Answer Happy

please help with the unanswered questions of my online lab. I do not understand how to use the given equations with that information.
its broken into 3 parts and I have some values that were given/found
Static Equilibrium EXPERIMENT Masses attached to a piece of string and suspended by pulleys will settle to static equilibrium. The angles the string makes for equilibrium to be obtained will be measured. The force vectors acting on the masses will then be used to demonstrate Newton's second law for stationary objects. INTRODUCTION An object is in static equilibrium when the vector sum of all the forces acting on that object is equal to zero. This is stated mathematically as, Σ F₁ = 0, where i = 1, 2, 3, ..., n, or F₁+F2+F3++F₂=0 (1) i-1 or in component form, Fix =0 and ŻF =0 i=1 i=1 where the F; are the individual forces and the x and y components separately sum to zero. If an object suspended by strings is stationary then there is no net force acting on it. The forces in this case are the tensions in the strings, which suspend the object (the knot). In this exercise mass will be hung from mass hangers and the tension in the strings will be generated by the mutual gravitational attraction between the masses and the earth. The force of gravity on the masses at the surface of the earth is given by, F(N) = m(kg) x 9.80(m/s²) (3) and is called the weight of the masses. Notice that Equation 3 gives the appropriate units to be used in the SI system of units. APPARATUS String 1 String 3 Two long support rods, table clamp, pulleys, pulley clamps, masses, mass hangers, string, and protractor. PROCEDURE Set up the apparatus as demonstrated in Figure 1. m₁ 1 8. Knot 0 String 2 m Figure 1
Part 1 Hang 100g at both ends of the strings, as my and m3 in Figure 1. Note that the mass hangers each have a mass of 50g. Now hang 90g at the center, m2 in Figure 1. Measure the angle between string 1 and the loop attached to the center hanger, string 2. This angle is labeled 0, in Figure 1. 0₂= 117° 01, see Figure 2, is then equal to ₁ minus the 90° between the horizontal and the vertical. m3 Da 0₁ = 27° 100g 100g Measure the angle 0, shown in Figure 1. Figure 2 0₂ 11° 4. 02 is then equal to 0, minus the 90° between the horizontal and the vertical. 0₂= 27° 5. T₁, T2, and T3 are the tensions in each of the strings, are shown in Figure 3. In figure 3, a) Draw the x-y coordinate system; b) Label the components Tx and Ty for each T; c) Label 0₁ and 02. T₁ T3 T₂ Figure 3 6. Since the system is in equilibrium, the tensions are equal to the weights hanging on the 2 2. 3. = m₂ 909
end of the strings. |T₁| r₁1 = 100g 17₂1 = 90g |7₂| = 100g 7. Use the measured angles 0₁ and 0₂ to calculate the horizontal (x) and the vertical (y) components of T₁, T2, and T3. Tix = T2x = T3x = Tiy= T2y = T3y = 8. Use the results in 7 to show that the equilibrium conditions of equation 2 are satisfied by your experimental values. Part 2 1. The masses used in Part 1 should still be hanging from the strings. Change my to 120g, and m3 to 150g (see Figure 1). Obtain measurements for 0₁ and 0₂ using the same procedure described in Part 1. m₁ =120g m3= 150g Ob 0₂= 0₁ Ba 06=126° 0₂ = 36° m₂=90g 2. Use equation 3 to calculate the new magnitudes of T₁, T2, and T3. |T₁| = |T3|= 3. Use the measured angles 0, and 0₂ to calculate the components of T1, T2, and T3. Tix = T2x = T3x = Tly = T2y = T3y = 4. Use the results in 3 to show that the equilibrium conditions of equation 2 are satisfied by your experimental values. 3 90°
Part 3 1. Each group will be given a different set of values for this part of the experiment. Ask your instructor for your group number. Highlight the m,, m3, and 0, values for your group in the table shown below. Group #1 #2 #3 #4 #5 #6 #7 #8 #9 #10 MI 55g 60g 65g 70g 75g 80g 85g 90g 95g 100g m3 65g 70g 75g 80g 85g 90g 958 100g 105g 110g 0₁ 259 30° 35⁰ 40° 45° 50° 55⁰ 60° 65° 70° 2. For the given mi, m3, and 0₁, use static equilibrium conditions to predict the m2 and the 9₂ values required for the system to reach static equilibrium. Show your work! 25° M 65g m₂ Figure 2 and 0₂= 40° 65g Your predicted values: m₂ = 3. Now hang m, and m3, Adjust m2 until the above given 0, is obtained. Measure and record m2 and 06. Calculate the angle 0₂. 0₂ = 0b = m2 = 4. Your predicted values in step 2 and your experiment results in step 3 should be close to each other. If not, identify the mistake(s) and make correction. 4 m 55g 0₁ 0₂