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Consider a system of three flipped coins. According to classical statistics,
how many different arrangements are available to this system:
(a) if the coins are distinguishable,
(b) if the coins are identical?
(c) For what fraction of the arrangements in (a) are all three heads or all
three tails?
(d) What is the true number of different heads/tails configurations available
to a system of three identical flipped coins?
(e) For what fraction of these arrangements are all three heads or all three
tails
Given the wavefunction of a standing wave: y(x,t) = A sin(πx)cos(2πt), where x and y are in meters and
t is in seconds. The position of the second anti-node from the end x = 0 is at:
Determine the area bounded by the curves y=6x =x^2 and y=x^2 2=2x
If the hoisting gear A has an initial angular velocity ωS = 8 rad/s and an angular deceleration αA = —1.5 rad/s². determine the velocity and acceleration of block C in 2 s.
Explain constant volume adiabatic combustion process in IC Engine
A pump driven at 1440 rev/min having a displacement of 12.5 ml/rev and a volumetric efficiency of 87% is used to supply fluid to a circuit with two cylinders. If the cylinder dimensions are 63 mm bore x 35 mm rod x 250 mm stroke, and 80 mm bore x 55 mm rod x 150 mm stroke, find the minimum cycle time for both cylinders to extend and retract fully.
A hydraulic cylinder having a bore of 125 mm, a rod of 80 mm diameter and a stroke of 350mm is fully extended and retract in a total time of 15 sec. The extend thrust to be exerted by the cylinder is 20 tomes, the retract thrust being 10 tormes. Determine:
(a) The theoretical pump delivery required
(b) The theoretical system pressure when the cylinder is extending.
(c) The theoretical system pressure when the cylinder is retracting.
(d) The actual pump displacement if the volumetric efficiency is 90% and the pump drive at 1440 rev/min. (e) The maximum power input to the pump if the torque efficiency is 85%.
A machine tool cylinder is connected regeneratively to give a rapid approach speed of 10 m/min for a stroke of 1 m with a theoretical thrust of 2.5 tonnes. It is then switched to conventional connection to provide a pressing speed of 0.25 m/min for 0.5 m with a theoretical thrust of 10 tonnes. The maximum pressure at the cylinder is to be 200 bar.
(a) Select a suitable standard size metric cylinder.
(b) Calculate the pump delivery required for both parts of the extend stroke.
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A cantilever beam of cross-section 90 mm. width 120 mm deep carries a UDL of 12 KN/m. over the entire length and a concentrated load of 15 KN at the right end. Find the bending stress in the beam, when the length of beam is 10 m.
