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Help With Net Force Formula and Newton's Second Law

  1. Mar 26, 2009 #1
    1. The problem statement, all variables and given/known data
    1. Compare the mass of the system to the slope. Does your data support Newton's Second Law?

    2. Using the words "directly" or "indirectly" briefly explain how force, mass, and acceleration are related to each other, making specific references to the parts of the Fletcher's apparatus used in this lab.

    The mass of the system is 2.7kg, while the slope of the best fit line (Fn on y-axis and a on x-axis) is 2.5kg.

    2. Relevant equations
    Fnet = ma


    3. The attempt at a solution
    For 1., I stated that my best fit line was close to the actual mass of the system. However, I don't understand how to explain the second part regarding Newton's Second Law.

    2. It was obvious to me that force was directly proportional to force and mass, both theoreticall and experimentally. However, I ran into trouble when I was comparing mass and acceleration. Although they should be inversely proportional from the formula (multiplying and same side of equation), both increase at the same time (although non-linear) from the experimental data.

    Thanks.
     
  2. jcsd
  3. Mar 26, 2009 #2

    Delphi51

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    Homework Helper

    Do you have a graph of F vs a? If so, you must decide whether or not a straight line fits the data points to within the accuracy of the experiment (error bars?) and whether the slope of the line is equal to the mass to within the accuracy of the experiment (would a line of slope m fit most of the error bars?) and the y-intercept is zero (to within ...). Only if all three conditions are met can you say that
    y = mx + b --> F = ma
     
  4. Mar 26, 2009 #3
    The line of best fit is a straight line. The equation of the line of best fit, calculated using linear regression, is y = 2.42x + 0.21. The slope from graphing the data is 2.5kg.
     
  5. Mar 27, 2009 #4

    Delphi51

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    Homework Helper

    Accuracy of the data? When you measured the force, what measuring device did you use? How accurate is it? How accurately did you record the force? If you have reasonably good equipment, the recording accuracy is a pretty good estimate. For example, if you recorded the force to the nearest tenth of a Newton then plus or minus 0.05 N is a reasonable estimate.

    How did you measure acceleration? A typical method is to record dots on tape every tenth of a second and measure the distance between dots to the nearest mm. Assuming that the timing is pretty accurate, the main inaccuracy comes from rounding the distance. For example, if each distance measurement is plus/minus .05 cm then the delta d is twice that - 0.1 cm. Doing v = d/t where t is 0.1 seconds gives you plus or minus 1 cm/s. Delta v is plus/minus 2 cm/s. and acceleration = delta v divided by 0.1 s is plus/minus 20 cm/s.

    If you put in vertical error bars for the force error and horizontal error bars for the acceleration error, then you will be able to say whether or not your straight line fits the data points to with their error bars representing the accuracy of measurement.

    Bear in mind that you can never "prove" any physics law or formula. The best you can say is that it fits the experimental data to within its measurement accuracy. Some say you try your best to disprove it and if you fail it stays on the books for a more accurate test later.
     
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