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ME3112 β MECHANICS OF MACHINES (Semester I : AY2011/2012)

QUESTION 1 A compound wheel C consisting of two cylinders (with R= 0.4 m and r= 0.3 m) is free to roll along a horizontal plane as shown in Figure 1. An inextensible cord is wound around the smaller cylinder and attached to a 1 kg block A via a pulley D. The cord is maintained horizontal between the wheel and the pulley. The compound wheel has a mass of 5 kg and a radius of gyration of 0.25 m. The pulley has negligible mass. (a) The system is released from rest. Find the velocity of the block A after it has moved through a distance of 0.5 m. (20 marks) (b) If the pulley mass is not negligible, will the answer in part (a) be smaller or larger? (5 marks) You may assume that there is no slipping at all contact surfaces.

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QUESTION 2 A uniform rod AB of length L and mass m1 is connected by a pin joint to the center of a uniform disc of radius R and mass m2. The system is placed in a vertical plane (as shown in Figure 2) and released from rest with ΞΈ=45Β°. (a) Draw the free-body diagrams for the rod and the disc. (10 marks) (b) Find the acceleration of the point B at the instant when the system is released. (15 marks) You may assume that the pin joint and the vertical wall are frictionless, and the disc rolls without slipping on the horizontal ground.

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QUESTION 3 A thin homogeneous wire of mass 1.6 kg is bent into the shape of a triangular frame with AB= AC = 0.5m and BC = 0.6 m as shown in Figure 3. The triangular wire frame is made to swing freely about the point A fixed to a pin Determine the natural circular frequency of the wire frame. Assume the gravitational acceleration g = 9.81 m/s2. (25 marks)

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QUESTION 4 A rigid link BCD is attached to rigid link AB and rigid link CE with pin joints at B and C as shown in Figure 4. The dimensions of the mechanism are AB = 0.2 m, BC = CE = 0.15 m and CD = 0.1 m. The pin joints at A and E are supported by the walls. At the instant shown in the figure, link AB and link CE are found to be parallel to each other and link BCD is normal to link AB. Moreover, link AB rotates with a constant angular velocity of 2 rad/s clockwise. Determine (a) the degrees of freedom of the mechanism. Is it a four-bar mechanism? (5 marks) (b) the angular velocities of link BCD and link CE, (10 marks) (c) the angular acceleration of link BCD, and (5 marks) (d) the acceleration of point D. (5 marks)

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ME3112 β MECHANICS OF MACHINES (Semester I : AY2010/2011) QUESTION 1 An 11-kg collar as shown in Figure 1 is constrained to travel along a rectilinear and frictionless bar of length L = 2 m. The springs attached to the collar are identical, and they are unstretched when the collar is at B. Neglecting air resistance, and knowing that at A the collar is moving upward with a speed of 23 m/s, determine the linear spring constant k so that the collar reaches D with zero speed. Points E and F are fixed. (25 marks)

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QUESTION 2 A 323-g bullet hits a 2-kg block that is initially at rest as shown in Figure 2. After the collision, the bullet becomes embedded in the block, and they slide a distance of 0.31 m. If the coefficient of kinetic friction between the block and the ground ΞΌk is 0.7, determine the pre-impact speed of the bullet. (25 marks)

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QUESTION 3 A compound wheel is made by welding two uniform cylinders of the same material together. A cord is wrapped around the smaller cylinder and the wheel is pulled up a slope of 30Β°with the cord maintained parallel to the slope, as shown in Figure 3.

