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20 Sep 2018

Leaving Certificate Examination 1937 Honours Applied Mathematics

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Question 1

A body of mass quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds units moves in a straight line so that its distance quicklatex.com-273ac051ff0a53582365352ee5b6950d_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds from a fixed point in the line of motion at time quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds is given by the equation : quicklatex.com-5d0c3b3cec17f65cfcd4e7a7e92ea2d2_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds.

Derive formulae for its velocity, acceleration and momentum at any time.

Given that when quicklatex.com-f4e68921830214bfa2b71e404ea8a1c1_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds the velocity, acceleration and momentum at any time.

Given that when quicklatex.com-f4e68921830214bfa2b71e404ea8a1c1_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds the velocity in quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds units and that the distances travelled when quicklatex.com-af11a671ea147428c4b168db973a1c52_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds, and quicklatex.com-54c45c8cbc7c23209477adcfe2a9c031_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds are quicklatex.com-0891223dcff91a7b7d35939934af1410_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds and quicklatex.com-e692b73d615952506a361133d605dadb_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds respectively, determine the values quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds, quicklatex.com-91dc9a245a0f25a550d41a6feb58273f_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds and quicklatex.com-5403eeae09f3e9689d2ad28aa6fe1599_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds in the above equation.

Question 2

A mass weighing quicklatex.com-a5990b654956436786b5311c7aada3b3_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds ton drops without rebound from a height of quicklatex.com-3c4de7b9ce82b47f9788dc2416e4c750_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds ft. on to the top of a pile weighing quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds cwt., and the pile is driven quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds inches into the ground by the blow.

Calculate in ft.lbs. the energy lost in the impact, and the average resistance offered by the ground to the motion of the pile.

Question 3

Calculate the effective h.p. delivered by the engine of a quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds ton motor vehicle in each of the following cases :-

(a) The vehicle is ascending an incline of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds in quicklatex.com-24746e8a1a6c5c694c7889aa45349e68_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds with a uniform speed of quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds miles per hour;

(b) the vehicle accelerates uniformly from a speed of quicklatex.com-9e7ec55fdcc4467668102a4d17def052_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds miles per hour to a speed of quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds miles per hour while travelling a distance of quicklatex.com-f8d719ce8e2cfbd1840cc41fa7d54324_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds yards along a level road.

The frictional resistances to motion may be taken as the same in both cases and equal to a force of quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds lbs. wt.

Question 4

State the laws of statical friction.

A uniform ladder quicklatex.com-dd065d3520106e3ce62efb2d1efb1157_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds feet long and weighing quicklatex.com-cde6f09d3cc0e14c252edf4ac6855889_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds lbs. is on the point of slipping when placed with its upper end against a smooth vertical wall and its lower end on a rough horizontal surface at a distance of quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds feet from the wall.

Calculate the value of the frictional force between the foot of the ladder and the ground and also the value of the coefficient of friction.

Question 5

A point quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds describes a circular path of radius quicklatex.com-95d7c225dd31ad7d6dd5fb9f0980b531_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds with a uniform velocity. quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds is the foot of the perpendicular from quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds to a fixed diameter of the circle. Show that the velocity and acceleration of quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds at any instant are equal to quicklatex.com-e1debd3706d57d629f1cf8607a17fc4b_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds and quicklatex.com-252c8f841827fde518436443e834bc90_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds respectively, where quicklatex.com-ada3765a264ac03a253ee0ccbe61f602_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds is the displacement of quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds fron [sic] the centre of the circle, quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds is the time for this displacement and quicklatex.com-d66dbaeb0eebc210a255b3fd356eacd0_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds is the angular velocity of quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds.

(b) Show that for small oscillations the bob of a simple pendulum may be regarded as having a similar motion of that of quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds and that the time of oscillation is quicklatex.com-70d9e77734359b71d020c94d01864a85_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds where quicklatex.com-7e66f8d3fbb50779ceb68e5184deb32d_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds is the length of the pendulum.

Question 6

Through what vertical height will the bob of a conical pendulum drop if its speed falls from quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds to quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds revolutions per minute?

Question 7

A train is travelling at the rate of quicklatex.com-9e7ec55fdcc4467668102a4d17def052_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds miles per hour round a circular track of quicklatex.com-798d2946921ab70671d5d7c258aea8e6_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds yards radius. The horizontal distance between the rails is quicklatex.com-0d5b79f8c98c15cb8ee4648dd054b6a0_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds inches. How much must the outer rail be raised [above the inner one so that there may be no side thrust on the rails ?

Question 8

The force acting on a body moving in a straight line is given at any instant by the formula

    quicklatex.com-25d8a14de2f03e7de4ce2516b2389887_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds

where quicklatex.com-8c28ca9825a5e0ff6a01cc15dd4efff1_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds is in lbs.-st. and quicklatex.com-ada3765a264ac03a253ee0ccbe61f602_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds is the distance in feet of the body at that instant from a fixed point in the line. If the motion is resisted by a constant force of quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds lbs.-wt., find the kinetic energy stored in the body in moving from quicklatex.com-e6c594ccda9b0b0d5cf63d9faa5cd207_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds to quicklatex.com-ed6c3305a512b9e786f9caeb477be24e_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds.

Question 9

A particle of mass quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds lbs. is placed on a smooth plane inclined at quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds to the horizon and is connected by a light string passing over the top of the plane to a particle weighing quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds lbs. which hangs vertically.

Find (a) the common acceleration;

(b) the velocity after quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds seconds of the centre of inertia of the particles.

Question 10

A body is projected up a smooth incline of quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds with an initial velocity of quicklatex.com-cde6f09d3cc0e14c252edf4ac6855889_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds feet per second. If the length of the incline is quicklatex.com-e2421346fe4da17e1d74a7cb53af7968_l3 | Leaving Certificate Examination 1937 Honours Applied Mathematics | Maths Grinds feet find the greatest height attained by the body and the range on a horizontal plane passing through the foot of the incline.

 


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/

Licence:

“Contains Irish Public Sector Information licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) licence”.

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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