1314SEM1-ME3112

ME3112

NATIONAL UNIVERSITY OF SINGAPORE

ME3112  –  MECHANICS  MECHANICS OF MACHINES

(Semester I : AY2013/2014)

Time Allowed : 2 Hours

Matriculation Number

 _____________________  ________________________________ ______________________ ______________________ ______________________ ____________________ _________ INSTRUCTIONS TO CANDIDATES:

1.

Write your Matriculation Number in the box above.

2.

This examination paper contains FOUR  (4)  questions and comprises TWENTYONE (21) printed pages.

3.

Answer  ALL  ALL FOUR (4) questions.

4.

Write your answers in the space provided in this question booklet.

5.

This is an OPEN-BOOK EXAMINATION. Question Number

Marks Obtained

Maximum Marks

1

25

2

25

3

25

4

25

Total

100

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QUESTION 1

(a)

An experiment was conducted by starting a wheel at rest and letting it roll down a  plane inclined at 30° to the horizontal. It was observed that the wheel rolls without sliding and it travels a distance of 24 m over a time period of 4 s. With this information, determine the moment of inertia of the wheel, given that its mass is 8 kg and its radius is 0.2 m. Acceleration due to gravity, g = 9.81 m/s 2. (15 marks)

Figure 1

(b)

The inclination angle of the plane was increased slowly and the experiment was repeated. It was found that the wheel starts to slip when the inclination angle reaches 45°. Determine the coefficient of static friction between the wheel and the incline  plane. (10 marks)

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QUESTION 2

Figure 2(a) shows an ice-cream cone which has a height h and an open base of radius r.

(a)

(b) Figure 2

(a)

Given that r = 0.5 h, determine the surface area of the shell. Also, obtain the distance of the center of mass from the apex O given that the mass density is uniform. (5 marks)

(b)

Determine the moment of inertia of the cone about its center of mass along an axis  perpendicular to OP. (10 marks)

(c)

The ice-cream cone is placed, touching a table top, with the axis OP horizontal and released from rest, as shown in Figure 2(b). Determine the angular acceleration of the ice-cream cone at the moment of release. You may assume that the table top is rough enough to prevent any slipping. (10 marks)

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QUESTION 3

A block is packed in a rigid container as shown in Figure 3. During the transportation the  block is assumed to be confined to vertical motion by the side frictionless supports. The internal packing is modeled as an equivalent spring with spring constant k = 2000 N/m and a viscous damper with damping ratio = c/cc = 0.05. c c is the critical damping constant and c is the damping constant of the equivalent viscous damper. The mass of the block is 20 kg.

(a)

If the base of the rigid container is subjected to a vertical displacement excitation of y = 0.2 sin t (in meter) with = 20 rad/s, determine the amplitude of vibration of the  block. (15 marks)

(b)

If

is near 10 rad/s, what can be done to protect the block? Justify your answer. (10 marks)

Figure 3

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QUESTION 4

Figure 4 shows two rotating disks with the left disk hinged at A and the right disk hinged at B. The two disks are connected together via a rigid bar hinged at point C of the left disk and  point D of the right disk. All the hinged joints are assumed to be frictionless. The left disk hinged at point A has a radius of 0.6 m. The right disk hinged at point B has a radius of 0.4 m. The distance between point A and point B is 1.2 m. Both the angles CAB and DBA are equal to 60 degrees at this instant.

(a)

If disk A is made to rotate 360 degrees, can disk B also make a full revolution? Define the mechanism using the Grashof’s criterion. (5 marks)

(b)

If the angular velocity of the left disk hinged at A is 20 rad/s clockwise at this instant, determine the angular velocity of the rigid link CD and the angular velocity of the right disk hinged at B at the same instant. (20 marks)

Figure 4

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