Phys1_02-Forces_aa8935a9-50b6-4b06-bb51-e89731381b92

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Georgia Institute Of Technology *

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2111

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Physics

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Apr 3, 2024

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Slide 1 Force and Acceleration Objectives Explore the relationship between force and acceleration. Use Newton's Second Law to experimentally find the mass of the device. Physics Overview Isaac Newton is quite well known for his work in both calculus and physics. He is perhaps most well known for his three laws of motion that describe patterns seen in how objects move. These three laws are as follows: 1. An object in motion will stay in motion and an object at rest will stay at rest if no external forces are exerted on the object. 2. If a force is exerted on an object, then that object will experience an acceleration throughout the duration of that force, or 3. For a system of interacting objects, the force that object 1 exerts on object 2 is equal and opposite to that of object 2 on object 1. This lab deals specifically with Newton's Second Law. According to Newton's Second Law, there should only be an acceleration when there is an applied force. Under ideal circumstances (no friction), when the force no longer acts on the object, it does not continue to accelerate. Instead it would continue to move at a constant velocity according to Newton's First law. By using the Force probe and Accelerometer, it is possible to plot Force vs. Acceleration and use the slope to find the mass in accordance with Newton's Second Law. Due to the fact that the mass of the device is unknown, this slope can be compared to the actual value. Therefore, by analyzing the motion of the device when under the influence of a force, it is possible to demonstrate the validity of Newton’s Second Law. If you wish to brush up on force concepts, you can view any of these problem solving videos: BlockTheRamp
force12
Slide 2 Let's try it out!
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Slide 3 Force (200 Hz) Remote 1 Time (s) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Fᵧ (N) -4 -3 -2 -1 0 1 2 3 4 5 ∆t: 3.96337 s μ: 0.126 N — σ: 0.62 N a: 0.501 Ns s: -0.00 N/s (r²: 0.00) Rezero sensor Accelerometer (200 Hz) Remote 1 Ax Ay Az Time (s) 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 a (m/s²) -5 0 5 10 15 20 25 30 ∆t: 3.96431 s μ: 0.024 m/s² — σ: 0.30 m/s² a: 0.094 m/s s: -0.00 m/s³ (r²: 0.00) μ: -0.124 m/s² — σ: 3.3 m/s² a: -0.493 m/s s: -0.04 m/s³ (r²: 0.00) μ: 9.807 m/s² — σ: 0.15 m/s² a: 38.878 m/s s: 0.00 m/s³ (r²: 0.00) Force and Acceleration: Time and Magnitude Qualitative Comparison Attach the plate to the force sensor. Press record and give the device a few shoves such as in the video below. The wheels should be facing up. Do your best to keep your pushes in the direction so the device does not start to spin. You can uncheck the and the boxes if you wish. We will only be looking at since the force was directed in the direction. 00 Pushes on device
You should see peaks on both the Force vs. Time and Acceleration vs. Time plots. These peaks correspond to when you pushed on the force plate. What do you notice about the positions of the peaks on the Force vs. Time plot in relation to the position of the peaks on the Acceleration vs. Time plots? Be sure to include a screenshot of your data in your lab report with the "zoom" selected to make all the data for both force and acceleration easy to read. Make a qualitative statement about whether forces and accelerations occur at the same or different times and whether they grow smaller or larger in a correlated manner. Base your discussion on YOUR graph.
Slide 4 Accelerometer (200 Hz) Remote 1 Ax Ay Az Time (s) 0 1 2 3 4 5 6 7 8 9 10 a (m/s²) -20 -15 -10 -5 0 5 10 15 20 ∆t: 2.22064 s μ: -0.023 m/s² — σ: 0.031 m/s² a: -0.051 m/s s: -0.01 m/s³ (r²: 0.09) μ: -9.791 m/s² — σ: 0.072 m/s² a: -21.741 m/s s: 0.04 m/s³ (r²: 0.11) μ: 0.138 m/s² — σ: 0.055 m/s² a: 0.306 m/s s: 0.04 m/s³ (r²: 0.17) Force (200 Hz) Remote 1 Time (s) 0 1 2 3 4 5 6 7 8 9 10 Fᵧ (N) -5 -4 -3 -2 -1 0 1 2 3 4 5 ∆t: 2.21774 s μ: -1.910 N — σ: 0.013 N a: -4.237 Ns s: 0.00 N/s (r²: 0.00) Rezero sensor Finding the "Known" Value of the Mass Watch the video below to find out how to find the mass of the device. Please note that the iOLab mass will be needed in many future labs and you should remember the procedure you've done here in order to repeat it for those labs. 01 Finding the Mass of the Device
