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L²Cc
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Homework Statement
Is this enough for an evaluation and conclusion? If not, what do you think I should add?
Homework Equations
Conclusion :
Our graphs further corroborate Newton’s Second law, which states that acceleration is directly proportional the net force, and inversely proportion to the sum of the masses. The slope of the best fit represents the net force that may have acted on the masses (refer to the graphs for slope).
When the sum of masses is constant, the best fit does not intersect with the origin. If x = zero, or (1/m1+m2) = o, the final solution is unreal since it is mathematically incorrect to divide one by zero. The numerator must be zero in order for this statement to be true.
When the difference of the masses is constant, the best fit intersects with the origin as evidenced in the first graph. As denoted in our hypothetical equation (refer to hypothesis), when m1-m2=0, acceleration, as result, equals to zero.
The y-intercepts are the acceleration values when the x values equal to zero, thus implying that there is no mass involved.
Evaluation:
The errors bars which stretch across the second graph indicate that we must have carried out some personal, as well as systematic, errors during the experiment. We may have made some arithmetic mistakes when determining the acceleration values and the uncertainties. For this experiment, we assume that the pulley is frictionless, and the string, “mass-less”. This assumption, being only applicable in an ideal world, hurts our results. When recording down our data, we only took into account the mass of the increments. The string is constantly rubbing against the pulley, yet we did not consider this when carrying out the calculations.
In situation two, row 1 of the second data table, we notice that our time measurements are inconsistent. This is mainly due to poor reflex. It may be possible that the equipment (i.e. Atwood Machine, stopwatch, pulleys) was poorly calibrated. Also, our method of measuring the distance between the table and the pulley may have caused the huge error bars. Maybe as we measured the length, the meter stick was not perpendicular to the table, causing our h value to be slightly off.
This lab would have been more reliable if we took into account the external forces (i.e. air resistance, friction, etc). Nevertheless, the graphical analysis enabled use to make the connection between Newton’s Second Law and the motion of the falling masses. If this experiment was more technology-driven, we would have ran into less systematic and personal errors. For example, we could have used a “smart pulley”, which comes with a photocell (a computer device which helps determine the velocity and acceleration of the system).