please solve them all

2. ( 40 points) Pressure and force balances. "How to stop the greedy cup". Watch the following video on YouTube. https://www.youtube.com/watch?v=1NTpXcp-pKM I'm going to use some vocabulary from the video - the 'fill fine' is the height beyond which the wine spilis, and the 'protrusion' is the middle cylinder. Let's assume an ideal cup for our calculations - see diagram below. The cup is a perfect cylinder of diameter of 3.50 inches; the protrusion has an outer diameter of 0.5 inches and a height of 3.20 inches; the inner diameter of the inner chamber in the protrusion is 0.12 inches. The fill line is 3.00 inches from the bottom and the total height of the cup is 5.00 inches. The atithor defeated the greedy cup by pouring a small amount of Gallium at the bottom of the cup. We'll perform an engineering calculation on Mercury instead. Let's try to minimize the amount of Mercury used in the cup, so the height of the Mercury in the inner chamber of the protrusion is just sufficient for one to fill the total height of the cup. a. (6 pts) Solving this problem involves the general manometer equation, which is derived by setting a force balance. At which point should the force balance be set? Circle one and only one: Force balance: POINT 1 POINT 2 POINT 3 b. (12 pts) Write the general manometer equation & rearrange it so that the height of the top of the mercury in the protrusion (h) is on the left-hand side and all other variables are on the right side. Do not perform the calculation! c. (7 pts) Use unit conversions to solve for height h in units of inches. Wine has a specific gravity of 1.05. h[in]= d. (15 pts) How much more wine can we drink in single wine glass using this mercury trick? This problem is several parts, in each part first setup the relevant equations using variables to solve for each requested value, this is necessary for full credit. Next calculate the numeric answer and express that value with correct units. To answer this question, i) Start by calculating the volume of wine that can be stored in the greedy cup without mercury. Next, ii) calculate the minimum volume of mercury required to defeat the greedy cup (using the height h found in part iii). Finally, calculate the extra wine. Perform all calculations in units of ounces. Please show your work. i) Volume wine to the fill line (without mercury) Write an equation for the volume of the wine to the fill line (without mercury). The lefthand side should be volume and the right-hand side should be algebraic and/or numerical values. Perform no calculations! Volume = Numeric answer (oz)= ii) Volume mercury found in part c. Write an equation for the volume of the mercury in the cup. The left-hand side should be volume and the right-hand side should be algebraic and/or numerical values. Perform no calculations! Volume ( mercury) = Numeric answer (oz)= iii) Volume difference for wine with mercury compared to no mercury. Write an equation for the volume difference of wine when the greedy cup has mercury vs. without. The left-hand side should be volume and the right-hand side should be algebraic and/or numerical values. You can just include the Volume of mercury (Vmercury) and volume of wine to the fill line (Vfill) in your equation. Perform no calculations! Volume difference = Numeric answer (oz)