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# Conditions for Equilibrium

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1. Introduction When we say equilibrium, it is a state of balance. It is a condition where there is no change in the state of motion of a body. Equilibrium also may be at rest or moving within a constant velocity. A simple mechanical body is said to be in equilibrium if no part of it is accelerating, unless it is disturbed by an outside force. Two conditions for equilibrium are that the net force acting on the object is zero, and the net torque acting on the object is zero. Thus, the following objectives were emphasized in this experiment: to determine the equilibrant force using the force table and the component method, to determine the unknown forces using the first condition and second conditions for equilibrium, to locate the centre of gravity of a composite body, and to demonstrate rational equilibrium. 2. Theory Equilibrant is equal in magnitude to the resultant but oppositely directed. The first condition of equilibrium is when a body at rest or moving with uniform velocity has zero acceleration. The center of Gravity is the point where the weight of a body is assumed concentrate. The second condition of equilibrium is satisfied when the sum of all torques acting on an object about any axis equals zero. In activity 1, TA or the tension acting on the string is the weight of the pan A plus the weight added to it and multiplied to 9. 8 m/s2 TB or the tension acting on the string is the weight of the pan B plus the weight added to it and multiplied to 9. 8 m/s2 Experimental Equilibrant is the weight of the pan A plus the weight added to it. Theoretical Equilibrant= % Error = Exp. – Theoretical X 100 Theoretical In activity 2, the equation T1 – T2 cos ? = 0 was used. From the equation, was derived to get the value of T2 where, T1 is the reading on the spring scale when the pin is exactly at the middle of the ring ? is the angle of the string makes with the horizontal Experimental Weight = T2 sin ? Theoretical Weight= % Error = Exp. – Theoretical X 100 Theoretical In activity 3, to check the results, the actual computation of center of gravity was used. Where XC and YC are the coordinates of the center of gravity of the circle, XS and YS are the coordinates of the center of gravity of the square, and are the coordinates of the center of gravity of the composite figure. In activity 4, the equation was used, where, X1 is the length of the cylinder used X2 is the length of the center of gravity of the cylinder. And X3 is the length of the cylinder minus the 5. 0 cm. 3. Methodology There are 4 different kinds of activity in the experiment to determine the conditions for equilibrium. The materials used were the following: Force table and accessories, force board, cylinder of unknown weight, spring scale, electronic gram balance, card board, aluminum bar, cylinder of unknown weight, and protractor. For activity 1, the group used a force table, its three pans and accessories. The three pans were weighed and labeled as A, B and C. Pan A was hung at 30 degree mark and a 100g was placed on it whereas on pan B a150 g was placed and was hung at 200 degree mark. The group balanced the two tensions in the strings by placing weight on the pan C or adjusting its position in the force table to obtain the magnitude and position of the equilibrant. The theoretical equilibrant of the two tensions was solved using the component method. The group then computed the % error using the values obtained by the component method as your accepted value for magnitude as well as direction. Figure 1: Set-up for activity 1 For activity 2, a cylinder of unknown weight was suspended on the force board by means of two strings. A spring scale was then attached to one of the strings. One member of the group pulled the string horizontally until the pin was exactly at the middle of the ring. The reading on the spring scale was recorded as T1. Another member of the group measured the angle that the other string makes with the horizontal and solved for the tension T2 of the other spring and the weight of a cylinder. Percent error was computed after. For activity 3, the group used a circle of diameter 10cm and a square of side 10 cm from the card board. The circle and the square was weighed and recorded as Wc and Ws. The group determined the center of gravity of the composite figure by using the balancing method and composite method. In balancing method, a pen was placed in the middle of the composite figure wherein the plumb method, the group used a string with a coin at the end then hung it from any point and measured where it intersects on the composite figure. Figure 2: Balancing Method Figure 3: Plumbing Method For activity 4, the group first located the center of gravity of the aluminum bar by balancing it on a pencil. The cylinder used in activity 2 was hung 5. 0 cm from one end of the bar. Using the force board, the aluminum bar was supported by means of a spring scale on the end and a string on the other end until the bar assumes a horizontal position. The group used the second condition for equilibrium to determine the weight of the bar and the tension in the string. Percent error was also computed. Figure 4: Set-up for Activity 4 4. Results and Discussion Activity 1 TensionsMagnitude (N)Position(°) TA1. 