Calendar: 1872-1873 Page 546

APPLIED SCIENCES 547 Two heavy particles are projected one up the other down smooth plane inclined at an angle of 45 with the same velocity which they would have acquired by falling down 100 ft of the plane determine how far the one which is projected up the plane will ascend before being brought to rest and the distance of the two particles apart at the end of 10 seconds Define Work If body of weight be dragged up rough plane inclined to the horizon at an angle through space and μ be the co-efficient of friction for motion prove that the work done is sin μ cos Find at what rate an engine of 40 horse-power could draw train weighing 100 tons up an incline of in 300 the resistance from friction being lbs per ton FIRST YEAR Prove that when two equal forces act on particle their resultant is represented in direction and magnitude by the dia- meter of the rhombus described on the lines representing the forces What are the properties of the centre of gravity From what property may the centre of gravity be found by expert- ment rod AB weighing 12lbs is found to balance about point feet from weight of lbs is hung at about what point will the weight now balance Find the relation between the power and veight when there is equilibrium on the third system of pulleys in which each string is attached to the weight If the weight of each pulley is 1J lbs find the weight which will be supported by the pulleys alone in this system when there are five moveable pulleys particle starts from rest under the action of the force of gravity in what time will it acquire velocity of 112Ί feet per second and what space will be described in that time body is projected up smooth inclined plane rising in with velocity of 15 feet per second find the time until it comes to rest and the space described State the laws of Friction If body weighihg 15 lbs will Μ Μ