## Engineering Mechanics (EM) - Dec 2015

### First Year Engg (Semester 2)

TOTAL MARKS: 50

TOTAL TIME: 2 HOURS
(1) Solve Q.1 or Q.2, Q.3 or Q.4, Q.5 or Q.6, Q.7 or Q.8

(2) Assume suitable data, if necessary.

### Solve any one question from Q1 and Q2

**1 (a)** The force system shown in Fig. 1(a) have a resultant of 200 N along positive Y-axis, determine the magnitude and position θ of force F.
(4 marks)
**1 (b)** Two blocks are connected by an inextensible string as shown in Fig. 1(b). If the system is released from rest, determine the velocity of the block A after it has moved 2 m by work energy principle. The coefficient of friction between block A and the plane is μ_{S}=0.25.
(4 marks)
**1 (c)** A stone is dropped from the top of a tower 50 m high. At the same time, another stone is thrown vertically upwards from the foot of tower with a velocity of 25 m/s. When and where the two stones cross each other?(4 marks)
**1 (d)** A cricket ball thrown by a fielder from a height of 2m at an angle of 45° to the horizontal with an initial velocity of 25 m/s hit the wicket at the height of 0.6m from the ground, find distance of fielder from the wickets:(4 marks)
**2 (a)** A semicircular area is cut from a trapezium as shown in Fig. 2(a). Determine the centroid of the shaded portion with respect to the origin.
(4 marks)
**2 (b)** A pendulum bob has a mass of 10 kg and is released from rest when θ=0° as shown in Fig. 2(b). Determine the tension in the cord at θ=30°. Neglect the size of bob.
(4 marks)
**2 (c)** A ball is dropped from an unknown height on a horizontal floor from which it rebounds to height of 8 m. If e=0.667, calculate the height from which the ball was dropped.(4 marks)
**2 (d)** A bullet moving at a speed of 300 m/s has its speed reduce to 270 m/s when it passes through a board. Determine how many such boards the bullet will penetrate before it stops.(4 marks)

### Solve any one question from Q3 and Q4

**3 (a)** A simply supported beam AB of span 6m is loaded and supported as shown in Fig. 3(a). Find the reactions at supported A and B.
(6 marks)
**3 (b)** Determine the magnitude and direction of a resultant force of a given force system as shown in Fig. 3(b) and locate its point of application on the slab:
(6 marks)
**3 (c)** A sphere weighing 1000 N is placed in a wrench as shown in Fig. 3(c), find the reactions at the point of contacts:
(5 marks)
**4 (a)** Determine the magnitude and position of force F so that the force system shown in Fig. 4(a) maintain equilibrium.
(6 marks)
**4 (b)** If each cable can sustain a maximum tension of 600 N, determine the greatest weight of the bucket and its contents that can be supported. Refer Fig. 4(b).
(6 marks)
**4 (c)** Determine the reactions at roller A and pin B for equilibrium of the member ACB as shown in Fig. 4(c).
(5 marks)

### Solve any one question from Q5 and Q6

**5 (a)** Members AB and BC can support a maximum compressive force of 800 N and members AD, DC and BD can support a maximum tensile force of 2000 N. Determine the greatest load P the truss can support. Refer Fig. 5(a).
(6 marks)
**5 (b)** The uniform rod having a weight W and length L is supported at its ends A and B as shown in Fig. 5(b), where the coefficient of static friction μ_{s}=0.2. Determine the greatest angle θ so that the rod does not slip. Refer Fig. 5(c)
(6 marks)
**5 (c)** Determine the horizontal force P needed to just start moving the 300 N crate up the plane. Take μ_{s}=0.3. Refer Fig. 5(c).
(5 marks)
**6 (a)** Determine the force in the member BE and BD of the truss which supports the load as shown in Fig. 6(a). All interior angles are 60° and 120°.
(6 marks)
**6 (b)** Determine the magnitude of pin reactions at A, B and D for the frame loaded as shown in Fig. 6(b).
(6 marks)
**6 (c)** A force P=mg/6 is required to lower the cylinder with the cord making 1.25 turns around the fixed shaft. Determine the coefficient of friction μ_{s} between the cord and the shaft. Refer Fig. 6(c):
(5 marks)