Lab 4 - Physics I
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Feb 20, 2024
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PHY201-B Physics for Engineers I with Lab
Lab 4: Atwood Machine
Prepared for: Dr. Choi
Timothy Allec
Bryan Luna
College of Engineering
California Baptist University
2-15-23
Purpose: The purpose of this lab is to be introduced to the concept of Newton’s 2nd law of motion involving force, mass, and acceleration. The goal of this lab is to become familiar with the three using a pulley that measures the acceleration.
Results: The lab required one to use an atwood machine where one would apply weights on both sides and have an unbalanced net force which leads to the force of gravity to accelerate the pulley. There were 3 total parts to the lab, one simply being the setup for the atwood machine and the second being measurements for acceleration using 7 different measurement runs. The last part involved an analysis of all the data and measurements made during the experiment. The results for all these parts are shown below in the attached pages.
DATA IS ATTACHED pages 2-5
Question 1: Using Newton’s 2nd law, the acceleration formula for the Atwood Machine when m2 > m1 is (m2+m1)a = (m2-m1)g
which can be simplified as:
a = (m2-m1)g
¿
(
m
2
+
m
1
)
Using this formula the theoretical accelerations (
At
) for each measurement run is shown:
Run#1: (5*9.8)/115 = 0.426 m/s^2
Run#2: (5*9.8)135 = 0.363 m/s^2
Run#3: (5*9.8)155 = 0.316 m/s^2
Run#4: (5*9.8)175 = 0.280 m/s^2
Run#5: (5*9.8)215 = 0.228 m/s^2
Run#6: (5*9.8)255 = 0.192 m/s^2
Run#7: (5*9.8)315 = 0.156 m/s^2
Question 2: To find the measured (graphical) acceleration (
Ay
)for each run from the
1/2At^2 + Bt + C equations displayed within the capstone program, one will multiply the A value by 2.
The calculated values for each run are shown below:
Run#1: 0.364 m/s^2
Run#2: 0.302 m/s^2
Run#3: 0.260 m/s^2
Run#4: 0.208 m/s^2
Run#5: 0.186 m/s^2
Run#6: 0.147 m/s^2
Run#7: 0.121 m/s^2
Note: measured (graphical) acceleration (Ay) is less than the theoretical acceleration (At).
Question 3:
As displayed in the mass vs. acceleration graph, the linear curve shows that the acceleration decreased as the mass of the system increased. This is because the offsetting weight during each test run was 5g, so everytime the total mass increased the acceleration would decrease because the ratio of the 5g to the total mass would be greater every time.
Question 4:
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As displayed in the inverse mass to acceleration graph, the linear slope of the trendline shows the
decrease in acceleration. This data gives us a y=mx+b
formula which gives the rate of decrease in acceleration in correlation to the inverse total mass. The x in the equation is the inverse total mass, so one could use the slope equation y =-0.0398x + 0.3859
to find the expected acceleration
of any inverse total mass amount.
Question 5: Percent Errors for each run using theoretical value as standard value:
(Observed value - standard value)/standard value
Run#
1: 14.6%
2: 20.2%
3: 17.2%
4: 25.7%
5: 22.6%
6: 30.6%
7: 22.4%
Question 6: It is true that the measured acceleration is less than the theoretical acceleration.
Three systematic errors that can conclude to this: (human error does not count)
1.
Friction within the pulley that slows down the acceleration
2.
Short distance of the fall which decreases the measured fall time
3.
Rotational Inertia of the pulley which needs to be overcome to accelerate the pulley Question 7: The values from am and ay are very close to one another. The uncertainty is therefore incredibly small. Below is shown the uncertainty comparing am to ay in each of the runs#1-7. The graphical method (ay)is more precise because it is a verifiable calculated value, whereas the calculated mean value (am) which only gives the average value.
Conclusion:
A first lesson on the concept of Newton’s second law is introduced. The lab helped give a basic understanding of the relationship between force, mass, and acceleration when putting an object (in this case a weight on a pulley) under an unbalanced net force. The lab helped us become familiar with various terms such as theoretical and mean acceleration, graph acceleration uncertainty, etc. Much of the concepts of measuring were straightforward and easy to understand. The tools provided during the lab to form the various measurements of the acceleration were easily applied. Forming various measurements using the provided tools of the pulley and Capstone, as well as applying mathematical concepts to derive a data analysis of the experiment is an important representation of the physics involved when it comes to Newton’s second law. This lab should be recommended to anybody who