Woolwich Mathematical Papers [Aftwerw.] Mathematical Papers for Admission Into the Royal Military Academy (and the Royal Military College, and Papers in Elementary Engineering for Naval Cadetships)
Woolwich Mathematical Papers [Aftwerw.] Mathematical Papers for Admission Into the Royal Military Academy (and the Royal Military College, and Papers in Elementary Engineering for Naval Cadetships).
This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1884 Excerpt: ...If / and It be the perpendiculars from the pole upon the tangent and VIII. STATICS. N.B.--Great importance will be attached to accuracy in results. Full marks may be obtained by doing three-fourths of this paper. 1. If the parallelogram of forces be true for the direction of the resultant of any force and each of two ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1884 Excerpt: ...If / and It be the perpendiculars from the pole upon the tangent and VIII. STATICS. N.B.--Great importance will be attached to accuracy in results. Full marks may be obtained by doing three-fourths of this paper. 1. If the parallelogram of forces be true for the direction of the resultant of any force and each of two other forces taken separately, then it will be true for the direction of the resultant of that force and the two other forces taken together. 2. Deduce the triangle of forces and the polygon of forces from the parallelogram of forces. If the resultant R of the two forces P and Q inclined to each other at any given angle make the angle 6 with P, prove that the resultant of the a forces (P+R) and Q at the same angle will make the angle-with P+R. 3. If any number of forces in one plane act upon a rigid body, prove that they may be always replaced by a single force acting at any point and a couple. 4. Find the centre of gravity of a pyramid. If ABCD be a tetrahedron, and if the plane CDE passing through the edge CD cuts AB in E, prove that the line joining the centres of gravity of the tetrahedrons ABCD and AECD is parallel to AB. 5. Find the conditions of equilibrium when any number of forces in one plane act on a rigid body. Four heavy rods, equal in. all respects, are freely jointed together at their extremities so as to form the rhombus ABCD. If this rhombus be suspended by two strings attached to the middle points of AB and AD, each string being inclined at the angle 6 to the vertical, prove that in the position of equilibrium the angles of the rhombus will be 20 and It-20. 6. Find the power necessary to support the weight W in a system of movable weightless pulleys in which each string is attached to the weight. If in such a system each pulle...
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