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19Sep2018

Leaving Certificate Examination 1936 Honours Applied Mathematics

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Question 1

A wheel rolls uniformly on the ground, without sliding, its centre describing a straight line with uniform velocity quicklatex.com-8bafe7d16e660869fc203e8bffd77abc_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds. Show that at any instant every point on the rim is turning about the point of contact of the wheel with the ground with an angular velocity equal to that of the wheel about its centre.

Question 2

A quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds ton lorry attains a speed of quicklatex.com-8a0f60b8ca3ec09a3984d53508863c9a_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds miles per hour from rest in quicklatex.com-4c8846d90c9db2c7945bc56cc2df5c3f_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds seconds during which time it travels a distance of quicklatex.com-4fbb80c3d7c3c9bdfaf780287e19f597_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds yards. If the average resistance to motion over this distance is quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds lbs. per ton-find the average Horse Power required.

Question 3

If the hodograph of the path of a moving point quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds be drawn, then the velocity of the corresponding point quicklatex.com-6ce7c226153d55058c10348c6739a4c5_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds in the hodograph represents in magnitude and direction the acceleration of quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds in its path.

Prove this theorem and use it to determine the magnitude and direction of the acceleration of a point moving in a circle of radius quicklatex.com-95d7c225dd31ad7d6dd5fb9f0980b531_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds with a uniform speed quicklatex.com-8bafe7d16e660869fc203e8bffd77abc_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds.

Question 4

The bob of a conical pendulum is moving in a horizontal circle with uniform velocity. With the aid of a clear diagram indicate the forces acting on it at any instant and analyse the motion.

If the bob makes quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds revolutions per minute, what is the vertical distance of the circle of rotation below the point of suspension of the pendulum?

Question 5

A machine part weighing quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds lbs. has a simple harmonic motion in a straight line. The distance between the end points of its travel is quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds inches and quicklatex.com-fef5d9bb0bd664dfe03d2ae1a00c063d_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds complete to-and-fro movements are made per minute. Calculate :-

(a) the acceleration and the accelerating force when it is quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds inches from its mid-position;

(b) its maximum velocity;

(c) the maximum accelerating force.

Question 6

Neglecting frictional resistance, calculate the least velocity with which a truck must enter the lowest point of a vertical circular track quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds feet in diameter in order to just “loop the loop.”

Find also the velocity of the truck and the reaction of the track when half way up.

Weight of truck = quicklatex.com-cbbca562b8a27132c102a81b44b1362d_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds lbs.

Question 7

Two long pendulums of equal length are suspended so that their bobs just touch when at rest. The masses of the bobs are quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grindslbs. and quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds lbs. respectively. They are pulled apart in opposite directions-the horizontal displacements from the rest positions being quicklatex.com-8d32db231cb78ed89774fadb2a7139a1_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds inches and quicklatex.com-9b76a990de169fd0a5fd60c221addbb3_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds inches respectively-and released simultaneously. In impact they join together and move as one body. The compound mass is found to have a maximum horizontal displacement of quicklatex.com-df83e03fdac48379cd00d645d7c303f6_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds inches from the mean positions.

On the assumption that the horizontal displacements represent to some scale the velocities of the masses at their mean positions,  show that these results verify the Principle of Conservation of Momentum.

Justify this assumption.

Question 8

Over a smooth pulley is passed a light string supporting at one end a mas of quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds lbs. and at the other a pulley of mass quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds lb. A string with masses of quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds lbs. and quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds lbs. attached to its ends passes over the second pulley.

Find the acceleration of each of the moving bodies and of the centre of gravity of the moving system.

Question 9

A box weighing quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds lbs. placed on a plank just slides down when the plank is tilted at an angle of quicklatex.com-e54188e31e12b3e42e4c5cc97eb346e2_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds to the horizontal.

The plank is then fixed at an incline of quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds to the horizontal and a weight quicklatex.com-054ef36c6e54f65ccdd586c0869b4fb0_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds lbs. is placed in the box. Find an equation showing the effort quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds lbs. acting parallel to the incline which will drag the box and weight up the incline at a slow uniform speed.

Write down expressions for the Mechanical Advantage and Efficiency of the arrangement.

Question 10

Two poles quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds and quicklatex.com-371fe833e9a89e2790fc66adb618b944_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds jointed together at their tops and making an angle of quicklatex.com-209c1958604e9f7d31e020b608033e83_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds with each other are used as shear legs. The ends quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds and quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds rest on the level ground an the plane of triangle quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds is inclined at quicklatex.com-43254279a766115b4c8c77b4f9e086ff_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds to the horizontal. A back stay joined at the top quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds and to a point quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds on the ground behind the legs is placed symmetrically with respect to them and makes angle of quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds with the plane of the legs.

Find the forces in the legs and back stay when a load of quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1936 Honours Applied Mathematics | Maths Grinds tons is hung from quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1936 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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