Calendar: 1873-1874 Page 617

THE SCHOOL 617 weight is at rest on rough inclined plane find the least horizontal force along the plane which will cause it to move and the direction in which it begins to move Enunciate the second law of motion and explain the mean- ing of the equation Ρ Mf weight of 25 lbs on smooth horizontal plane is moved along the plane by force of lbs determine its acceleration Distinguish between force and an impulse and explain how the latter is measured Two equal elastic balls impinge directly on each other with given velocities find the change in the motion of each produced by the impact 10 Prove that point moving from rest with constant acceleration will describe in the time space and that if be this space the velocity of the point at the time will be fi If the point have initially velocity η in the direction of the acceleration explain why it is erroneous to assert that its velocity after passing over space is ί and investigate the true expression 11 Show that the time in which particle will slide down any chord of circle drawn through its highest point is constant Find the lines of quickest descent -1st from point to straight line 2nd from one given circle to another the lines and circles being all in the same vertical plane 12 Prove that the path of projectile is parabola If an inclined plane perpendicular to the vertical plane of projection pass through the point of projection find the condition that the motion of the body when it strikes the plane may be horizontal and the range on the plane in that case and in the same case if the body be inelastic find the time in which it will return to the point of projection the plane being smooth 13 From point upon the surface of smooth circular hollow cylinder and inside particle is projected in direction making an angle with the generating line through the point find the velocity of projection that the particle may rise to given height