(a) Using the expression for mass moment of inertia of a uniform cylinder, show that the mass moment of inertia for the compound wheel about its axis is given in the form

where Ο is the mass density of the material. State the values of the constants A and B. (5 marks) (b) Given that the wheel rolls without slipping, draw the free body diagram for the wheel on the slope. (5 marks) (c) Hence, write the equations of motion for the wheel. (5 marks) (d) For the case where r = R/2, find the maximum cord tension that can be applied without causing the wheel to slip. The static coefficient of friction between the wheel and the surface is 1/3. (10 marks)

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ME3112 β MECHANICS OF MACHINES (Semester I : AY2011/2012)

QUESTION 1 A compound wheel C consisting of two cylinders (with R= 0.4 m and r= 0.3 m) is free to roll along a horizontal plane as shown in Figure 1. An inextensible cord is wound around the smaller cylinder and attached to a 1 kg block A via a pulley D. The cord is maintained horizontal between the wheel and the pulley. The compound wheel has a mass of 5 kg and a radius of gyration of 0.25 m. The pulley has negligible mass. (a) The system is released from rest. Find the velocity of the block A after it has moved through a distance of 0.5 m. (20 marks) (b) If the pulley mass is not negligible, will the answer in part (a) be smaller or larger? (5 marks) You may assume that there is no slipping at all contact surfaces.

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QUESTION 2 A uniform rod AB of length L and mass m1 is connected by a pin joint to the center of a uniform disc of radius R and mass m2. The system is placed in a vertical plane (as shown in Figure 2) and released from rest with ΞΈ=45Β°. (a) Draw the free-body diagrams for the rod and the disc. (10 marks) (b) Find the acceleration of the point B at the instant when the system is released. (15 marks) You may assume that the pin joint and the vertical wall are frictionless, and the disc rolls without slipping on the horizontal ground.

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QUESTION 3 A thin homogeneous wire of mass 1.6 kg is bent into the shape of a triangular frame with AB= AC = 0.5m and BC = 0.6 m as shown in Figure 3. The triangular wire frame is made to swing freely about the point A fixed to a pin Determine the natural circular frequency of the wire frame. Assume the gravitational acceleration g = 9.81 m/s2. (25 marks)

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QUESTION 4 A rigid link BCD is attached to rigid link AB and rigid link CE with pin joints at B and C as shown in Figure 4. The dimensions of the mechanism are AB = 0.2 m, BC = CE = 0.15 m and CD = 0.1 m. The pin joints at A and E are supported by the walls. At the instant shown in the figure, link AB and link CE are found to be parallel to each other and link BCD is normal to link AB. Moreover, link AB rotates with a constant angular velocity of 2 rad/s clockwise. Determine (a) the degrees of freedom of the mechanism. Is it a four-bar mechanism? (5 marks) (b) the angular velocities of link BCD and link CE, (10 marks) (c) the angular acceleration of link BCD, and (5 marks) (d) the acceleration of point D. (5 marks)

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ME3112 β MECHANICS OF MACHINES (Semester I : AY2010/2011) QUESTION 1 An 11-kg collar as shown in Figure 1 is constrained to travel along a rectilinear and frictionless bar of length L = 2 m. The springs attached to the collar are identical, and they are unstretched when the collar is at B. Neglecting air resistance, and knowing that at A the collar is moving upward with a speed of 23 m/s, determine the linear spring constant k so that the collar reaches D with zero speed. Points E and F are fixed. (25 marks)

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QUESTION 2 A 323-g bullet hits a 2-kg block that is initially at rest as shown in Figure 2. After the collision, the bullet becomes embedded in the block, and they slide a distance of 0.31 m. If the coefficient of kinetic friction between the block and the ground ΞΌk is 0.7, determine the pre-impact speed of the bullet. (25 marks)

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QUESTION 3 A compound wheel is made by welding two uniform cylinders of the same material together. A cord is wrapped around the smaller cylinder and the wheel is pulled up a slope of 30Β°with the cord maintained parallel to the slope, as shown in Figure 3.

(a) Using the expression for mass moment of inertia of a uniform cylinder, show that the mass moment of inertia for the compound wheel about its axis is given in the form

where Ο is the mass density of the material. State the values of the constants A and B. (5 marks) (b) Given that the wheel rolls without slipping, draw the free body diagram for the wheel on the slope. (5 marks) (c) Hence, write the equations of motion for the wheel. (5 marks) (d) For the case where r = R/2, find the maximum cord tension that can be applied without causing the wheel to slip. The static coefficient of friction between the wheel and the surface is 1/3. (10 marks)

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