down the slope against t, then the slope of the curve is velocity.
If you then plot the velocities found against t, then the slope of that curve (or line) gives acceleration.
However - if you have a measurement for s and t and you are using the formula s = ut + (1/2)at^2, then assuming uniform acceleration a = (2s)/t^2
In that case you don't really need to plot a graph - plotting a graph would come in handy if you had different measurements of distance traveled at different times.
You'd use Newtons laws if you were trying to calculate a theoretical value for a, which you might want to think about after your experiment.
Your equations are correct and you are already using Newtons Laws. It is, however, unclear as to what you really want to do. You can calculate the expected acceleration without doing an experiment. I am not sure why you want to plot s/t vs t. I am not sure why you want to use five distances since
a = 2s/t^2
One distance is all you need. You can get an average if you use five distances. Friction will affect your results. Your experiment can be used to measure the effect of friction on your cart. You can even distinguish between static and dynamic friction if you wish.
I am not sure why you want to plot s/t vs t. I am not sure why you want to use five distances since
a = 2s/t^2
One distance is all you need. You can get an average if you use five distances. Friction will affect your results. Your experiment can be used to measure the effect of friction on your cart. You can even distinguish between static and dynamic friction if you wish.
" is this fine?" -- it is just fine (neglecting friction) (s/t is just the average velocity)
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"because to get better accuracy, imagine plotting 5 s/t with t compared with plotting 1 s/t and t" --- properly done, it will not give you more accuracy (or less either).
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In any case friction will rear its ugly head. The smaller the angle the more influence friction will have. Nevertheless it may be neglected depending on your final purpose.
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by: WaterStreetPosted on 2008-11-30 at 17:10:58ID: 23065648
It's been a long time for me but I think the calculations involving the acceleration of the incline would simply need to be multiplied by the sine of the angle of the incline.