310530° TB1. 7962200° Experimental Equilibrant0. 6241360° Theoretical Equilibrant0. 5545356° % Error13% Table 1: Results of Activity 1 Table 1 shows the magnitude and the positions of the equilibrants and the tensions acting on the pans. The theoretical equilibrant of the two tensions was solved using the component method. The % error was computed using the values obtained by the component method as the accepted value for magnitude and the direction. Some factors that contributed the 13% error in this activity were the accuracy of the force table and its accessories used. Activity 2 T1 (N)63 N ? (°)44° T2 (N)8. 7 N Experimental Weight (N)6 N Theoretical Weight (N)6. 3 N % Error13. 2 % Free Body Diagram of ring Table 2: Results of Activity 2 Table 2 shows the different unknown forces acting on the cylinder using the first condition for equilibrium. Some factors that contributed the 13. 2% error in this activity were the accuracy of the spring scale used and the pulling of the string horizontally. Activity 3 Weight of Square= 8. 36 g Weight of Circle= 6. 94 g MethodCenter of Gravity X – coordinateY – coordinate Plumb line Method105. Balancing Method9. 554. 5 Computation9. 545 Table 3: Results of Activity 3 Table 3 shows the x and y coordinates of the center of gravity of the component figure using plumb line method, balancing method and the actual computation. In balancing method, a pen was placed in the middle of the composite figure wherein the plumb method, the group used a string with a coin at the end then hung it from any point and measured where it intersects on the composite figure. The actual computation was written in the manual. Activity 4 Reading of Spring Scale (N)5 N Weight of cylinder (N)5. 3238 N Experimental Weight of bar(N)0. 7418 N Theoretical Weight of bar(N)0. 7977 N % Error7 % Free Body Diagram of bar Table 4: Results of Activity 4 Table 4 shows the different unknown forces acting on the bar using the second condition for equilibrium. One factor that contributed the 7% error was due to the person holding the string at one end to make the cylinder bar in horizontal position 5. Conclusion Different activities in this experiment were accomplished to understand more about the conditions for equilibrium. Based from the results obtained by the group in the different activities, the group was able to determine the equilibrant force by using the force table and the component method. The unknown forces using the first and second conditions for equilibrium were determined. Using the square and circle figure, the center of gravity of a composite body was located. Rotational equilibrium was demonstrated because the sum of all of the torques equals zero 6. Application 1. State the first condition for equilibrium. If a body is in equilibrium, are there no forces acting on it? Equilibrium means the sum of all forces in all directions is equal to zero. It doesn’t mean that there are no forces acting on it. It just means that the forces that are acting on it are equal and opposite. 2. The Russell Traction system is used for a fractured femur. Identify the forces acting on the femur. If the weight hang is 5. 0 kg, find the force needed to immobilize the femur. What will supply this force? 3. What happens to the center of gravity of a person under the following situations? A. ) His upper right extremity is amputated. B. ) He carries all his books using the right arm only. )When ones upper right extremity is amputated, the center of gravity of the person would lean towards the right part of the body since the gravitational force on the remaining arm will push the center of gravity towards the right. b)When a person carries his books using only his right arm, the pull of gravity on the book would push the center of gravity of the body towards the left. 4. Devise a way by which you could determine your center of gravity. If the object is irregular in shape, the center of mass is always located closer to the more massive end. Use felt pens to outline your partner’s body on a piece of butcher paper. Determine your partner’s approximate center of gravity by carefully cutting out the human outline and balancing it on your finger. Mark the center of gravity on your partner’s body with a piece of tape. Get a six foot piece of butcher paper and tape it to a flat wall. Outline your partner’s entire body while he is standing evenly on two feet. Mark their approximate center. Another way is to lie horizontally across the arm of a couch. The point where you are balanced is your center of gravity. 5. In general, the women’s centers of gravity tend to be lower than men’s. Can you explain why? Women’s centers of gravity tend to be lower than men’s because women have a bigger pelvis area. The skeletal structure of women make it so that their pelvis is bigger, since they will need the extra support come the time that they become pregnant, and their bodies support a baby. This means that the lower body of women is generally heavier in comparison to their whole body, as opposed to the lower body of men. This would make the center of gravity of women slightly lower, because more of their body mass is concentrated at the lower portion of their body.

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