Please help me do the calculations for table 1. Please show all the calculations step by step so I can understand how to do it. Also, please do it on paper so it's easier to understand since it's really confusing when it's shown here.

I'll post the theory and then the exercise

Theogy There are basically two types of quantities in physics: scalars quanties and vector quantities. A scalar quantity is simply a number that has no direction. Examples of scalars are 32 ft, 10 kg, and 8.6 s. A vector quantity has both a magnitude (which is just a scalar) and a direction (which tells you which way the vector is pointing). Forces, velocity, and acceleration are examples of vectors. They are often designated by putting an arrow over the symbol like this representation of a force vector:_F. The symbol used for drawing a vector is an arrow. The length of the arrow represents the magnitude (aer choosing a scale such as 1 inch = l newton). The angle the arrow makes with the x-axis gives us the direction of the vector. The angle is measured from the positive 1: axis, cmmtehcloclmdse from 0 to 360. A forceF of magnitude 90 N acting at angle 0 = 200 would be drawn using an arrow as shown in Figure 1. Another way of describing a vector Vis by decomposing it into its components ELandVy in the x and y directions as shown in Figure 2. BOTH way of expressing the vector V tell us the magnitude and direction of the vector. 1) magnitude V and angle 0 2) the components VR and 36,, Fig. lGraph cf force?omagnimde 90X acting at an angle 5 = \"00' Fig. 2 Victor V damp-and into its 2: and 3' components Expc:imenL 3 We can use trigonometry to go back and forth between these two expressions: 1) From the magnitude and angle to the components: SE, = V cos 9 and X); = V sin 9 (1) 2) From the components to the magnitude and angle: V = '\\l V1 2 + )6; 2 and (2) 9 = tan-1 (33,, 4' V1). WARNING: There are TWO solutions of the equation tan 9 = 36M Vx. To nd the correct value of 6 use these facts: (1) both x and y are positive in quadrant 1 (2) x is Egg and y is positive in quadrant 2 (3) both x and y are negative in quadrant 3 (4) x is m and y is negative in quadrant 4 Vector Addition You can add vectors in both representations - either as components or graphically. Adding Vectors As Components To add two vectors as components, add the components which are in the same direction. for example, to add vector A + vector B to obtain the resultant vector C, you would add AX + 13X to obtain the value of CK and the value of A3? + B). to obtain the value of Cy. We now know the two components Q, and C). of the resultant vector C. You can add more than one vector the same way: The sum 3 of adding three forces F 1, F 2, I; 3, is found by summing all three components and using Equation (2) to nd the magnitude and direction of the sum: = 2',va sum of all Eff =(g3) Sj=m= sum ofall E} S =magnitude ofthe sum 5: = \\/S.{3+ S} = angle of 5* = tan" (5,, xsg (mg a 50 gms). This is due to the imbalance of the two forces string since when the sum of forces is not zero a net force is string present, and an acceleration (ie a motion) begins to occur. This shows Newton's second law, namely: EF = ma Fig. 4. Well Centered Forces UNITS NOTE: Grams are units of mass, not force. You would have to multiply masses by the acceleration of gravity g to find their weight (W = mg, g = 9.8 m/s2) which is the force due to gravity. We are going to simplify our calculations and use grams as a proxy for the force.Procedure Part I: Finding the Opposing Force by Adding Components In Part I, we will add vectors F1 and F2 using the component method and then calculate their opposing force. Copy this table onto your data sheet: PART I DATA Magnitude (grams) e () Ex (grams) Ev (grams) F2 Sum 10 Experiment 3 (1) Set a pulley at 0" and load the string with any mass you choose unless directed otherwise by your instructor. This mass + massbejar is the magnitude of force vector F1. Set the second pulley at 90 and load it with a different mass. This is force vector F2. Calculate the vector components of F1 and F2 using Equation (1). Sum the vector's components in both x and y directions. (2). Copy the table below onto your data sheet and enter the components of the sum. Then find the magnitude and angle 0 of the sum using Equation (2). Show your calculations (including units) to three significant digits. Write the magnitude and direction of the opposing force. It has same magnitude as the sum but the opposite angle OOPPOSING = OSUM + 180 PART I CALCULATIONS Sum of Sum of Does it Ev (gm) Ev (gm) Magnitude (gm) Check? (Y/N) Sum X Opposing X X Force (3) Check if your calculations are correct by setting up the third pulley at the angle OOpposING and load it with the magnitude of the opposing force. Verify that the ring is perfectly centered on the pin as shown in Fig. 4 and note this observation on your data sheet (Y/N). DO NOT CONTINUE UNTIL YOU HAVE THE RING CENTERED. If you can't center it, and you can't find your mistake, CALL YOUR INSTRUCTOR