side a vacuum chamber. The chamber is isolated from the nvironment by a piston, which is free to move up or down. mbient pressure exerts a force on the piston, which ompresses the spring. The spring has a force constant of 250 N/m, and the piston has a diameter of 12 mm. a) At sea evel, where ambient pressure is 1 atm, the spring is ompressed by distance x, relative to its relaxed length. alculate xo. b) Suppose the pressure gauge is lowered into

Consider a 16ft-long canoe (A-E) shown in Figure 3.1 with two individuals positioned at B and D. respectively. Assume that the buoyant force of the water (po) is uniformity distributed over the length of the canoe as shown below. The weight of the person at B is 200 lb. Assume that the canoe does not move and is in equilibrium. a) Determine the weight of the person at D (Reminder: The canoe is in equilibrium and perfectly horizonal). b) Determine the amplitude of po c) Using the results from parts a) and b), draw the shear and bending moment diagrams between A and E (i.e., along points A, B, C, D, and E). 30- W₁ = 200 lb 8 ft Figure 3.1 5 ft W 8 E Po 8 ft

A semicircular, hinged gate separates two fluids on either side of a partition. Part (a) of the figure shows the geometry of the gate, and part (b) of the figure shows the whole system in side view. The radius of the gate (4 m) is equal to the height of the fluid on the right side of the gate (fluid 2), and the specific weight ratio of the fluids is γ2/γ1 = 1.5. At what height, h, will thegate just start to open?

1. A cylinder of diameter 1.5 m and length 3 m is located in the edge of an oil tank as shown in the figure. The cylinder and the wall are smooth and the cylinder is in equilibrium. Calculate (a) The horizontal contact force of the wall. (b) the weight of the cylinder in kN. oil, p = 800 kg/m

Question 1 A 1.2 m x 1.2 m square gate located in the vertical side of an open tank is pivoted about the frictionless hinge as shown in Figure Q1 where h is depth in meter. A horizontal force P, is required to keep the gate from rotating. (a) Determine the magnitude of the hydrostatic force acting on the square gate in terms of h. (b) Determine the location of the hydrostatic force acting on the square gate in terms of h. (c) Determine the moment of the hydrostatic force acting on the square gate in terms of h with respect to an axis which coincides with the hinge. (d) Determine the depth h for the situation when P=0. (e) If the water in the open tank is replaced by oil, would the depth h increase, decrease or remain unchanged for the situation when P=0? State the reason. Given that the specific weight of oil is 8.95 kN/m³. Note: Force P is not needed to solved part (a), (b) and (c). water h 0.7 m hinge —— Figure Q1 1.2 m gate Continued...

As shown in Figure 2.1, liquid of density pis trapped by a gate ABC of unit width into the plane of the page. The gate is hinged at C, and consists of a vertical section AB of length H and an inclined section BC also of length H inclined at an angle with respect to the horizontal. Obtain an expression for the force P required to hold the gate in position. Neglect the weight of the gate and friction in the hinge. Some geometric properties of a rectangle are provided in Figure 2.2, where the symbols have their usual meanings. |6|2 b y + X C Figure 2.1 b N|O 2 Rectangle H H P a Area A = ba 2 C: Centroid a 1xx,c= |yy,c= 1 12 1 12 ·ba³ ab³

Problem: Use a unit length for the gate, determine the height h (m) in fluid 2 in the figure below if the weightless triangular hinged gate is in equilibrium in the position shown. Assume y₂ = 1.5 ₁ Triangular Gate 1m Fluid 1 45° Hinge Fluid 2

A vat contains a mixture of oil and water. The water forms a lower layer which is 0.8 m deep, and above it there is an oil layer 0.3 m thick. The density of water is 1000 kg/m³, and the density of oil is 800 kg/m³. Find the force on a flat door at the bottom of the vessel that has a cross-sectional area of 0.5 m². The acceleration due to gravity is 9.81 m/s². Oil, P. = 800 kg/m³ h, = 0.3 m %D Water, pw= 1000 kg/m3 h, = 0.8 m A = 0.5 m² O a. 5.1 kN O b. 5.4 kN Ос. 1.28 kN O d. 4.32 kN е. 10.2 kN