Lab 5 - The Atwood Machine

The Atwood Machine Introduction: The acceleration of a system is directly proportional to the net applied force and inversely proportional to the system’s mass, as stated by Newton’s 2nd Law of Motion. For an Atwood’s machine, the net force is the difference between the two masses times the acceleration of gravity, or F net= ( m 1−m2) g acting on the system of both masses with acceleration due to gravity g. Both masses are accelerated with weighted hooks on opposite sides of the pulley The purpose of this laboratory activity is to study the relationship between force, mass, and acceleration using an Atwood's Machine apparatus. Procedure: The slope of linear velocity vs time graph is acceleration a exp= masses on Atwood’s machine. ∆ velocity of two hanging ∆ time Experimental acceleration a exp= a theory = ∆ velocity is compared with theoretical acceleration ∆ time F net g ( M 2−M 1) = . m1 +m 2 M system DATA Table #1 Constant Total Mass M1 (kg) M2 (kg) (m/s2) 0.105 0.110 0.115 0.120 0.125 0.130 0.135 0.095 0.090 0.085 0.080 0.075 0.070 0.065 0.447 0.900 1.36 1.84 2.33 2.78 3.25 aexp Fnet N 0.098 0.196 0.294 0.392 0.490 0.588 0.686 Experimental acceleration a exp= a theory = M 1 + M2 0.200 0.200 0.200 0.200 0.200 0.200 0.200 atheory % diff (m/s2) Accel 9.18 8.51 7.77 6.32 5.02 5.59 5.39 6.83 0.490 0.980 1.47 1.96 2.45 2.94 3.43 ave = ∆ velocity is compared with theoretical acceleration ∆ time F net g ( M 2−M 1) = . m1 +m 2 M system Data Table #2 Constant Net Force M1 (kg) M2 (kg) 0.105 0.110 0.115 0.120 0.125 0.130 0.135 0.095 0.100 0.105 0.110 0.115 0.120 0.125 aexp (m/s2) 0.447 0.423 0.415 0.399 0.383 0.362 0.345 Fnet N 0.098 0.098 0.098 0.098 0.098 0.098 0.098 M 1 + M2 0.200 0.210 0.220 0.230 0.240 0.250 0.260 atheory % diff (m/s2) 0.490 0.467 0.445 0.426 0.408 0.392 0.377 ave = Accel 9.18 9.82 7.08 6.57 6.40 7.96 8.84 7.98 QUESTIONS 1. Compare the experimental acceleration with the theoretical acceleration by determining the percentage difference. What are some reasons that would account for the percentage differences? Personal Error Human error, i.e. measurement of time Systematic Error Physical factors of the Atwood machine, such as drag from air resistance, elasticity of string, addition of mass from the string are some examples of systematic error. Random Error Calibration of the Atwood machine cannot be 100% accurate in the real world, and this can contribute to random error within the experimental results. 2. For the Constant Total Mass data, plot (in EXCEL) a graph of F net vs. aexp.  Add a Trend line - the best-fit line on your plot - and display the equation. Net force vs. Experimental Acceleration 0.800 0.700 0.600 f(x) = 0.208821237553059 x + 0.00696346955752447 Fnet N 0.500 Fnet N Linear (Fnet N) 0.400 0.300 0.200 0.100 0.000 0.000 0.500 1.000 1.500 2.000 2.500 3.000 3.500 Experimental Acceleration (m/s2) What does the slope of the best-fit line represent? (Account for any excess in the value.) The slope of the line represents the total mass. The slope value being larger than the total mass is because of factors such as the mass and friction of the string, which is not taken into account for the experiment. 3. How does the Force vs. Acceleration plot relate to Newton's Second Law? Newton’s Second Law is acceleration a = Fnet / Msystem. The plot uses both F net and M system as its x and y axis. Conclusion: The acceleration of a system is directly proportional to the net applied force and inversely proportional to the system’s mass, as stated by Newton’s 2nd Law of Motion. For an Atwood’s machine, the net force is the difference between the two masses times the acceleration of gravity, or F net= ( m 1−m2) g acting on the system of both masses with acceleration due to gravity g. Both masses are accelerated with weighted hooks on opposite sides of the pulley The relationship between force, mass, and acceleration using an Atwood's Machine apparatus has been represented in this experiment. The percent difference between the acceleration for the constant total mass was 6.83%, while for the constant net force it was 7.98%. The percent difference is a combination of factors from the following error analysis. Error analysis: - Personal error for measurements of the acceleration, mass and experimental technique - Systematic error for calculations involving these measurements assuming that there is no mass in the string, no friction from the string and the pulley, and no air resistance. - Random error for calculation of the calibration of the Atwood’s machine.