Two systems of forces and moments are given, are they equivalent? Prove your answer. System 2 -= 101 – 59 + 5k(kN) System 1 FA -= -10î + 10j - 15k(kN) FC = 30î + 5j + 10k(kN) FB = 10î + 20f – 10k(kN) FD -- =-901 + 150f + 60k (kN) FA Fp y (6, 3, 3)m (6, 0, 0)m SYSTEM 1 SYSTEM 2

2. H On the cylindrical container above with a cross section area A we open a hole as shown with an area Ah. Initially the hole is closed. Ignoring all friction forces find: a) The pressure of the water at the bottom hole if it is closed and no water exits. b) Write the continuity and Bernoulli equation. c) Solve for the speed of the water as it leaves the hole. d) Assuming the velocity at the top is given by the function dy Vy = -C/y,(Vy = ) with y=0 at the height of the small hole and Ca known Constant. dt Solve the differential equation for the time it takes to empty the container as a function of C,h,H

1 A SPHERICAL PORCELAIN BALL, WITH RADIUS R, IS DROPPED WITHOUT INITIAL VELOCITY IN A TEST TUBE CONTAINING GLYCERIN. DURING FALL, THE BALL IS SUBJECT TO THE FOLLO... A spherical porcelain ball, with radius r, is dropped without initial velocity in a test tube containing glycerin. During fall, the ball is subject to the following forces: P its weight; A the thrust of Archimedes; fluid friction force f = k v with k = 6 πrn; n: viscosity (Pa s) of Glycerin, V, velocity Density of Glycerin pg= 1.3 g/mL; density of porcelain pp = 2.3 g/mL; r ball radius= 1.0 cm; n = 1.0 s.Pa; g = 10 N/kg; volume of a sphere V = 4/3 πr³. The speed limit (in m/s) is: 0.11 0.22 0.44 0.33 0.55

A wind turbine is designed to produce the power of 5 kW. What is the percentage of mechanical and electrical conversion if the value of C, is 0.45, Wind speed is 5 m/s length of the blade is 15 m density of air is 1.12 kg/m?.