Please show all work for a & b. Problem 1.An aircraft's propeller consists of a rigid hub of radius R and a flexible taperedblade of length 3R that has density p (kg/m³). The propeller is rotating about the center of the hubwith a steady angular velocity, thereby creating an effective axial distributed force in the blade.Neglect forces due to gravity. The cross sectional area distribution of the blade is A(r), defined asA(r) = (5-±)4₂ : if R hubbladeR3R

To find the mass moment of inertia of the propeller, we need to consider the rigid hub and the…

Answered: Problem 1. An aircraft's propeller…

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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The in-plane angular speed of the bent bar indicated below is w = 0.2 rad/s. The dimensions of the bar are L = 0.4 m and H = 0.6 m. Find the magnitude of the velocity (in m/s) of the endpoint B. H B L Figure is from "Engineering Mechanic An Introduction to Dynamics", McGill and King.
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L W (1) (25pts) Find the description of the linear acceleration vector of the mass center of the segment (B) as functions of the distance (r), angular displacement (0), angular velocity (0), and angular acceleration (a). (2) (bonus: 5pts) Find the mass moment of inertia of the lower leg about the knee joint. Assume that the lower leg can be modeled as a cylinder. The length of the lower leg L is 30cm, and the diameter D is 4cm. The mass of the lower leg segment is 2kg. * This is a bonus problem - you learned how to calculate the mass moment of inertia in physics.
A uniform rod of mass M = 2.3 kg and length L = 0.2 m, lying on a frictionless horizontal plane, is free to pivot about a vertical axis through one end, as shown. The moment of inertia of the rod about this axis is given by 1/3 ML2. If a force F = 7 N, q = 47° acts as shown, what is the resulting angular acceleration (in rad/s2) about the pivot point?
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Dynamics
A solid bar of mass m and length L stands vertically on a frictionless table and is then released to fall down. The moment of inertia about the center of mass is Ic = mL²/12. At the moment when the top end B just reaches the ground (0-0), (a) what are the angular velocity and angular acceleration? (b) what is the center-of-mass acceleration? (c) what is the normal force of the ground to end D? Hint: It may be helpful to find out the instant rotation axis. В m. L D
A weight with mass mw=150 g is tied to a piece of thread wrapped around a spool, which is suspended in such a way that it can rotate freely. When the weight is released, it accelerates toward the floor as the thread unwinds. Assume that the spool can be treated as a uniform solid cylinder of radius R=4.00 cm and mass Ms=200 g. Find the magnitude ?a of the acceleration of the weight as it descends. Assume the thread has negligible mass and does not slip or stretch as it unwinds. Use ?=9.81 m/s2. Find the tension T in the thread.
A single cylinder reciprocating engine has speed 240 rpm, stroke 300 mm, mass of reciprocating parts 60 kg, mass of revolving parts at 200 mm radius is 37 kg. If three-fifth of the reciprocating parts and all the revolving parts are to be balanced, find: the balance mass required at a radius of 500 mm, and the residual unbalanced force when the crank has rotated 60° from top dead center. 28.00 kg, 3481.74 N 20.33 kg, 1406.76 N 25.13 kg, 2637.68 N 21.94 kg, 1899.13 N 29.20 kg, 4220.29 N
Block String Rod Disk Mech 3. As shown above, a uniform disk is mounted to an axle and is free to rotate without friction. A thin uniform rod is rigidly attached to the disk so that it will rotate with the disk. A block is attached to the end of the rod. Properties of the disk, rod, and block are as follows. Disk: Зт, radius R, moment of inertia about center ID = mR² mass = %3D Rod: m, length = 2R, moment of inertia about one end IR mR? mass = Block: mass = 2m The system is held in equilibrium with the rod at an angle 0, to the vertical, as shown above, by a horizontal string of negligible mass with one end attached to the disk and the other to a wall. Express your answers to the following in terms of m, R, 00, and g. (a) Determine the tension in the string.
A variation of the Scotch-yoke linkage in the posture shown is driven by crank 2 at w2 = 36 rad/s ccw. Find the velocity of the crosshead, link 4. yA 3 4 W2 105° 45° 02 Figure P3.26 RAO2 250 mm. %3D
finished in an analytical way

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