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2 Apr 2018

Leaving Certificate Examination 1926 Honours Applied Mathematics

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Question 1

State the conditions of equilibrium of three forces acting on an extended body in one plane.

quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds is a point vertically above quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds, the pivot of light rod quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds, and quicklatex.com-828ab187d74b7da76b2e94b8674e3c85_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds. quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds is attached to quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds to quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds by a cord and a mass quicklatex.com-7a02bd7300eeadcf269af0186938941e_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds is attached to quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds. Show that the thrust on the rod is Independent of the length of the cord and find the tension of the cord when quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds makes an angle quicklatex.com-d6ffefedf9d4e7e4f42ba65b9f3b9416_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds with the horizontal.

Question 2

State the laws of friction.

A ladder with its centre of gravity at its mid-point rests with one end of the ground and the other against a vertical wall. Show that the greatest inclination to the wall consistent with equilibrium is quicklatex.com-9aca667792d8e97020e64e9988a336c3_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds where quicklatex.com-74ddc0a71cf47b34f1f6eb6eda14a2ea_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds is the coefficient of friction both with ground and wall.

Question 3

A body revolves with initial angular velocity quicklatex.com-894e559d8f73c82dd29e8e403aa5eb8a_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds and uniform angular acceleration quicklatex.com-0dce58ae1ea930bb9c39e85ab5e4c977_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds: write down equations giving the angular velocity and the angle described in time quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds and derive and equation not involving quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds.

A wheel is making quicklatex.com-fd983a118a39c1da7f969dad01b752c9_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds revolutions per minute and quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds seconds later it is found to be making quicklatex.com-8724bfc6727f4058fdcae81e2e468027_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds revolutions per minute: what is its acceleration (supposed uniform)? How many revolutions has the wheel made in the interval.

Question 4

Th resistance to a train weighing quicklatex.com-054ef36c6e54f65ccdd586c0869b4fb0_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds tons and travelling at quicklatex.com-8bafe7d16e660869fc203e8bffd77abc_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds miles per hour is quicklatex.com-b90475b22ab5c52e8edfa41828a34159_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds lbs. wt. per tone: find the rate of working of the engine.

The train consumes quicklatex.com-d66dbaeb0eebc210a255b3fd356eacd0_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds tons of coal per hour and the burning of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds lb. of coal produces quicklatex.com-273ac051ff0a53582365352ee5b6950d_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds ft.-lbs. of energy: what proportion of the energy is usefully employed by the engine?

Evaluate when quicklatex.com-f01008de59e92c2783303f47a6313ce0_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds, quicklatex.com-17abce142abdd9a85546e1fcbda4f590_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds, quicklatex.com-fd9372e59ecb3d710f1ecb37aa3b49b3_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds, quicklatex.com-b166c09625a10cdb91839f1407d55f1d_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds, quicklatex.com-311389d3ce89e12e9781482a9bb9df8f_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds.

Question 5

The equation of the path of a projectile referred to horizontal and vertical axes is quicklatex.com-a7df03ef5432bfa1f0c2609fa1a43b99_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds; find the angle at which it was projected and the initial velocity. Find also the direction of motion after quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds seconds. (Note.-quicklatex.com-32a1fff034751d4fc3e4edc15ca376af_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds may be taken as quicklatex.com-094ee6d517670326a569d5b0dc00b494_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds).

Question 6

A number of unequal particles are distributed in a straight line: find a formula for the position of the centre of gravity. Two masses quicklatex.com-cbfc2b823986c7623815c2cf6f04b686_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds and quicklatex.com-b999b237e25bf5d241351c6ff0601b69_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds are attached to the ends of a light string passing over a smooth peg: show that the acceleration of the centre of gravity is quicklatex.com-25895caacb0ecb6f25f314484207a77b_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds.

Question 7

A mass quicklatex.com-7a02bd7300eeadcf269af0186938941e_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds hangs from a light spiral spring. Show that, if quicklatex.com-7a02bd7300eeadcf269af0186938941e_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds is pulled down slightly and released, it will move with simple harmonic motion. Find the greatest velocity and the periodic time of quicklatex.com-7a02bd7300eeadcf269af0186938941e_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds, showing clearly on what they depend.

Question 8

In a pulley system a weight quicklatex.com-054ef36c6e54f65ccdd586c0869b4fb0_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds is raised with uniform acceleration by means of a load quicklatex.com-6ce7c226153d55058c10348c6739a4c5_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds: show that the ratio of the accelerations of quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds and quicklatex.com-054ef36c6e54f65ccdd586c0869b4fb0_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds is equal to the velocity ratio of the machine, friction and the weight of the pulleys being neglected.

If in any system of pulleys there is equilibrium when a weight quicklatex.com-6ce7c226153d55058c10348c6739a4c5_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds is supported by a load quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds, show that if quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds be increased to quicklatex.com-6ce7c226153d55058c10348c6739a4c5_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds, quicklatex.com-054ef36c6e54f65ccdd586c0869b4fb0_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds will ascend with acceleration quicklatex.com-94ee624ce40d5b02ad3a22b8bc1d05fa_l3 | Leaving Certificate Examination 1926 Honours Applied Mathematics | Maths Grinds.

 


Citation:

State Examinations Commission (2018). State Examination Commission. Accessed at: https://www.examinations.ie/?l=en&mc=au&sc=ru

Malone, D and Murray, H. (2016). Archive of Maths State Exams Papers. Accessed at: http://archive.maths.nuim.ie/staff/dmalone/StateExamPapers/

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