Problem 2:   Hydraulic systems utilize Pascal's principle by transmitting pressure from one cylinder (called the primary) to another (called the secondary). A certain hydraulic system is designed to exert a force 85 times as large as the one put into it. Part (a)  What must be the ratio of the area of the secondary cylinder to that of the primary cylinder?  Part (b)  What must the corresponding ratio of their diameters be?

A 61.0-kg survivor of a cruise line disaster rests atop a block of Styrofoam insulation, using it as a raft. The Styrofoam has dimensions 2.00 m ✕ 2.00 m ✕ 0.0870 m. The bottom 0.022 m of the raft is submerged. A. Write Newton's second law for the system in one dimension, using B for buoyancy, w for the weight of the survivor, and wr for the weight of the raft. (Set a = 0. Solve for Fy, the y-component of the net force. Let upward be the positive y-direction.) Fy = (     ) = 0 B. Calculate the numeric value for the buoyancy, B. (Seawater has density 1025 kg/m3. Enter the answer to at least the ones digit.) C. Using the value of B and the weight w of the survivor, calculate the weight wr of the Styrofoam. D. What is the density of the Styrofoam? E. What is the maximum buoyant force, corresponding to the raft being submerged up to its top surface? F. What total mass of survivors can the raft support?

Problem 4.1 An incompressible liquid with density p is contained in a tank with rigid, vertical walls. The tank is open to the atmosphere on the top and divided into two sections, Side A and Side B. The height h of the liquid and the cross-sectional or foot-print area A on each side of the tank (area perpendicular to the coordinate h) is shown in the figure. There is a hole in the partition and the liquid can flow freely between the two sides. Assume that the system is the mass of liquid in both tanks. hA AA a) Draw a system diagram. b) Write an equation for the mass of the system, msys, in terms of the given information. One approach is to find mys, and msys, separately and then add them together to find msys. Your answer should only contain symbols. Ав c) Using your result from Part (a), calculate the first derivative of the system mass with respect to time: dmsys/dt. Your answer should include two derivatives dh/dt and dhp/dt. What is the physical meaning of these two terms and why…