lab 4 doc.doc

Abstract: Through this experimental procedure, we reinforced Newton?s First Law of Motion that the sum of all forces and torques equal zero when an object is moving at constant velocity or at rest. Moreover, our experiments proved to be successful with errors that approach zero. The concept of statics is very important and will prove to be very useful in the area of construction as applied to engineering and architectural design. Objectives: In this lab, we will explore the concept of statics as an application of Newton?s First Law, where the sum of all forces equals zero if an object is at rest or moving at constant velocity. We will learn the importance of statics in solving engineering problems that involve the design of stationary objects. We will use a pulley system and ruler balance strategy to determine the roles played by the application of vectors and the concept of torque in statics. Experimental Procedure: Pulleys Start with three pulleys on the statics table. F1 has a pulley 1 set at 30 degrees with mass m1, 100 grams. F2 has a pulley 2 set at 130 degrees with mass m2, 150 grams. Assume zero error in both masses and angles. Find the mass placed at pulley 3, where the center ring is balanced so that the extending metal rod is in the center of the ring, with no part of the rod touching the ring. This will give F3. Lastly, carefully determine the error of F3 by finding the smallest added mass for which the ring moves off-center when the table is tapped, and record findings. Measure and record the error in angle as well. Clean up surroundings by replacing masses from pulley 3 and fixing the angles of any moved pulleys. Make sure pulleys 1 and 2 have masses of 100 and 150 grams. Pivoted Ruler Start with a pivoted ruler which has a weight hanger on the shorter end. This ruler is fixed at a position not equal to its center of mass on the balance. Adjust the hanging weight on the shorter side of the ruler so that the ruler balances with both sides raised in the air. Measure the mass of the ruler for further calculations and record findings. Clean up surroundings by randomly replacing the weight hanger at a place that does not balance. Also, check that the fixed point of the pivoted ruler is still correct. Experimental Results: Pulleys Measurements m1 = 100g ?1 = 30° m2 = 150g ?2 = 130° m3 = 166g ± 3g (measured) ?3 = 273° ± 3° (measured) Calculations QUOTE assuming zero error in F1x, F2x, ?1, and ?2 QUOTE assuming zero error in F1y, F2y, ?1, and ?2 Check: Is QUOTE and QUOTE ? Pivoted Ruler Measurements Mass of ruler: 128.8g Mass of hanging mass: 51.5g Pivot position: 44.35cm Center of mass: 49.75cm Position of hanging mass: 30.82cm Calculations (0.1288kg)(9.8 QUOTE )(0.4975-0.4435m) QUOTE (0.0515kg)(9.8 QUOTE )(0.4435?0.3082m) 0.0682 QUOTE 0.0683 QUOTE |??| QUOTE = 0.0001 QUOTE ??1 = QUOTE assuming that QUOTE = 0.001m ??2 = QUOTE assuming that QUOTE = 0.001m ?(??) = QUOTE Check: Is |??| QUOTE ?(??)? 0.0001 QUOTE 0.001 Experimental Analysis: Pulleys My data does indeed follow Newton?s First Law, that the sum of all forces add up to zero given a stationary object or an object moving at constant velocity. In our case, the object, a ring being acted on three gravitational forces facilitated by pulleys, was stationary and fixed. Our F total =0 with an total error of 0.09 N done by error propagation of F3?s components and then using the formula: Pivoted Ruler: The center of mass for our ruler is found to be 0.5000m. As proven by calculations above, the sum of torques follows Newton?s First Law of Motion regarding the sum of forces: ?? = I? = 0 Our sum of torques had an error of 0.0001, though it is still very close to 0, and our errors can be accounted for through random human errors. Conclusions: To conclude, our experiments towards proving Newton?s First Law of Motion in relations to force and torque were relatively successful. Each task yielded errors near 0, which are beneficial in regards to the accuracy of our performance. Both these applications can be applied towards the study of statics, a concept frequently used in engineering to calculate support points and balancing forces for fixed objects such as bridges. To assure ?rest? at a point, the sum of all forces and torques must add up to zero to balance out. This knowledge will be immensely helpful in the construction of bridges, tall buildings, and other fixtures needing support.