A Collection of Cambridge Mathematical Examination Papers, Vol. 1

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Excerpt from A Collection of Cambridge Mathematical Examination Papers, Vol. 1: As Given at the Several Colleges 10. In uniformly accelerated motion the whole space from rest is proportional to the square of the whole time of motion. 11. The time of falling down an inclined plane of given height is proportional to its length. 12. Twelve pounds weight is so distributed at the extremities of a cord passing over a pulley, that the more loaded end descends through seven feet in as many hours. What weight is at each end of the cord? 13. Given the direction, and velocity of projection, find the range on the horizontal plane, the time of flight, and the greatest height attained by the projectile. 14. Find the length of a pendulum that will oscillate seconds, and of one that will oscillate four times in a second. Trinity College, 1824. 1. Explain what is meant by the moment of a force, and shew that the moment of the resultant of two forces is equal to the sum of the moments of the component, taken with their proper signs. 2. If three forces, represented in quantity and direction by the three sides of a triangle taken in order, act upon a point, they will be in equilibrium, prove this, by resolving the forces in the direction of rectangular co-ordinates. 4. A rod of given weight and length, has a moveable weight attached to it, and is placed with one end against a vertical wall, and the other upon a horizontal plane, find the position of the moveable weight, when a given sustaining force is just sufficient to prevent the rod from sliding when in a given position. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully, any imperfections that remain are intentionally left to preserve the state of such historical works.