Lab 1 - Vector Addition

Lab 1 - Vector Addition Eva Bambace PHY-105-201W July 16 2023

Abstract The purpose of this lab experiment is to demonstrate how the graphical and component methods of vector addition can be verified using the Force Table Simulator. This setup involves changing the position and mass of hanging masses to change their magnitudes. This then shows how to find the resultant vector by finding either an equivalent or an equilibrium vector. Depending on the situation, the type will differ. There are 3 different setups for this experiment and all have calculated resultant values. The purpose of the Force Table Simulator is to ensure that the red dot in the center of the circle is evenly balanced. The second part is where you will apply the graphical method of adding vectors. This is done on graph paper with a ruler and a protractor to create tip-to-tail drawings. These drawings will help measure the magnitude. The results of the experiment will be used to assess the relative accuracy of the graphical and component methods of vector addition. They will also be used to draw conclusions about their effectiveness in determining the resultant vector in various scenarios Introduction This experiment aims to investigate and verify vector addition principles through both graphical and component methods. The concept of vector addition in physics involves combining multiple vectors to calculate their resultant, which represents their combined effect. To perform the experiment, a VPL Force Table

B = 150 at 90°. ????? 3. To approximate the equilibrant , position an additional pulley ⃗? approximately opposite to the given forces. Gradually add mass to the pulley until the central ring is nearly centered on the red dot. Fine-tune both the amount of mass and the pulley's position until the ring is as close to perfectly centered on the red dot as possible. 4. Record the hanging mass and direction determined in step 3; these measurements represent the magnitude and direction of the equilibrant . ⃗? 5. Repeat steps 2 through 4 for = 150 30° and = 120 110°. ? ????? ?? ⃗? ????? ?? 6. Continue the process by repeating steps 2 through 4 for = 200 0°, ? ????? ?? = 100 70°, and = 100 160°. ⃗? ????? ?? ? ????? ?? By following these steps, you will gather valuable data regarding various force combinations and equilibrant vectors using the force table simulator. Data Analysis → A → B → C → E Setup 1 100 grams @ 0° 150 grams @ 90° 180 grams at 236° Setup 2 150 grams @ 30° 120 grams @ 110° 190 grams @ 250° Setup 3 200 grams @ 0° 100 grams @ 70° 100 grams @ 160° 170 grams @ 225°

Force tables 1. 2. 3.

Math Here is the math for setup one: R = √ ❑ R = √ ❑ R = √ ❑ R = 180.278 R= 180 grams at 56.3 degrees Here is the math setup for two: R = √ ❑ R = √ ❑ R = √ ❑ R = 192.094 R= 192 grams at 40 degrees Conclusion Throughout this lab the total theme and exercise is to learn how to add vectors and find both their magnitude and directions. In all three parts of this experiment, there were examples of different ways they may appear. There were some things that may have caused issues. This could be the protractor not being totally on the dot accurately, not aligning the red dot in the middle to be centered. Items that have to be left to interpretation are very hard to perfect. The process of adding vectors is now very easy and there are multiple ways for me to visualize what the math I am doing will be very helpful. I now understand the building blocks of vectors.