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Can someone verify if my lab results make sense?

  1. Sep 27, 2009 #1
    1. The problem statement, all variables and given/known data
    A cart is released from rest with varrying masses down an inclined track. Determine whether or not mass affects acceleration in this case.

    This is what I calculated through all the data:
    θ = approx 5 degrees
    M1: Vavg = 0.7816 --> Aavg = 0.977
    M2: Vavg = 0.8385 --> Aavg = 0.719
    M3: Vavg = 0.7809 --> Aavg = 0.710


    2. Relevant equations
    a = gsin(θ)
    a(y) = g
    V = at


    3. The attempt at a solution
    I would think that the accelerations should ideally be the same, but I suppose with increased mass comes increased friction and potentially air resistance which could explain the decrease in acceleration through the increase in mass. But we haven't learned how to mathematically use friction yet... My friend who is a physics major says my data is wrong and my sister's boyfriend who is an engineer says it's fine. So is my data faulty, a realistic expectation of real-world physics, a mixture of both, or is my understanding of the concept all wrong?
     
  2. jcsd
  3. Sep 28, 2009 #2

    Andrew Mason

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    Science Advisor
    Homework Helper

    If your data is correct then Galileo and Newton were wrong. Redo the experiment and calculations. Something does not fit.

    AM
     
  4. Sep 28, 2009 #3
    You're attributing the inconsistencies to very minor, and even unrelated factors.

    Air drag is proportional to surface area increase. The one you got by adding on more mass is irrelevant. Not only that, but the force of air drag, if we can agree that it does not vary between the two situations, now has to declaration a larger mass. Its effect would have LESSENED rather than increased with the increase in mass.

    You'll probably learn this in a couple of lessons, but friction, regardless of mass, provides the same declaration for a mass sliding down an inclined plane. Same goes for rolling resistance, which is what I suspect you're dealing with here.

    Ideally the accelerations should be the same, but your system is far from ideal. Have you considered factors such as the system shaking, or the angle being changed due to the additional weight? At such small angles, you could have anywhere from half the acceleration, to twice the acceleration without even noticing you've made the shift!

    A very small change in [tex]\theta[/tex] is very considerable when you consider that a change of 2 degrees, something you cannot even perceive with your eye, is a 40% difference in [tex]\theta[/tex]

    And just to explain something really quickly, yes, the acceleration depends on the sine of [tex]\theta[/tex] rather than on [tex]\theta[/tex] directly, but at small angles [tex]\sin{\theta}\approx \theta[/tex] so the drastic difference affects the sine almost exactly as much as it does the angle.

    I crunched your numbers, and assumed that for each of the average accelerations:

    [tex]A_{avg}=g\sin{\theta}[/tex]
    Isolating for [tex]\theta[/tex] I got that the angles were 5.7°, 4.2° and 4.1° degrees, respectively. As you can see, a very very small difference in the angle can have a drastic effect on the accelerations.
     
    Last edited: Sep 28, 2009
  5. Sep 28, 2009 #4
    Thank you! This makes perfect sense, I do remember someone bumping into the table at one point in the experiment. I didn't even think to readjust the track.
     
  6. Sep 28, 2009 #5
    It might not even be the drastic change caused by the bump that made the difference.
    Is your ramp spring-based? It could be that the additional weight just compressed it a tiny bit more and got you the smaller angle.

    Two good ways to compensate for this flaw in the design of your experiment would be to use a longer ramp (You'll find it easier to measure the angle more accurately before each run) or to use a larger angle, where the effect of a small difference in [tex]\theta[/tex] won't be so noticeable.
     
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