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A uniform solid cylinder C with mass m and radius a rolls on the rough outer surface of a fixed horizontal cylinder of radius b. In the motion, the axes of the two cylinders remain parallel to each other. Let θ be the angle between the plane containing the cylinder axes and the upward vertical.
Taking θ as generalised coordinate, obtain Lagrange's equation and verify that it is equivalent to the energy conservation equation. Initially the cylinder C is at rest on top of the fixed cylinder when it is given a very small disturbance.
Find, as a function of θ, the normal component of the reaction force exerted on C. Deduce that C will leave the fixed cylinder when θ = cos-1(4/7). Is the assumption that rolling persists up to this moment realistic?
Write a simple Matlab script to obtain the sample mean values with n = 4 for a total of 2000 sample combinations. A sampling combination from the population can be obtained by using: rand sample (population, 4, true). For each combination, the sample..
An adiabatic piston cylinder contains 1 kg of R-134a. Initially the conditions inside the piston are 200 kPa and 0 degrees C. An electric heater inside the device runs with constant voltage of 110 V and a constant 0.1A of current for one hour.
If the cooling curve was obtained at the center of the casting sketched in the figure, determine the mold constant, assuming that n = 2.
a 250-kg crate b is suspended from a cable attached to a 20-kg trolley a which rides on an inclined i-beam as shown.
r134a is condensed at a constant temperature of 30degc as it flows through the condenser of a refrigerator by rejecting
Two nuclear states have magnetic moments that differ by one nuclear magneton. When B = 0.1 tesla, the populations of the two levels are in the ratio 1 : 2. What is the temperature?
What is the maximum allowable power if the chip is flush mounted in a substrate that provides for an unheated starting length of 20 mm?
he force R is the resultant of the forces P1. P2, and P3 acting on the rectangular plate. Find P1 and P2 if R= 40kN and P3 = 20kN.
Steam at 3MPa and 400C enters an adiabatic nozzle steadily with a velocity of 40m/s and leaves at 2.5MPa and 300m/s. Determine the exit temperature in degrees C. the ratio of the inlet to exit area
An electrical current of 700 A flows through a stainless steel cable having a diameter of 5 mm and an electrical resistance of 6 X 10-4 ?/m (i.e., per meter of cable length). The cable is in an environment having a temperature of 30°C, and the tot..
Find: Determine the acceleration of P - Write your answer as a vector in terms of its x-y components. Use the following parameters in your analysis: x = 2 ft, ?x = -10 ft/s and ¨x = 0
If you let this gas expand freely until the electrons were sufficiently far apart that they could be treated as a classical gas, what then would be the temperature of the gas?
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