Answer Happy

PROCEDURE . . . The following was observed when using the Force Table: Confirmed that the table was leveled “by eye” and that the pulleys spin freely. The pulley assembly was against the machined edge of the table. When measuring, the ring was centered on the pin and that the strings extended radially outward from the center pin. The weight of the hangers was determined using a scale and was included as shown below. The angles were measured counterclockwise and recorded below. Either the S.I. unit of Newtons or the gram may be used as the force unit as long as consistency is maintained. . . The instructor will assign one of the following Assignments to students: + دارابرادا 50g/75 Non-Rectangular Part I Three concurrent, coplanar forces Part III # Component A Component B Equilibrant Force A Force B Force C Equilibrant 1 297g/120° 125g/195° 170g/120° | 160g/340° 2 63g/75° 328g/150° 140g/130° 240g/220° 200g/335° 3 156g/110° 228g/160° 200g/20° 120g/180° | 150g/300° 4 214g/130° 144g/155° 140g/130° 240g/220° 200g/335° 5 350g/70° 402g/1959 340g/???° | 140g/112° 170g/345° 150g/2499 90g/???
Part I - Non-Rectangular vector components 1. The two pulleys were placed on the force table at the angles given shown in the above table. The required component weights A and B were added to the pulleys. 2. A third line and pulley with a weight force to balance the first two weight forces was used such that the ring was centered and did not touch the center pin. This is the actual or experimental value of the equilibrant. (A light tap to jog the system minimized friction and assured a correct value.) 3. The equilibrant was record in above Table. (Weight force may be measured in grams (g) or newtons (N). To convert from grams to newtons, multiply grams by 0.0098cm/s.) Table 1 Non-Rectangular Vector Components Sketch Weight (g) Force (N) Angle (degrees) Component Vector A Component Vector B 340 Equilibrant (from force table) Resultant 4. Make a vector sketch in the space in Table I for this force system showing the resultant and its components A and B using the graphical method. Using graph paper, make a complete to- scale diagram which should be included in your lab report. Styles Pane Part II - Rectangular vector components 1. A 300g weight force at 0' and a 400 g weight force at 90° were suspended. Experimentally found the equilibrant using the force table. The values of the experimental equilibrant were recorded in Table II. 2. Make a vector sketch showing the components and their resultant in the space below. Using graph paper, make a complete to-scale diagram which should be included in your lab report. Sketch Calculations 3. Calculate the value of the resultant using the given components. Show this calculation above and in Table II below.
Table II Rectangular Vector Components Sketch Force (N) Weight (g) 505 Angle (degrees) Equilibrant (experimental) Resultant (experimental) Resultant (calculated) 4. Find the % difference error, in magnitude only, for the experimental resultant using its calculated value as the accepted value. Show this calculation. Part III - Resultant for 3 concurrent, coplanar forces 1. On the force table, three component vectors A, above. and C were setup from the assignment table 2. Using the force table, the experimental values for the equilibrant were found in the assignment table above. Table III Resultant for Three Concurrent, Coplanar Forces Weight Force Angle Degrees % Difference Error Exper. & Graphical vs Analytical 90 Styles Pane Equilibrant (experimental) Resultant (experimental) Resultant (graphical) Resultant (analytical) 3. Determine the experimental uncertainty of the equilibrant as follows: a) Carefully 1 gram increments weights were added until the ring was observed to move off center. b) The equilibrant pulley was moved to each side until the ring is observed to move off center. c) These weight force and angular uncertainties were record below. Find the % error for the amount of force uncertainty for the magnitude of the equilibrant. Show this calculation.
Experimental Uncertainties Weight Force 5 g Angular_3_ Percent % 4. Using the graphical polygon method, neatly construct a graphical solution for the three force vectors. Measure the resultant in magnitude and direction. Record your answer in Table III. Attach this graphical solution to your lab report. 5. Calculate the magnitude and direction for the resultant using the analytical method of summing x and y components for the three force vectors. Use the Summary Table to summarize and sketch your solution. Summary Table of Analytical Components + Sketch Weight Force Angle Degrees x Component y Component Vector A B С Total QUESTIONS 1. Why can't a % error be calculated for the angle? Use an example to justify your answer. 2. Explain how the preceding calculations and results in Table II verify that a vector can be replaced with its rectangular components projected on the x and y axes. 3. From Part III, Table III, compare the experimental and graphical results with the analytical. Give reasons for % differences. 4. From Part III, compare the equilibrant experimental uncertainty obtained from the force table with the % difference calculated using the analytical value. What does this indicate regarding force table, "real world" measurements versus analytical calculations?
5. If the weights of each hanger were exactly the same, could they be neglected? Explain your answer. 6. For two forces, A=300g and B=500g, with an angle of 45° between them, find the resultant (R) analytically by using the Law of Cosines: R² = A - 2AB coso + B?. Compare to the result given by the resolution of Vectors. (they should be the same) Ꮎ 45 7. List some possible factors contributing to errors in this experiment. 8. Write a concluding statement for this lab.