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21 Sep 2018

Leaving Certificate Examination 1938 Honours Applied Mathematics

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Question 1

A body travels in a straight line so that the distance quicklatex.com-273ac051ff0a53582365352ee5b6950d_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds feet travelled in time quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds seconds from a fixed point in the line of motion is shown by the following equation :-

    quicklatex.com-0c1f754ac66f199c2a1090287755109c_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds

.

Show that the body is travelling with uniform acceleration, find the value of the acceleration, and calculate the maximum distance from the fixed point reached by the body in the initial direction of motion.

Question 2

A simple pendulum hanging vertically inside a railway carriage, incline at quicklatex.com-64829e38c48b85fe16c9eb8cce02ea07_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds to the vertical while the train is travelling round a circular curve on a horizontal track at a speed of quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds miles per hour. Calculate the radius of the curve.

Question 3

Prove that in the case of a body moving in a straight line with simple harmonic motion the acceleration is proportional to the distance of the body from its mean position.

If the acceleration of such a body is quicklatex.com-f1f207cf5d3c4f0c0d76a93586bcd29b_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds feet per sec., per., when it is at a distance of quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds feet from the mean position, find the period of vibration.

Question 4

The vertical load which is carried by one wheel of railway truck is quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds tons. The wheel itself weights quicklatex.com-f9e692a6460ddd19961c6d80050cd59c_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds lb. and is quicklatex.com-c20f4cdda6f8d62e84bdeecce0a65eb8_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds feet in diameter.

If the centre of gravity of the wheel is quicklatex.com-899671086cd7cba69e4b7f31b1b36cd8_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds inch from its geometric centre calculate the greatest and least pressures of the wheel on the track when the train is travelling at quicklatex.com-9e7ec55fdcc4467668102a4d17def052_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds miles per hour.

Question 5

A force quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds inclined at quicklatex.com-3b9acebec4196695229990ebdaf9f395_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds to the horizontal is just able to drag a body of weight quicklatex.com-054ef36c6e54f65ccdd586c0869b4fb0_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds slowly and uniformly along a rough horizontal surface.

Show that quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds is equal to quicklatex.com-3bf07a57b4cb72581c986d114741073f_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds.

(quicklatex.com-74ddc0a71cf47b34f1f6eb6eda14a2ea_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds represents the coefficient of friction.)

If the coefficient of friction is quicklatex.com-407e22ac069a9a8dfd4b89676a5c9a7d_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds, prove that quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds is a minimum when quicklatex.com-d6ffefedf9d4e7e4f42ba65b9f3b9416_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds is equal to quicklatex.com-12a271039065eb4a552f0902287112eb_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds.

Question 6

What time will be required to accelerate the speed of a quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds ton motor car from miles per hour to quicklatex.com-9e7ec55fdcc4467668102a4d17def052_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds miles per hour, if the motion is resisted by a constant force of quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds lb. per ton? It is assumed that the engine is working at the rate of quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds horse-power at the beginning of this period and that it exerts a constant tractive effort on the wheels.

Question 7

A uniform pole leans against a vertical wall, the upper end touching the wall and the lower end resting on horizontal ground. The coefficient of friction at each end is quicklatex.com-c1202576eb6006ba366f3dcac824fc44_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds. If the pole is on the point of slipping, find the value of the angle it makes with the horizontal.

Question 8

In the case of a group of particles whose individual masses, velocities, and accelerations are known, show how the velocity and acceleration of the centre of gravity of the system may be calcualted.

Two particles of mass quicklatex.com-ae688913a749c2b1ee1631da8f880525_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds grm. and quicklatex.com-0d7f64ee36de9328eff9d1e69ba1ac35_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds grm. respectively are connected by a light, inextensible string passing over the edge of a horizontal table. The heavier mass rests on the table and the other hangs vertically. Neglecting frictional resistances find the tension in the string and the acceleration of the centre of gravity of the system.

Question 9

A body is projected from a height of quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds feet so that it passes horizontally over the top of a building quicklatex.com-c5f69e9eeba45e1e339b5d42ff256076_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds feet high. The centre line of the building is quicklatex.com-4fbb80c3d7c3c9bdfaf780287e19f597_l3 | Leaving Certificate Examination 1938 Honours Applied Mathematics | Maths Grinds feet from the point of projection of the body.

Calculate the magnitude and direction of the velocity of projection of the body. How far horizontally from the point of projection will the body hit the ground! [sic]

Question 10

Explain how the velocity of one body relative to another is obtained.

Two ships are sailing along straight courses with such constant, different velocities that they will collide unless their velocities are altered. Show that it would appear to a person on either of the ships, as if the other were always moving directly towards him.

 


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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The EU Directive 2003/98/EC on the re-use of public sector information, its amendment EU Directive 2013/37/EC, its transposed Irish Statutory Instruments S.I. No. 279/2005, S.I No. 103/2008, and S.I. No. 525/2015, and related Circulars issued by the Department of Finance (Circular 32/05), and Department of Public Expenditure and Reform (Circular 16/15 and Circular 12/16).

Note. Circular 12/2016: Licence for Re-Use of Public Sector Information adopts CC-BY as the standard PSI licence, and notes that the open standard licence identified in this Circular supersedes PSI General Licence No: 2005/08/01.

Links:

https://circulars.gov.ie/pdf/circular/per/2016/12.pdf

https://creativecommons.org/licenses/by/4.0/legalcode

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