PUBLISHED BY W. P. G RANT, AND SIMPKIN & MARSHALL, LONDON. 1831. MECHANICS. TRINITY COLLEGE, MAY 1822. 1. If three forces acting together on a particle of matter produce no motion in it, and three straight lines be drawn making, with the directions of those forces, the same angle respectively, and each meeting the other two: then shall the sides of the triangle thus formed be proportional to the quantities of the respective forces. 2. Find generally the conditions of equilibrium on the inclined plane. 3. What force must be exerted to sustain a ton weight on a screw, the thread of which makes 150 turns in the course of 12 inches, and which is acted on by an arm 6 feet long? 4. If P sustains W on an isosceles wedge, and the wedge be put slightly into motion ; prove that the velocity of P: that of W::W: P. 5. Explain the construction of the steel-yard. 6. In the system of pullies in which every string is attached to the weight, find the relation between the power and the weight. 7. Find the centre of gravity of any number of heavy particles placed in the same straight line. 8. If a body be suspended by any point it will not remain at rest unless its centre of gravity is in a vertical straight line drawn through that point. 9. The centres of two balls A and B move along the same straight line with the velocities a and b. Find the velocity of each after impact, when 6A = 5B, a = 7 feet in a second, 4a + 5b= 0, and force of elasticity : force of compression :: 2 : 3. PART II. B |