1. This examination paper contains FOUR (4) questions and comprises FIVE (5) printed pages.
2. Answer ALL questions.
3. All questions carry equal marks.
4. This is an Open Book examination.
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ME3112E
Question 1
The 20-g bullet is fired horizontally at a velocity (v B)1 = 1200 m/s into the 300-g block which rests on the smooth surface as shown in Fig. 1. The spring has a stiffness k = 200 N/m and is originally unstretched. Determine : (a) The velocity of the block immediately after the bullet has been lodged into the block; and (10 marks) (b) The distance the block moves to the right before momentarily coming to rest. (15 marks)
Fig. 1
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ME3112E
Question 2
The 6-kg collar shown in Fig. 2 is released from rest in the position shown. If the spring constant is k = 4 kN/m and the unstretched length of the spring is 150 mm, how far does the mass fall from its initial position before rebounding? (25 marks)
Fig. 2
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ME3112E
Question 3
The system shown in Fig. 3 starts from rest with the 4-kg slender bar horizontal. The mass of the suspended cylinder is 10 kg. What is the angular velocity of the bar when it is in the position shown? (25 marks)
Fig. 3
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ME3112E
Question 4
The cart shown in Fig. 4 has a mass of m1 and is attached to two springs, each having a stiffness of k 1 and k 2, respectively. If both springs are unstretched when the cart is in equilibrium shown, determine : (a) The equivalent spring stiffness of the system; and (10 marks) (b) The natural frequency of oscillation. (15 marks)
