Calendar: 1872-1873 Page 545

546 APPLIED SCIENCES iHerfjatricsi SECOND AND THIRD YEARS State the theorem called the parallelogram of pressures and prove that it is true for the magnitude of the resultant assuming that it is true for the direction of the resultant rough plane is inclined at an angle of 30 to the horizontal body of given weight is placed upon it and it is found that force acting parallel to the plane and equal to Jths of the weight of the body will just make it move up the plane What is the ςο-efflcient of friction between the bodj and the plane Draw an equilateral triangle ABC Suppose force of 10 lbs to act from to another force of 10 lbs to act from Β to and third force of 15 lbs from to find their resultant and show by diagram exactly how it acts wall 20 ft high can just sustain on its summit horizontal thrust outward at the rate of Ρ lbs per foot of the length of the wall find Ρ when the wall is ft thick also find Ρ if the wall is supported by buttresses reaching to the top of the wall which re 12 ft apart from centre to centre project ft from the wall and have horizontal section of sq ft the weight of the material of the wall and buttresses being 150 lbs per square root Show how fo find the centre of gravity of triangular pyramid An embankment of brickwork has section whose form is an equilateral triangle each of whose sides is 10 ft will the embankment be overthrown when the water reaches the top the specific gravity of the brickwork being 2-168 State and explain the third law of motion Two weights of and oz are connected by cord that goes over fixed pulley through what space must the heavier weight descend in order to acquire velocity of 32 ft per second Supposing the heavy weight to be stopped when it has acquired this velocity through what space will the oz weight ascend before it is brought to rest