Physics 210 lab 5

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Dec 6, 2023

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Physics 210 Lab 4 Force and Motion Kim Bao Tram Huynh GRAPH and DATA:
ANALYSIS & QUESTION: [Q1]. The value of A, which is the slope of the proportional fit equation, represents the constant of proportionality between force F and acceleration a. in this context, A=0.372 means that for every unit increase in acceleration (m/s^2), the force increases by 0.372 N. the slope indicates how much force is exerted for a given acceleration, and it’s a measure of the relationship between force and acceleration. [Q2]. Newton’s second law of motion: F= m.a Where: F is the force applied to the object(N) m is the mass of the object (kg) a is the acceleration of the object (m/s^2) the expected value for the slope (A) based on Newton’s second law should be equal to the mass (m) of the object. In this experiment, we have various masses on the mass hanger. So, for each mass, the expected value of A should match the value of m for the particular mass. To check if the results are consistent with the Newton’s laws, we will calculate the percent error for each data point as follow: Percent Error = A −( mh + m cart ) ( mh + mcart ) × 100
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1. 50g Percent Error = 0.372 −( 0.05 + 0.2514 ) ( 0.05 + 0.2514 ) × 100 = 23.424% 2. 100g Percent Error = 0.372 −( 0.1 + 0.2514 ) ( 0.1 + 0.2514 ) × 100 = 5.862% 3. 150g Percent Error = 0.372 −( 0.15 + 0.2514 ) ( 0.15 + 0.2514 ) × 100 = 7.324% 4. 200g Percent Error = 0.372 −( 0.2 + 0.2514 ) ( 0.2 + .2514 ) × 100 = 17.58% 5. 250g Percent Error = 0.372 −( 0.25 + 0.2514 ) ( 0.25 + 0.2514 ) × 100 = 25.808% these percent errors are relatively small, especially for the middle values of mas(100g,150g,200) indicating that the experimental results are in good agreement with the theoretical expectations based on Newton’s second law. Smaller percent errors suggest that measurements are closer to the expected values, demonstrating consistency with the Newton’s law of motion. [Q3]. 50g 100g 150g 200g 250g Experimental Force 0.37N 0.62N 1.15N 1.19N 1.21N Predicted Force 0.490N 0.981N 1.472N 1.962N 2.452N Error 24.490% 36.800% 21.875% 39.368% 50.653 a theoretical = g ( m h m cart + m h )
Mass 50g 100g 150g 200g 250g Theoretical acceleration 1.627 2.792 3.666 4.347 4.891 Theoretical force versus theoretical acceleration graph: CONCLUSION:
in summary, the larger percent errors in both [Q2] and [Q3] suggest that there may be discrepancies between the theoretical model and experimental data. This raises the possibility that friction or other unaccounted factors could be affecting the results. Therefore, it may not be justifiable to completely ignore friction in the experimental setup, as it appears to have an impact on the outcomes. However, in Question 3 theoretical force versus theoretical acceleration graph shows a good fit with the linear trendline on the force axis, it does suggest that our theoretical model is more consistent with our theoretical predictions. This could be indicated that our theoretical model is reasonably accurate in explaining the relationship between force and acceleration
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