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# Indian Institute of Technology New Delhi - (IIT) 2009 B.Tech Mechanical Engineering AML110 Engineering mechanics ,IIT - Question Paper

Wednesday, 23 January 2013 05:20Web  AML 110 MECHANICS

Major Examination

Max. Marks 120 Max. Time 2 hours

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20-11-2009

Please answer all the 7 questions. The value of g't acceleration due to gravity on the earths surface can be taken as 9.81 m/s2. Q1. A truss has the loading as shown in the figure. All the horizontal and vertical members are 1 m in length. Neglect the weight of the members.

a)    Identify the zero force members by inspection.

b)    Find the forces in the members CD. CH and BC.

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Q2. A horizontal force of 100 N is applied to the cart as shown in the figure. The cart has two wheels each having a mass of 10 kg and radius 0.3 m. The mass of the cart excluding the wheels is 50 kg. The wheels may be considered to be solid circular disks, connected to the cart by an axle passing through their centre. a)    Determine the acceleration of the cart if the motion starts from rest and the wheels roll without slipping.

b)    Determine the minimum value of the coefficient of friction between the wheel and the ground required to ensure rolling without slipping. | ytOsOQ)

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Q3. A toy is made by welding a thin rod of length R and mass M to a ring of radius R and mass M as shown.

a)    Find the coordinates of centre of mass of the toy. * x.

b)    If the toy moves in plane motion on the ground such that there is no slip at the contact (point D) with angular velocity co and angular acceleration a (as shown in the figure), express the velocity and acceleration of A in terms of the given quantities.

c)    Consider the case when g> = 0 but a t 0. About which of the points A, B and D can we use the relation dH/dt = M.

Give reasons for each of the answers. No marks will be awarded if reasons are not given.

d)    Consider the case when co t 0 and a t 0. About which of the points A, B and D can wo use the relation dH/dt -M. Give reasons for each of the answers. No marks will be awarded if reasons are not given.

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Q4. Starting from first principle derive the formulae nos. 5 and 6 given in the formula sheet.

C IC. -rnvr Q5. In the position shown the thin rod moves at a constant speed u = 1m/s out of the tube BC. At the same time tube BC rotates at constant rate (02 = 2 rad/s with respect to arm CD. The entire assembly rotates about the X axis (fixed to ground) at a rate <01 = 1 rad/s.

a)    Determine the angular velocity and angular acceleration of the tube BC with respect to a ground frame of reference.

b)    Determine the velocity and acceleration of the end A of the rod with respect to ground frame of reference. 20 traffcl)

Q6. Consider a cross made by fixing 2 slender rods (of length L and mass M each) at right angles at their centres as shown.

OH = AB = L .

a)    Determine I** and lxy of the cross about the axes shown in the figure (origin at O). You can start from the formula of moment of inertia of a slender rod.

b)    The cross is now pinned to ground at O. A bullet ol mass m, travelling with a velocity V i hits the cross at E and gets embedded in it at E. Find the angular velocity of the body just after the impact.

c)    Find the implulse exerted at O during the impact.

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Q7. The mechanism shown is released from a state of rest in the configuration shown. Calculate the velocity of the centre of the disc C, when the angle made by the rod AB with the horizontal (q) is 30. All elements of the mechanism move in

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