Calendar: 1865-1866 Page 541

APPLIED SCIENCES 543 which by being driven along smooth horizontal plane raises weight vertically Apply this result to the case of rough screw whose thread makes turns in height of foot the radius being inches and the power acting at an arm of 15 inches the sine of the limiting angle of friction being Explain how teeth with radial flanks may be traced out by the rolling of circles on one another proving the property on which it depends What are the disadvantages of having radial flanks on all the wheels If rack is substituted for one of the wheels what is the form of the teeth on the wheel which works with it train is going up an incline of in 70 at the rate of ten miles an hour the friction being lbs per ton the incline is 500 feet in length and when the train is half-way up coupling chain breaks find how far the train will go up the incline and in running back find its velocity at the foot of the incline From first principles find the velocities of two imperfectly elastic bodies after direct impact their velocities before impact and their weights being given ball whose elasticity is and weight lbs impinges obliquely at an angle of 45 on fixed rough plane whose co-efficient of friction is with velocity of 14-14 feet per second find its direction and velocity after impact Find the greatest height reached by the ball in the last question and its range on the horizontal plane ball weighing 10 lbs is attached by rod feet long to point in vertical axis about which it turns uniformly so that the velocity of the ball is 12 feet per second find the tension of the rod and its inclination to the vertical Also show that the time of revolution is the same as the time of complete vibra- tion of simple pendulum whose length equals the depth of the ball below the point of suspension 10 Find the whole normal pressure on any surface exposed to the pressure of liquid cricket ball inches in diameter whose specific gravity is is floating on the surface of water find the whole pressure on its surface and compare it with the resultant pressure 11 stone wall whose section is trapezium with one side