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2. Two parallel shafts connected by rolling cylinders turn in the same direction 150 rpm and 100 rpm

respectively. The smaller cylinder is 16 in. in diameter. How far apart are the axes of the shafts?


in a reversible cycle 100 KJ of heat is recieved at 500K then a adiabatic expansion occurs to 400K at which temperature of 50 KJ of heat is recieved , then a further adibatic expansion at 300 K at which temperature of 100 KJ is rejected : (1)find the change in entropy which occurs as the system is restored to its initial state in the remainder of the cycle


1.) A and B are rolling cylinders connecting the shafts S and T. C and E are cylinders fast to these shafts and slipping on each other at P. Find the diameters of C and E if the surface speed of E is twice that of C.


2.) Two solids of right section 2 and 4 are in pure rolling contact between the circular arcs. What is the angular speed ratio for the position shown? Determine the size of the angles , β, and Ø in degrees, and of the radii x and y in inches.


3. Two shafts, having axes in the same plate intersecting at an angle of 45°, turn in opposite senses at 30 rpm and 90 rpm. Draw a pair of cone to be located on these shafts and turn in pure rolling contact. Diameter of base of smaller cone is 1 in. Calculate the cone angles.


4. Two shafts A and B are connected by rolling cones and turn in the same direction. Shaft A makes 300 rpm while shaft B makes 100 rpm. Calculate the cone angle of each cone and the diameter of each base if the base of cone B is 2 in. from the vertex. θ = 30°




1. Two parallel shafts, 11 in. apart and rotating at 75 rpm and 200 rpm, are connected by cylinders in pure

rolling contact. Determine the diameters of the cylinders: (1) when they turn in opposite directions; and (2)

when they turn in the same direction.

2. Two parallel shafts connected by rolling cylinders turn in the same direction 150 rpm and 100 rpm

respectively. The smaller cylinder is 16 in. in diameter. How far apart are the axes of the shafts?

3. Two parallel shafts, 24 inches apart and having a speed ratio of 3, are connected by cylinders in pure rolling

contact. Determine the diameters of the cylinders: (1) when they turn in opposite directions; and (2) when

they turn in the same direction


Find the new location of point G, initially at G = [3 0 -1] If, (i) it is rotated by 60deg. about z-axis and then translated by 3 units along y-axis, and (ii) it is first translated by 3 units along y-axis and then rotated by 60deg bout z-axis. Are the two locations same? Check and justify, whether the final position in two cases is same or different. 



Given the following contingency table for hair colour and eye colour. Find



the value of Chi-square. Is there good association between the two?



Hair Colour



Fair Brown Black



Eye Colour



Blue 15 5 20



Grey 20 10 20



Brown 25 15 20

when we in the united states says a car's tire is filled "to 32 lb," we mean that its internal pressure is 32 lbf/in^2 above the ambient atmosphere. if the tire is at sea level, has a volume of 3.0 ft^3, and is at 75 degree fahrenheit, estimate the total weight of air, in lbf, inside the tire.


Find the final weight, volume and pressure of the gas. 


Continuous cable ADB runs over a small frictionless pulley at D to support beam OABC which is part of an entrance canopy for a building (see figure 3). A downward distributed load with peak intensity q0 = 5 kN/m at O acts on the beam. Assume that canopy weight W = 8 kN and that cable cross-sectional area is 100 mm2 . a) Find cable force T and pin support reactions at O and D b) Find the normal stress in the cable in the cable ADB c) Determine the required diameter of pins A, B, D and O if the pins are in double shear and the allowable shear stress is 80 MPa? Note that OA = AB = BC = 1.5m. 


what is the sequence in the making of Extreme Constructions The Meraviglia Cruise Ship




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