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Here are some instructions in words: Take off the plate and attach the screw instead. Turn the device so that the y-axis is pointing downwards. Press record and let it sit there for 1 second. Then use the screw to lift the device. Hold it steady. Find the average force and acceleration (in the direction) once you have picked up the device. This will give you the force due to gravity and the acceleration due to gravity, respectively. Again, since the force of gravity is in the direction, you can uncheck the and the boxes. Using the gravitational force equation, you can find the mass. Be certain that you include a sceenshot of your own data in your lab report in the "Analysis Mode", while highlighting the region over which you wish to average the data. Be certain to extract meaningful numbers into a clear table and explain in detail how you use the measurements to calculate the mass of your iOLab.
Slide 5 Force (200 Hz) Remote 1 Time (s) 1 2 3 4 5 6 7 8 9 10 Fᵧ (N) 0 1 2 3 4 5 6 7 8 9 Rezero sensor Accelerometer (200 Hz) Remote 1 Ax Ay Az Time (s) 1 2 3 4 5 6 7 8 9 10 a (m/s²) -5 0 5 10 15 20 25 30 Quantitative Measurement of Force and Acceleration Part I 1. Attach the plate to the force probe. 2. Make sure your dongle is plugged into the computer and your device is turned on. 3. Turn on the Force and Accelerometer sensors. 4. With the wheels up, give the device 5 consecutive shoves of increasing strength and find the peak values of both the force and the acceleration for each shove (just by using the cursor). 5. Record these values in a chart such as the one below. 6. Use Excel to plot the Acceleration vs. Force (using the peak values you just found). 7. Add a linear trendline to this plot and display it. 8. Using the equation for a line and the slope of your plot, find the mass.
9. Compare this to the known value of the mass. Please note that we have ignored friction. However, looking at your acceleration vs. time plot, you should be able to compare the magnitude of the positive acceleration peaks to the short time of negative acceleration that follows them. Comment on the comparison of these values. Be certain that your lab report contains a plot of the data zoomed to show all five peaks, as well as a plot showing the data zoomed to show a single peak. Show a neat table of your data
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(UNITS) as well as the plot of Force vs. Acceleration and the slope of the trendline that fits the data. If you wish, you can force the trendline to run through the origin. Refer to the data in the prior section and conclude whether your data supports or refutes F=ma.
Slide 6 Force [Fᵧ] vs Accelerometer [Ay] (100 Hz) Swap axis Accelerometer (m/s²) -15 -14 -13 -12 -11 -10 -9 -8 -7 -6 -5 Force (N) -3.0 -2.8 -2.6 -2.4 -2.2 -2.0 -1.8 -1.6 -1.4 -1.2 2 4 6 8 10 12 14 16 18 20 Procedure Part II This part is described further in the video below. 1. Attach the screw to the force probe and the long spring to the screw. 2. Using the binder clip, secure the other end of the spring to a textbook and allow the device to hang from the spring. 3. Turn on the Force and Accelerometer sensors. 4. Give the device a small pull and allow it to oscillate vertically. 5. Make a parametric plot of acceleration vs. force and find the slope. (There is more information about how to do this in the video below.) 6. Compare the two values of the mass found in Parts I and II, both to each other and to the known value (found on the previous page). 02 Parametric Plot
Be certain that your lab report contains a copy of the parametric plot, a table of (at least two) data points taken from the plot, and a good description of how you calculated slope. Finally use your data from all these sections to determine whether the masses are in agreement.
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Slide 7 Error Analysis The error in the mass When you found the mass in slide 4 of this manual, you used the mean of the force of gravity and the acceleration due to gravity. However, these values also include uncertainties, and To find the mass you used, Rearranged, this is Therefore, to find the uncertainty in m , you will need to use the multiplication/division rule from the error and uncertainty guide. Parts I and II After finding the value of the mass, both in Parts I and II, you can see if the values fit within the uncertainty of the value you found in the steps outlined above. You can also find the percent difference between the value from Part I and the known value, as well as the value from Part II and the known value.