Force and Acceleration Objectives Explore the relationship between force and acceleration. Use Newton's Second Law to experimentally find the mass ot 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 1f 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 Fe; = ma. 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. \fError Analysis 'When you find the average velocity of the cart (in both the positive and negative direction), you will also be given for both values. Therefore, when you find the change in velocity after a hit by your hand, you will have But both and have errors associated with their values. Therefore you will have to use the addition/subtraction error propagation rule to find the error in Here are a couple more things to look out for when conducting your error analysis: * When comparing the slope of the Displacement v. Time plot to the average value of velocity: Make sure the slope is within the uncertainty range given by * When comparing the change in velocity to the area under the acceleration vs. time plot: You must find the error in by using the addition/subtraction error propagation rule. Then make sure the area of the acceleration vs. time plot fits within the spread. What to include in your lab reports Explain all calculations. Do your results match expectations? Explain. This question is especially important for this lab. Explain why each plot looks the way it does and how they relate. Error Analysis Explain all plots and what information you gathered from them! Questions 1. What does the Accelerometer read when the device is sitting on the table? 2. What about when the device was in free-fall? Does this make sense in relation to question 1?7 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. 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, 6, and oy4,. To find the mass you used, F, =mg. F Rearranged, this is m = . Therefore, to find the uncertainty in 72, you will need to use the multiplication/division rule from the error and uncertainty guide. Parts I and 11 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. What to include in your lab reports Explain all calculations. * Do your results match expectations? Explain. e Error Analysis Explain all plots and what information you gathered from them! Questions 1. How do you find the mass of the device from the slope of the plots? 2. Do the values for mass you found in Parts I and II match the known value from slide 4 (within uncertainty)? tion/Phys 1101 03 Forces.html 8359 . 0 Remote 2. Not Paired 12 Restart Quit Player 5 18 Acquisition Sets Run1 (ID 39fee8a5-db7d-4041-b124-f402953e6a4f) [Remove] Force [Fv] vs Accelerometer [Ay] (100 Hz) Swap axis X: -6.5589 m/s 1,500 y: 645.9376 N 1,400 1,300 1,200 1, 100 .000 Force (N) 900 800 700 600 as 500 400 -16 -14 -12 -10 -8 -6 4 Accelerometer (m/s?) 14 18 2 8 10 12 16 1:48 ENG 6/12/20This 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. \fYou 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. \fBe 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 10Lab. Force (200 Hz) Remote 1 At: 2. 16500 s J: 42.029 N - 6: 1.8 N a: 90.993 Ns s: -0.32 N/s (r2: 0.01) JAWNSO- NWAUT Fy (N) 2 3 4 5 6 7 8 9 10 Rezero sensor Time (s) Accelerometer (200 Hz) Remote 1 Ax Ay O Az 20 - At: 2. 15935 s 15 J: -0.233 m/s2 - o: 0.012 m/s2 a: -0.504 m/s S: -0.00 m/s3 (r2: 0.01) a (m/s?) Nadbond 0 1 2 3 4 5 6 7 8 9 10 Time (s)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. Acceleration Force (m/s2) (N)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 whether 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 (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