Download Engineering Mechanics Exam for Biomedical Engineering Students, Autumn 2008 and more Exams Mechanical Engineering in PDF only on Docsity! Cork Institute of Technology Bachelor of Engineering in Biomedical Engineering – Stage 2 (EBIME_7_Y2) Autumn 2008 Engineering Mechanics (Time: 3 Hours) Answer Five Questions All questions carry equal marks Examiners: Dr G. McGuinness Mr. M. Murphy Dr. K. Bryan Ms. S. Bryan 1. A cantilever consists of a steel tube having an outside diameter of 100mm, an inside diameter of 75mm, and a length of 2.4m. Find the total uniformly distributed load if the maximum stress due to bending is 75 N/mm2. (20 marks) 2. (a) State the advantages of hollow as compared with solid shafts in terms of weight and torque transfer capabilities. (4 marks) (b) Table Q2(b) below gives values of the torque, T, and the corresponding angles of twist, α, as observed during a test of a bar in a simple torsion-testing machine. The specimen was 12.5mm in diameter, and the angle was read over a gauge length of 0.75m. (i) Determine the modulus of rigidity of the material. (ii) What would be the maximum shear stress in the bar if angle of twist is α= 2.0 degrees (16 marks) T, Nm 0 0.75 1.5 2.25 3.0 4.5 5.25 6.0 6.75 7.5 8.25 α, degrees 0 0.7 1.5 2.2 3.0 4.0 4.7 5.4 5.8 6.3 7.1 Table Q2(b) 3. Consider a person strengthening the shoulder muscles by means of dumbbell exercises. Figure Q3(a) illustrates the position of the arm when the arm is abducted to the horizontal. The free-body diagram of the arm is shown in figure Q3(b) along with a mechanical model of the arm. Also in figure Q3(b) the forces acting on the arm are resolved into their rectangular components along the horizontal and vertical directions. O corresponds to the axis of the shoulder joint, A is where the deltoid muscle is attached to the humerus, B is the centre of gravity of the entire arm, and C is the centre of gravity of the dumbbell. W is the weight of the arm, W0 is the weight of the dumbbell, Fm is the magnitude of the tension in the deltoid muscle, and Fj is the joint reaction force at the shoulder. The resultant of the deltoid muscle force makes an angle θ with the horizontal. The distances between O and A, B and C are measured as a, b, and c, respectively. (i) Determine the magnitude Fm of the force exerted by the deltoid muscle to hold the arm at the position shown. Also determine the magnitude and direction of the reaction force at the shoulder joint in terms of specified parameters. (ii) Calculate the magnitude of Fm and the magnitude and direction of the reaction force at the shoulder joint when: a = 15cm, b = 30cm, c = 60cm, θ = 15°, W = 40 N, and W0 = 60 N. (20 marks) 4. As illustrated in figure Q4, consider a block of mass m = 50kg, which is being pulled on a rough, horizontal surface by a person using a rope. Assume that the person is applying a constant force of T = 150 N on the block, the rope makes an angle θ = 30° with the horizontal, and the coefficient of kinetic friction between the block and the horizontal surface is µ = 0.2. Determine the acceleration of the block if the bottom surface of the block remains in full contact with the floor throughout the motion. (20 marks) Figure Q3(a) Figure Q3(b) Figure Q4
