UNIVERSITY OF MAURITIUS

FACULTY OF ENGINEERING

PAPER NO

BEMfgE/05S/13

BEME/05S/21

BEM/05S/18

EXAMINATION

Second Semester 2005/2006

BEng (Hons) Manufacturing Engineering

Level 1

BEng (Hons) Mechanical Engineering

Level 1

BEng (Hons) Mechatronics Level 1

DATE

Monday 29 May 2006

SERIES

May 2006

PAPER

Mechanics of Materials and Machines 1

[MECH 1001Y(1)]

TIME

9:30 12:30 Hours

This paper contains EIGHT (8) Questions, FOUR (4) Questions in SECTION A and FOUR (4) Questions in SECTION B. Candidates are required to answer :

SECTION A : ANY THREE (3) Questions

SECTION B : ANY THREE (3) Questions Take g = 9.81 m/s2 wherever required. USE SEPARATE ANSWER BOOKS FOR EACH SECTION.

SECTION A

Answer ANY THREE (3) Questions from this Section. Use separate Answer Books for each Section. Question 1 (a) State the TWO conditions for static equilibrium of a body (ie, the Principle of

Equilibrium). [4 marks] (b) A man raises a 10kg joist of length 4 m by pulling a rope as shown in Figure Q1.

Find the tension T in the rope and the reaction at A. [21 marks]

Figure Q1

45o

25o

A

4m joist

rope

Question 2 (a) State the Principle of Conservation of Energy and the Principle of Conservation of

Momentum. [4 marks] (b) A hammer of mass 0.5 kg hits a nail of 25 g with a velocity of 5 m/s and drives it

into a wooden block by 25 mm. Find the resistance offered by the wooden block showing clearly all your derivations. [21 marks]

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Question 3 (a) Derive the THREE equations for the motion of a rigid body under constant

angular acceleration. [6 marks] (b) The turntable of a record player attains its operating speed of 33 1/3 rpm in

5 revolutions after being turned on. Determine the initial angular acceleration of the turntable if:

(i) the angular acceleration is constant. [5 marks] (ii) the angular acceleration decreases linearly with angular velocity such that it

is one quarter of its initial value when the operating speed is reached. [10 marks]

(iii) If the moment of inertia of the turntable is 0.001 kg m2, find the

corresponding torque required for cases (i) and (ii). [4 marks] Question 4 (a) With the help of appropriate sketches, explain briefly the meaning of SHEAR

FORCE and of BENDING MOMENT. [6 marks] (b) A light beam AB is 4 m long and is loaded with an uniformly distributed load of

2 kN/m over a length CD of 1 m as shown in Figure Q2 below. A 4 kN point load also acts at C. Sketch the Shear Force and the Bending Moment diagrams for the beam showing all the salient values.

[19 marks]

A B

4 kN 2 kN/m on CD C D

1.5 m 1 m 1.5 m

Figure Q2

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SECTION B

Answer ANY THREE (3) Questions from this Section. Use separate Answer Books for each Section. Question 5 The pin-jointed framework shown in Fig Q5 is supported on hinges and horizontal rollers at the left and right hand supports respectively. Determine the type and magnitude of the forces in the members A, B and C.

[25 marks] Question 6 A horizontal beam of the section shown in Fig Q6 is 4m long and is simply supported at its end. Determine the maximum uniformly distributed load it can carry if the tensile and compressive stresses must not exceed 32 and 56 MN/m2 respectively.

[25 marks]

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Question 7 The mechanism shown in Fig Q7 consists of a crank AB which rotates about A clockwise at 250 rev/min, connected by a link BC to a solid triangular link CDE pivoted at D. The link EF connects the triangular link to a slider F which is constrained to move in vertical guides. AB = 100 mm; BC = 270 mm; CD = 230 mm; DE = 140 mm; EF = 320 mm. For the configuration shown, determine:

(i) the velocity of the slider F. [15 marks]

(ii) the angular velocity of the triangular link CDE. [10 marks] Question 8 The turning-moment diagram of an engine, which has been drawn to scales of 1 mm to 50 Nm and 1mm to 1 of rotation of the crankshaft, shows that the greatest amount of energy which has to be stored by the flywheel is represented by an area of 2250 mm2. The flywheel is to run at a mean speed of 240 rev/min with a total variation of 2 per cent. If the mass of the flywheel is to be 450 kg, determine its radius of gyration.

[25 marks]

END OF QUESTION PAPER /nr

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