phy lab 2

Lab Report for Lab 2 – Phy 201 WB 06/23/2023 Lab 2 Dealing with Vectors Purpose: The purpose of this experiment is to study the difference of 10 sets of added vectors by using a simulation that lets us observe the results of vectors one makes using the component method. Introduction: A vector is a quantity that has both magnitude and direction. For example you shove someone with 10 Newtons of force to the left. In this experiment we learn more about vector addition which is the process of combining two or more vectors. The resultant vector or the symbol R is one of the important vectors because it also results from adding two or more vectors. To find the resultant you use either the graphical method and component method. In this experiment we use a simulation that allows us to visualize the addition of vectors with the component method. The component method involves finding the total X and Y components in order to get the resultant magnitude and the angle of resultant. Using the simulation we make 10 sets of vectors on a graph, and for each set two different vectors were labeled with blue (Vector 1), green (Vector 2) and red (Vector 3). You drag the arrow on to the graph and stretch the arrow in any direction. Above it will show x and y total. Once we are able to sort out the two vectors in which they are touching head to tail, we press the resultant button to create the resultant line which is Pink, and it reaches from the tip of Vector 1 to the head of Vector 2. As we continue with this experiment you get to understand the rules of vectors and how magnitude and direction matter. Theory of Rules of Addition: Rules of Adding the Vectors F1x = F1cos θ 1 F1y = F1sin θ 1 F2x = -F2sin θ 2 F2y = F2cos θ 2 F3x = -F3cos θ 3 F3y = -F3sin θ 3 F4x = F4sin θ 4 F4y = -F4cos θ 4 Rx = F1x + F2x +F3x +F4x Ry = F1y +F2y + F3y + F4y Rules of Determining the Magnitude R = √ (Rx^2 +Ry^2)

Rules of Determining the Angle for the Direction θ = tan^-1(Ry/Rx) Percentage Error Formulas (Res Mag-Exp Mag)*(100/Res Mag) (Res Angle-Exp Angle)*(100/Res Angle) Results (sets of vectors): 1st set 2nd set 3rd set 4th set

Calculations: Set; Vector 1: x-total Vector 2: y-total Res Mag: Res Angle: Exp Mag: Exp Angle: 1 7 4 8.1 29.8 8.1 29.7 2 5 4.5 6.8 42 6.7 42 3 3 7 7.7 66.9 7.6 66.8 4 13 5.5 14.2 23 14.1 23 5 3 6.5 7.2 65.3 7.2 65.2 6 13 8.5 15.6 33.2 15.6 33.2 7 4.5 1 4.7 12.6 4.6 12.5 8 0 0 0 0 0 0 9 -8 1 8.1 172.9 7.9 -7.1 10 -8 6 10 143.2 5.3 -36.9 Percentage Error Analysis: Sets: Mag: Angle: Exp Mag: Exp Angle: Percent Error: 1 Same 29.8 Same 29.7 %(angle)= 0.3

2 6.8 Same 6.7 Same %(mag)= 1.5 3 7.7 66.9 7.6 66.8 %(angle)= 1.3 %(mag)= 0.1 4 14.2 Same 14.1 Same %(mag)= 0.7 5 Same 65.3 Same 65.2 %(angle)= 0.2 6 Same Same Same Same n/a 7 4.7 12.6 4.6 12.5 %(angle)= 2.1 %(mag)= 0.8 8 Same Same Same Same n/a 9 8.1 172.9 7.9 -7.1 %(angle)= 2.5 %(mag)= 104.1 10 10 143.2 5.3 -36.9 %(angle)= 47 %(mag)= 125.8 Discussion and Conclusion: This experiment observed the addition of vectors and how magnitude and direction affected the resultant and angel. We also took the graphical and component method and used them and observed their relation to vectors. When going over my calculation i've come to the conclusion that is the x component is negative the error percentage is high. I'm not sure what would be the case if the y component was negative but I believe it would give me a high error percentage as well. After using the rules of addition vectors, some of the resultant magnitude and resultant angle were different from the standard value by 0.1 or less. I would like to see if having a negative x or y component would change the experimental magnitude or angle.