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Q1.At the instant depicted, assume that the particle P, which moves on a curved path,

18 / 01 / 2019 Mechanical engineering

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Q1.At the instant depicted, assume that the particle P, which moves on a curved path, is 80m from the pole O and has the velocity v and acceleration a as indicated. Determine the instantaneous values of r ̇,r ̈,θ ̇,θ ̈, and the n- and t- components of acceleration. 
The two particles of mass m and 2m, respectively, are connected by a rigid rod of negligible mass and slide with negligible friction in a circular path of radius r on the inside of the vertical circular ring. If the unit is released from rest at θ=0,  determine the velocity of v of the particles when the rod passes the horizontal position. 
Q3. The truck carries a 1500mm diameter spool of cable with a mass of 0.75kg per meter of length. There are 150 turns on the full spool. The empty spool has a mass of 140kg with radius of gyration of 530mm. The truck alone has a mass of 2030kg with mass center at G. If the truck starts from rest with an initial acceleration of 19.6m/s2. Determine, 
The tension T in the cable where it attaches to the wall, The normal reaction under each pair of wheels. 
Q4.The center of the 100kg wheel with centroidal radius of gyration of 100mm has a velocity of 0.6m/s down the incline in the position shown. Assuming no slipping occurs, 
Calculate the angular velocity of the wheel as it rolls past position A, 
Calculate the normal reaction N under the wheel as it rolls past A. 

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