Azam Alsadi Experiment IV

Azam Alsadi Physics lab 2011 September 28, 2023 Experiment IV Introduction : In our experiment today, we investigate various approaches to force equilibrium that involve both scalar and vector quantities. Scalar and vector magnitudes with direction are distinguished from magnitudes only. The experimental approach, in which we establish known forces and look for an equilibrant (FE) to maintain equilibrium, is one of our three main strategies. As it has the same magnitude but points in the opposite direction as the resultant force (FR), this equilibrant is essential. For example, in trigonometry, Fx = F cos θ and Fy = F sin θ, along with θ = tan-1(Fy/Fx), to calculate horizontal and vertical components of forces. Additionally, we apply { 𝐹?𝑥 = F ? cos ? }, { 𝐹?𝑥 = F ? cos ? }, {FAY =FA sin α}, and {F By =F B sin β} to combine forces at angles α and β. At the least, the graphical method includes creating resultant forces visually, calculating their magnitudes using scales, and calculating their angles using protractors. These mathematical and graphical investigations are made possible by the force table, pulleys, string, metal ring, mass hangers, and masses in our experimental setup. Apparatus: Force table, metal ring, masses, braided string, force table pulleys (4), and Mass hangers (4) Procedure: We began by building the force table by tying strings to its central ring, directing them through pulleys, and connecting them to mass hangers. The main goal of this game is to reach equilibrium, which is when the central ring is perfectly centered, and these mass hangers tension the strings in the process. Once the ring is balanced, you can achieve this by experimenting with various angles and adjusting the masses suspended from the pulleys. Note the mass and angle necessary to achieve this equilibrium. Transfer the information you've gathered to the designated table. Next, using mathematical relationships involving the sum of forces acting in various directions, determine the Resultant Force (R) and the angle x. Sketching vectors in a Cartesian coordinate system with Fx, Fy, and R along with their angles will help you visualize these forces. The last step is to create a tail-to-tail vector diagram for the selected dataset, label the axes, and use an appropriate scale. You can learn more about how the forces interact during equilibrium by clearly illustrating the resultant and equilibrant forces in this diagram. Data: - Activity 1 Table 1 Data Set F 1 F 2 F E θ E I 200g at 0˚ 200g at 120˚ 200g 241˚ II 200g at 0˚ 200g at 90˚ 290g 226˚ III 300g at 53˚ 150g at 180˚ 245g 261˚ Table 2 Data Set F 1 F 2 F E θ E IV 100g at 0˚ 100g at 120˚ 245g 256˚ V 200g at 0˚ 200g at 225˚ 290g 308˚

- Activity 2 F(g) θ F x F y F 1 100 0 100 0 F 2 100 90 0 100 F 3 100 120 -50 86.60 ΣF x = 50 ΣF y =186.60 Picture 1 - Activity 3 Data Calculations: - Activity 1 No math calculations needed we were doing the experiments to find the numbers in table 1 and 2. - Activity 2 To find F x : F x =Fcosθ 100 cos (0) = 100 100 cos (90) = 0 100g = 5cm F R = 9.5 5cm = 100g 9.5 = 100/5 x 9.5 = 190g θ x = 75˚

Analysis: We examined the concepts of force equilibrium in our experimental study, paying particular attention to the difference between scalar and vector quantities. The component method, which involved trigonometric calculations for the horizontal and vertical forces, and the graphical method, which used visual representation of the forces, were the two main approaches we used. In our analysis, the equilibrant, a force of equal magnitude and direction to the resultant force, was crucial. It was essential that the experimental equilibrant determined using the force table agree with the equilibrant values obtained using the component and graphical methods. The accuracy of our experimental findings and the validity of the equilibrium and vector analysis concepts depended carefully on this alignment.The calculated percent error for the equilibrant magnitude was roughly 1.58%, indicating that the experimental value and the methods' predictions were very close to one another. However, it is important to take into account possible sources of experimental error, such as inaccurate weight and angle measurements. Furthermore, precise calculations and a thorough force analysis during equilibrium depended on knowing the mass of the hangers. Overall, our analysis demonstrated fundamental physics and mechanics concepts in relation to force equilibrium. Conclusion: In conclusion, our experimental research provides significant insight on vector analysis, force mass relationships, and force equilibrium. To determine equilibrant values, we investigated a variety of techniques, including component and graphical approaches. The alignment between these calculated values and the experimental equilibrant discovered using the force table validated the ideas of equilibrium and vector analysis, confirming the precision of our findings with a small percent error of roughly 1.58%. Even though our methods are reliable, it is important to acknowledge possible sources of experimental error, such as inaccurate measurements. Additionally, knowing the hangers' mass was essential for performing accurate calculations and a thorough analysis of the forces at play during equilibrium. Last but not least, our experiment emphasized the fundamental relationship between force and mass, as described by Newton's second law of motion, highlighting the significance of mass in determining the force necessary to change an object's motion. Overall, our study showed how important these principles are for analyzing forces and achieving equilibrium in complex systems.