Calendar: 1871-1872 Page 534

534 applied sciences iHat tmattii See Department of General Literature and Science iHec antti SECOND AND THIRD YEARS Enunciate and prove the triangle of forces If be the centre of the circle circumscribing triangle ABC and DEF the middle points of the sides the system of forces OA OB will be equivalent to the system OE OF Define centre of gravity Show how to find the centre of gravity of series of heavy particles lying in one plane fiin uniform wire is bent into the form of triangle and particles of weights are placed at the angular points prove that if the centre of gravity of the particles coincide with that of the wire Ρ where represent the sides of the triangle respectively opposite to the angles Two men carry uniform bat of iron AB 16 feet long weighing 80 lbs one man is placed at distance of feet from and the other foot from Bm find the pressure on each supposing weight of 10 lbs be suspended on the bar feet from weight Ρ is supported on an inclined plane by two equal forces Ρ and one acting horizontally and the other along the plane required the inclination of the plane closed framework ABCDF has its sides FA AB Β CD forming part of regular hexagon ABC DEF Forces represented by FE AE BE CE DE act on the framework Draw diagram of forces which will show the strain on the several parts of the framework The wall of reservoir of brickwork is feet thick and 12 feet above the surface of the ground the foundations are 12 feet deep the natural slope of the earth is 60 and it weighs