Calendar: 1899-1900 Page 773

FACULTY OF SCIENCE CXXl On rough plane inclined at an angle of 30 to the hori- zon5 body of mass 15 lbs rests being just kept from sliding down the plane by string parallel to the plane passing over pulley and carrying body of lbs mass find the coefficient of friction between the body and the plane and shew that the hanging weight may be increased to 13 lbs without producing motion Water falls from height of 10 feet into vessel 100 gallons falling per minute find the pressure upon the base of the vessel after the fall has gone on for minutes Considering the vessel as machine for transforming energy at what H-P is it working Into what form is the energy converted What is couple rectangle ABCD is able to turn about one corner and is acted on by forces equal to the weight of 15 lbs in DB and lbs in BC if AB feet BC feet what couple will keep the rectangle at rest and what force in CD will supply this couple gun of 15 tons mass fires shot horizontally with velocity relative to the muzzle of 1000 feet per second find the velocity of the gun's recoil If this recoil be taken up by letting the gun run up plane inclined to the horizon at in 30 shew that the gun will run 5e17 feet up the plane State and prove the triangle of forces horizontal table ABC has pulleys at and three threads knotted together pass over these pulleys carrying weights proportional to BC CA AB respectively shew that the knot will rest where the perpendiculars from on the opposite sides meet bench 12 feet long is supported on two legs distant JO inches from each end If the bench weighs 50 lbs and man of 11 stone seats himself 25 inches from one leg what will be the pressure borne by each leg In square plate one corner is doubled down symmetric cally so that the corner lies at the centre If the side of the gquare be 12 inches find the position of the centre of gravity