Calendar: 1893-1894 Page 888

clxx SCIENCE AND SAMBROOKE EXHIBITIONS Define work energy and horse-power load of 10 tons is dragged up an inclined plane by an engine which produces on it an acceleration of foot sec per sec Assuming the length of the plane to be half mile and that its inclination makes an angle of 30 with the horizon find the horse-power of the engine and the energy expended in raising the load friction being neglected Assuming the truth of the proposition known as the Parallelogram of Forces as far as the direction of the resul- tant is concerned prove its truth for the magnitude of the resultant uniform door feet high and feet broad is supported by two hinges one at each corner The upper hinge is per- fectly smooth find the direction and magnitude of the force exerted at the lower the weight of the door being taken as 56 lbs י י Shew how to find the position of the centre of gravity of uniform triangular lamina square uniform lamina ABCD of weight has heavy particles Ρ and fixed to it at Β and it is suspended by string fastened at prove that AC is inclined to the horizon at the angle whose tangent is W' Give description of the third system of pulleys Which is the least advantageous of the three systems of pulleys in the case in which each pulley is of the same weight and the load 12 times the weight of one of the pulleys sup- posing there are movable pulleys State the laws of friction Two given weights and of different materials are laid on given inclined plane and connected by string in state of tension the coefficients of friction being μ and μ' Shew that the angle of the plane θ when both weights are on the point of motion is given by Find also the tension of the string