Force & Acceleration Lab PHY 133-1 PDF

Preview

Summary

Force And Acceleration Lab...

Description

James Prawdzik 9/14/20 PHY 133 L69 (Hemmick) TA: Mikhail Litvinov Force and Acceleration Lab

Introduction This lab was conducted to determine the relationship between force and acceleration by using Newton’s Second Law to find the mass of the IOLab device. Newton’s Second Law connects force, mass, and acceleration. When gravity is a factor, the gravitational force equation will also be used. Friction will be unaccounted for and ideal circumstances will be assumed.

Fnet =ma F g=mg

By performing several different tests with the device we were able to test these relationships and use IOLab software to visualize it. Tables and graphs were also constructed based on the raw data that was retrieved from IOLab. The expected result of the experimental data is that as the force increases the acceleration will also increase.

Methods Slide 3 1. Turn on IOLab device and make sure Remote 1 is paired. 2. Screw the plate attachment onto the force sensor. 3. Place the device down onto a surface with enough room around it for some movement. Make sure the wheels are facing up and the device is in a vertical orientation.

1

Figure 1: Orientation of device for activities on Slide 3.

4. Hit record, push the plate a few times to move the device in the other direction. 5. After a few small pushes, stop, and then hit the stop button. Try to only move the device in the Y direction when pushing it. Slide 4 1. Replace the plate with the screw attachment. 2. Place the device on its head so that the Y is pointing downwards. 3. Hit record, and let the device sit there at rest for one second before lifting the device with the screw. 4. Place it back down on the surface and stop recording. 5. Find the average acceleration and force by using the ‘Data Analysis’ feature in IOLab. The average force is the force of gravity and the average acceleration will be the acceleration due to gravity. These values can be used in the equation below in order to find the mass of the device. F g=mg

2

Slide 5 1. Fit the plate onto the force probe. Place device on a flat surface with enough space for 5 pushes of increasing power. The wheels will be facing up. 2. Push the plate attached to the device 5 consecutive times. Stop recording once finished. 3. Record the peak force and acceleration by using the cursor on each of the five peaks. 4. Create a table with these 10 values for Force (N) x Acceleration (m/s^2). Then, use Excel to graph this data in a Force (N) x Acceleration (m/s^2), force being the x-value and acceleration being the y-value. 5. Add a trendline to the graph and use the equation of the line to find the mass. 6. Compare the two mass values found. Determine if your data supports the equation below.

F=ma

Slide 6 1. Attach the screw to the force probe. Connect one end of the long spring to the screw in the device and the other end to a textbook leaning off the edge of a desk. The device should be hanging in the air.

3

2. Pull the device slightly and wait until it begins oscillating. Once it starts begin recording. Record for 20 seconds and then stop recording. Try to limit movement on the x-axis and instead focus on the y-axis.

Figure 2: Set-up on activity on slide 6. This depicts the device being pulled down before it is released and begins oscillating.

3. Make a parametric plot in IOLab. Highlight a portion of the data with ‘Data Analysis’. Press the y value under ‘Norm’ and that will be your resulting parametric plot in regards to Y. 4. Use your cursor to take two data points from the parametric plot and copy them into a table. Then, use these coordinate points and use the slope formula to find the slope. 5. Compare mass found here, in Part 1, and on Slide 4.

4

Results

Figure 3: Screenshot of Slide 3 data. Charts are zoomed in accordingly, no smoothening applied.

5

Figure 4: On top is the screenshot of data used to find the average force. On the bottom is the screenshot of data used to find the average acceleration. Both are zoomed accordingly with no smoothing applied.

Table of Significant Values for Slide 4 Data Average Value Sigma Value Figure 4 Screenshot 1 -2.013 N 0.028 N Figure 4 Screenshot 2 -9.859 m/s^2 0.037 m/s^2 Figure 5: Table of significant values for Figure 4 screenshots. Average force and acceleration are listed as well as their sigma values.

6

Figure 6: Screenshot of all 5 peaks on slide 5. Zoomed accordingly and smoothened to 5.

Figure 7: Screenshot of only one peak on slide 5. Zoomed accordingly and smoothened to 5.

