Experiment 04 Atwood Machine

Experiment 04: Atwood Machine Experiment performed on: September 28, 2020  Report submitted: October 5, 2020 Introduction In this experiment we tested the works of an atwood machine and the relationship between mass and tension/acceleration of masses. An atwood machine is a massless and frictionless pulley that has two masses on it (m1>m2). The relationships depicted by the use of the atwood machine are demonstrated by the equation: ay=(m1-m2)/(m1+m2)g, or T=(2m1m2)/(m1+m2)g. This equation demonstrates that the acceleration and tension of the string is dependent on the masses and gravity. Acceleration is also the same for each mass just portrayed in opposite directions. Theory The atwood machine is a frictionless and massless pulley. It can be described by the following equations: ay=(m1-m2)/(m1+m2)g, or T=(2m1m2)/(m1+m2)g. The first equation is derived from the fact that acceleration is equal to the net force (gravity) and the total mass. This equation is based on the fact that m1>m2, and the total mass is represented by m1-m2. The net force is determined by (m1+m2)g. The total acceleration is also related to the acceleration of gravity, gravity will be a downward force on both masses, but will pull m2 downward less, due to its upward acceleration. The second equation describes the tension of the string and is operating under the same assumption that m1>m2 and gravity is acting upon both forces. The tension of the string will be dependent on the masses and the force of gravity acting upon it. Procedure For this experiment, we created a pulley, and ran it through the photogate software. We tested 5 different mass combinations 3 times. The mass combinations were 30g vs 50g, 40g vs 60g, 50g vs 70g, 60g vs 80g, and 80g vs 100g. We positioned the pulley so that the lighter mass would be lower in height than the heavier mass. We ran the experiment through the photogate software, which created a velocity vs. time graph where we could extrapolate the acceleration of the mass for the trial. Discussion 1. Theoretical Relationship C. If the two masses were equal the acceleration would be 0, because the numerator in the equation would be equal to 0. The tension would be equal to mg, because this is simplified from 2m^2/2m x g. If mass 1 was much greater than Mass 2 than, we could neglect mass 2 in the total mass. Acceleration would be equal to acceleration of gravity, which is 9.81 m/s^2, due to the equation m/m x g derived from the acceleration equation neglecting mass 2. Tension would be equal to 2m2. This is derived from the tension equation T=(2m1m2)/(m1)g. If tension was zero m2 would have to be very little and close to zero. This comes from the same equation from the above statement, T=(2m1m2)/(m1)g. 2. Systemic Error There could have been many systemic errors in this experiment that could affect the measurements collected. For example, if mass or friction was non-negligible than, g would be less. This is due to the fact that friction is an opposable force to gravity.Another situation, might be jerking on the string when we let the pulley go. Although we might think this causes error, it would not, because we only take the linear fit of the straight-line part of the velocity vs time graph of the pulley. In other words, if there was a jerk, this would not be a part of the straight-line part of the velocity vs time graph. The pulley also has sources of error, it may have unequal weights on each part of the wheel, or an unsmooth surface which causes a wobbly wheel. If this occurs this can decrease our acceleration, because it would decrease the amount of spins of the wheel. Also the string's mass could affect our measurement of tension. If the string had a mass this would decrease the tension, which would increase our g. Another possible source of error could be the string diameter. If the diameter of the string was greater than the distance per spoke for the pulley would be altered. This would increase the distance per spoke. If the photogate was not adjusted, this would alter all our measurements. Results Through the data collected, we can extrapolate g from the graph. My value of acceleration due to gravity was measured to be 8.64993 m/s^2. With uncertainties (+/- 0.365835) in mind, g was not in agreeances with 9.81 m/s^2, acceleration of gravity. Error Analysis There were multiple sources of error in this lab. For one, friction was not accounted for. The pulley may have experienced friction, due to the material and age of the pulley. This could have decreased our measurements of acceleration, which would ultimately lead to a lower value of g. There could have also been friction, in the form of air resistance. Air resistance would have acted as an opposable force against acceleration. In result, acceleration would be less and so would our measurement of g. There could have also been some error in the masses of the weights. They may have not been exactly 30 kg, 40kg, etc. This would affect our Average acceleration vs (M1-M2)/(M1+M2) graph. Our measurement for g would then be affected, because of the altered slope. Conclusion Through this experiment we were able to test the equations of acceleration and tension, and its validity with measuring g. Our measurement of g, 8.64993 +/- 0.365835 m/s^2, was not in agreement with average acceleration of gravity, 9.81 m/s^2. In order to perform this experiment better with less sources of error. We could weigh the weights before using them in the pulley, instead of assuming their weights. Also we could use a more modern pulley that would be less susceptible to friction.