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Unformatted text preview: Victor Liou Partner: Brian Kelly Feb 28, 2008 Torque Equilibrium Abstract: This experiment sought to help us understand the second condition of equilibrium which relates to r igid body rotation. In this experiment we show that about a certain point, a system will be in equilibrium when the torque counterclockwise is the same in magnitude as the torque clockwise. Torque can be defined as T0=mass*arm length. This condition can be added and subtracted to make an equilibrium system. In part one, we show this simple definition by setting up a system with a mass of 200 grams 30 cm from the left side of the ruler. Through calculation, we show that a mass of 100 grams would need to be positioned 88.5 cm away for equilibrium. Our tested value ended up being 85.5 cm which gave us an error of 3.4%. For the second part we use the center of mass of the ruler at 45.5 cm as our weight to the r ight of the fulcrum. The calculated value shows that to balance the torque produced by the ruler, we would need a mass of 200 grams 7.2 cm from the left side of the ruler. Our tested value gave us 8.9 cm which was a 19.1% error. Finally, the third part of the experiment included both the center of mass of the ruler and additional masses. In this system, we show the additive properties of torque and calculate that a mass set at 50.6 cm away would have to be 247 grams. Our tested value was 258 grams which gave us an error of 4.45%. The equation I used to solve this was . 200kg*20cm=.145kg*49.5cm-40cm+x*50.6cm-40cm. Theory: Torque, also known as moment of force, is a measure of the tendency of that force to produce rotation. Torque can be defined as the product of the force and the perpendicular distance from the axis of rotation to the force action line. In a standard r ight-hand coordinate system, we find that counterclockwise moments of force are positive and vice versa for clockwise moments. If many forces act on a r igid body and the body is in equilibrium as a net result of the action of all the forces, then the net force and torque acting on the body will be zero. In mathematical terms, if Fx=0 and Fy then T0. These equations are known as the first and second conditions of equilibrium. If a single extended r igid body is in equilibrium about a given axis, then its weight acts along a line which passes through i ts center of gravity. The center of gravity of a body is the point that the entire weight of the body is "concentrated." 1 Torques can be computed about any axis and the chosen axis is determined out of convenience. In this experiment with parallel vertical forces only torque in the x direction matter. Objective: To study equilibrium with respect to extended, rigid body rotation. Procedure: There were three parts ot the experiemnt all with relatively the same procedure. I first weighed my meter stick. I then put on the balance holder and adjusted the meterstick in the holder until it balanced horizontally. I then clamped the meterstick by turning the tightning knob. I set all my measurements with 0 cm starting from the left side. For the first part (figure 1), I positioned a 200 gram weight 30 cm from the end of the ruler and 100 gram a certain distance from the other end of the ruler (other side of the holder), until the ruler balanced horizontally. I recorded this distance. I calculated the actual distance for the ruler to balance and calculated the percent difference of my distances. For the second part (figure 2), I set the balance holder at 25 cm and put a 200 gram weight on the left side of the ruler until the entire system was balanced. I recorded the distance from 0 that the weight was at and calculated the actual distance the weight should be at for equilibirum and again found the percent error. For the last part (figure 3), I set the balance holder at 40 cm, placed a 200 gram mass at 20 cm and then positioned a unknown weight at a position until the system balanced horizontally. From my data, I derived an equation for this case and solved for the expected value. I finally found the percent difference from my value and the expected value. Data: Mass of ruler (kg)=.145kg Distance of balance=49.5cm Part 1: Mass (g) 100 g Part 2: Mass (g) 200 g Part 3: 2 Distance from 0 (cm) 8.9 cm Distance from 0 (cm) 85.5 cm Mass (g) 258 g Distance from 0 (cm) 50.6 cm Calculations: Part 1: .200kg49.5cm-30cm=-.100kg49.5cm-x;x=88.5cm Percent error=85.5cm-88.5cm88.5cm*100%=3.4% Part 2: .200kg*25cm-x=.145kg*(49.5cm-25cm);x=7.2 cm Percent error=8.9-7.2cm8.9cm*100%=19.1% Part 3: .200kg*20cm=.145kg*49.5cm-40cm+.258kg*50.6cm-40cm; 4kg*cm4.11kg*cm Mass at give distance should have been:0.247kg Percent error=.258kg-.247kg.247kg*100%=4.45% Qualitative Error Analysis: The error in this lab was very much due to human error and faulty equipment. Balancing the ruler perfectly was next to impossible since air circulating in the room would mess with the equilibrium. Furthermore, the ruler was not uniform in distribution of weight. Quantitative Analysis: Part 1: Percent error=85.5cm-88.5cm88.5cm*100%=3.4% Part 2: Percent error=8.9-7.2cm8.9cm*100%=19.1% Part 3: Percent error=.258kg-.247kg.247kg*100%=4.45% Results: Part 1: Mass (g) 100 g Part 2: Mass (g) Distance from 0 (cm) 3 Distance from 0 (cm) 85.5 cm 200 g Part 3: Mass (g) 258 g 8.9 cm Distance from 0 (cm) 50.6 cm Part 3 equation .200kg*20cm=.145kg*49.5cm-40cm+x*50.6cm-40cm Conclusion: Our results show torque equilibrium about a certain point in rotation. From our experimental data we show that each measured mass and distance was relatively close to the actual calculated value. For the first part when we balanced a simple system, we show that torque=mass*arm length. Our distance tested was found to be 85.5 cm and the calculated distance was 88.5 cm. This gave us a 3.4% error. In the second test, we also balanced a system but included the center of mass of the ruler as an acting force. This center of mass was located at 49.5 cm. We found that our .200kg weight to balance at 8.9cm from the left side of the ruler when in calculation it should have been 7.2 cm. This difference gave us a 19.1% error. Finally in the last part of the experiment, we hoped to include all aspects of force of torque by balancing a larger system which included the center of mass of the ruler and weights on both sides of the fulcrum. I was able to derive an equation which states that the torque pushing counterclockwise but equal the torque pushing clockwise for the system to be in equilibrium. This equation with given masses included was: .200kg*20cm=.145kg*49.5cm-40cm+x*50.6cm-40cm X represents the mass which was necessary to balance the system when put 10.6 cm to the right of the fulcrum. The value calculated should have been .247kg compared to our tested value of .258kg and this gave us a 4.45% error. 4 ...
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- Spring '08