7

Force (N) Acceleration (m/s^2) 1.645 6.963 1.889 7.641 2.096 8.608 2.795 13.064 3.284 15.168 Figure 8: Table including peak Force (N) and Acceleration (m/s^2) values of each peak from Figure 6.

4

3.5

y = 0.2239x R² = 0.9967

3

Force (N)

2.5

2

1.5

1

0.5

0 0

2

4

6

8

10

12

Acceleration (m/s^2)

Figure 9: Excel plot visualizing the data from Figure 8. Trendline set to origin. Knisley format followed.

8

14

16

Figure 10: Parametric plot of data in Slide 6.

Coordinate Point 1 Coordinate Point 2

Table of Coordinate Points Gathered from Figure 10 x -13.6323 m/s^2 -2.6385 N -6.1658 m/s^2 -1.2460 N

Figure 11: The two data points gathered from figure 10 in order to find the slope (mass).

Calculations

F g=mg 2

m −2.103 N =m (−9.859( ) ) s m=0.213 g

Slope ¿ graph=0.224

y 2 − y 1 / x 2− x 1 = m −1.2460+ 2.6385 /−6.1658 + 13.6323=m m=0.1865 g=0.187 g F=ma

9

y

m 2 2.096 N=(0.224 g)(8.608( ) ) s 2.096 N 1.928 N Value falls within uncertainty value below so F=ma is supported by the data in Part 1. Uncertainty in m

( ) | |√ ( ) ( )

A A σ = B B

|

|

−2.013 N m 2 −9.859( ) s σ

√

(

σA 2 σB + A B

2

(

2

m 0.037 ( ) s 0.028 N + −2.013 N m 2 −9.859( ) s

)

2

)

2

( AB )=0.2185859006=0.219

0.219 g =0.978=97.8 % certainty for Part 1 0.224 g 0.187 g =0.854=85.4 % certainty for Part 2 0.219 g

10

Percent Difference for Mass ¿(accepted value−measured value)∨

¿ × 100 (accepted value)

% Difference :¿ ¿(0.224 g−0.213 g)∨ ¿

¿ × 100 (0.224 g)

4.91 % is the percent difference for Part 1 mass .

¿(accepted value−measured value)∨

¿ × 100 (accepted value)

% Difference :¿ ¿(0.187 g−0.213 g)∨ ¿

¿ ×100 (0.187 g)

13.90 % is the percent difference for Part 2 mass .

Discussion/Conclusion Force and acceleration of the IOLab device were tested throughout the experiment, the results were as expected. In all of the tests run we saw that as force increased, acceleration also increased. It also evident that as the force is applied and then stopped, the acceleration will decrease at the same time until it reaches zero. Each acceleration peak had a moment where it went below zero and this can either be down to error or the object is simply slowing down. Once it reaches zero we can assume that movement has ceased or that the device is simply moving at a

11

constant rate. Overall, the hypothesis was supported and force and acceleration both increased at the same time. The direct positive relationship between force and acceleration was expected. A bonus were the mass recordings that were recorded on Slide 4,5, & 6. The mass of slide 4 was 0.213g, this was our measured value and the benchmark for the other values. The mass of slide 5 was 0.224. This was gathered by plotting the peak force and acceleration values of the 5 peaks in Slide 5’s activity. The slope of the trendline is what ended up being the mass. For slide 6, the mass was 0.1865. This one seemed far off in comparison but it was within the uncertainty value 0.219. The mass of this slide was taken by picking two random points on the parametric plot and using the slope formula to find the slope. This slope is what translates as a mass value. The percent differences of the mass’s for Slide 5 and 6, respectively, were 4.91% and 13.90%. This signifies that the difference between the measured and observed masses was quite small. All of the mass values fell within the error range and so, confidence in these answers and techniques is justifiable. There were no observed outliers in this experiment. Possible sources of error in this experiment were mainly human error. Some of them could be: pushing the device incorrectly in the slide 5 activity so that the pushes do not increase in force each time, setting up the apparatus incorrectly on the Slide 6 activity, letting the spring touch the desk or anything else for that matter (Slide 6), and possibly even moving the device on different axis altering the results. Other than that the only technical error may be simply doing something incorrectly or forgetting to rezero the sensor. Ultimately, this experiment was performed successfully and the main hypothesis was supported.

12

13...