PHY 111 Lab 5

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School

Grand Canyon University *

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Course

111L

Subject

Mechanical Engineering

Date

Dec 6, 2023

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docx

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5

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Lab 5: Static Equilibrium 1. Testable Question: How are force in the X direction (F X ) and force in the Y direction (F Y ) related to the angle ( )? ϴ 2. Hypothesis: As the angle increases, F X will decrease and F Y will increase because static equilibrium must be maintained. 3. Variables: Control(s): Gravity (g), Force of the Mass (F 200 ) Independent: Angle ( ) ϴ Dependent: Force in the x Direction (Fx) & Force in the Y direction (Fy) 4. Experimental Design: Control(s): g = 9.81 m/s 2 , F 200 = 1.96 N i ° ϴ Sin ϴ Cos ϴ M x (kg) M y (kg) F x (N) F y (N) 1-10 5. Materials: Level 3 pulleys with clamps 200g mass 3 strings Mass holder Mass & hanger set Force table 6. Procedure: 1. Before the trials, the force table is set up with the 3 strings and pulleys. On one of the strings sits the 200 g mass, and the other two strings hold 5 gram weight hangers. 2. The X string is set at 180 ° and the Y string is set at 270 ° . The third string starts at 0 ° . 3. Weight will be added to the X and Y strings with hangers until static equilibrium is reached. 4. After static equilibrium is reached, record the weight in the X and Y direction.
5. Next, move the string with the 200g mass to 10 ° . Add or remove weight from the hangers in the X and Y direction until static equilibrium is reached. Record the weight added to each string. 6. Repeat step 5, for each 10 ° increment until 90 ° is reached. 7. Using the data, calculate the Sin , Cos , F ϴ ϴ x (N), and F y (N) for each increment. 8. Using Microsoft Excel, plug in F x (N), and F y (N) v. ° to find the first graph. ϴ 9. Then, use Force in the X Direction Fx (N) v. Cos ϴ and Force in the Y Direction F Y (N) v. Sin ϴ , to create the next two graphs. 10. The equation of the line and the R 2 value of F x and F y was found based on the scatter plot diagram for Graph 2 and 3. 11. The equation being investigated is F 200 = F x cosΘ + F y sinΘ 7. Data: Control(s): g = 9.81 m/s 2 , F 200 = 1.96 N i ° ϴ Sin ϴ Cos ϴ M x (kg) M y (kg) F x (N) F y (N) 1 0 0.0 1.0 0.2 0.0 1.96 0.0 2 10 0.174 0.985 0.195 0.042 1.91 0.412 3 20 0.342 0.94 0.185 0.065 1.81 0.638 4 30 0.5 0.866 0.107 0.147 1.74 1.05 5 40 0.643 0.766 0.15 0.125 1.47 1.23 6 50 0.766 0.643 0.125 0.15 1.23 1.47 7 60 0.866 0.5 0.105 0.175 1.03 1.72 8 70 0.94 0.342 0.075 0.19 0.736 1.86 9 80 0.985 0.174 0.035 0.195 0.343 1.91 10 90 1.0 0.0 0.0 0.205 0.0 2.01
8. Analysis: Graph-1: Force in the Y & X Direction v. ϴ 0 10 20 30 40 50 60 70 80 90 100 0 0.5 1 1.5 2 2.5 Force in the X Direction Fx & Force in the Y Direction Fy (N) vs. (°) ϴ Fx Fy (°) ϴ Force in the X Direction Fx & Force in the Y Direction
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