A 30-lb slender rod AB is 5 ft long and is pivoted about a point 0 which is 1 ft from end B. The other end is pressed against (NOT connected with) a spring of constant k = 150 lb/ft until the spring is compressed 1 ft. The rod is then in a horizontal position. The mechanism is designed such that no interference occurs during all motions. If the rod is released from rest at this position, when it rotates 45°, determine: a) The angular velocity of rod AB. b) The angular acceleration of rod AB, as well as the magnitude of the reaction force at 0. 5 ft 1ft B

A 30-lb slender rod AB is 5 ft long and is pivoted about a point 0 which is 1 ft from end B. The other end is pressed against (NOT connected with) a spring of constant k = 150 lb/ft until the spring is compressed 1 ft. The rod is then in a horizontal position. The mechanism is designed such that no interference occurs during all motions. If the rod is released from rest at this position, when it rotates 45°, determine: a) The angular velocity of rod AB. b) The angular acceleration of rod AB, as well as the magnitude of the reaction force at 0. 5 ft 1ft B

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

See similar textbooks

Similar questions

In a satellite model for a science project, given the masses of the three satellites m=1.8 kg, mg= 4 kg, and m.=5 kg that are connected with massless rods, joined at the point the rotation axis is passing through. The satellites have the distances rad R=1.5 m, R = 1 m, and Rc=2 m, from the rotation axis. The system rotates with an angular speed w = 2.7 mA RA RB RC mc 1. Calculate the moment of inertia I; for this model: /, = kg m2 m2 kg 2. Calculate the magnitude of the angular momentum L, = 3. Calculate the rotational kinetic energy K, = J 4. As the system is rotating counter-clockwise the direction of the vector is The mass mc was not properly glued and breaks away during the rotation. 1. Calculate the moment of inertia /f for this model now. If= |kg m2 2. Using the conservation of angular momentum, calculate the angular speed wf after the mass m, has broken away during rad the rotation. Wf= 3. Calculate the rotational kinetic energy in this situation: K=
25
A slender, uniform, metal rod with mass M is pivoted without friction about an axis through its midpoint and perpendicular to the rod. A horizontal spring with force constant k is attached to the lower end of the rod, with the other end of the spring attached to a rigid support. If the rod is displaced by a small angle 0 from the vertical and released, show that it moves in angular SHM and calculate the period. (Hint: Assume that the angle 0 is small enough for the approximations sin 0 z 0 and cos 0 z 1 to be valid. The motion is + w?0 = 0, and the period is then T = 21 ) simple harmonic if dt2 d²0 :)
The system is at rest with the spring unstretched when theta = 0. the 5.3 kg uniform slender bar is then given a slight clockwise nudge. The value of b is 0.45 m. (a) if the bar comes to momentary rest when the angle = 58, determine the spring constant k. (b) for the value k = 65 N/m, find the magnitude of the angular velocity of the bar when the angle = 38 degrees. a) k = 70.634 N/m
The system shown below consists of a uniform disk D that has a mass of mp = 3.0 kg and a radius of r = 1.0 meters. The disk is connected by a massless cable to a block. The system is released from rest and the disk starts rolling without sliding with the angular acceleration of a = rad 30 s2 in the clockwise direction. Determine the magnitude of the friction force (in Newtons) developed between the disk and the inclined surface at this instant. Consider 0 = 40° and g = 10 m. mp
The following mass-and-spring system has stiffness matrix K. The system is set in motion from rest (x1′(0)=x2′(0)=0)in its equilibrium position (x1'(0)=x2'(0)=0) with the given external forces F1(t)=0and F2(t)=540 cos 4t acting on the masses m1and m2,respectively. Find the resulting motion of the system and describe it as a superposition of oscillations at three different frequencies. m1 m2 k1 k2 k3 x1 x2 K= −k1+k2 k2 k2 −k2+k3 m1=1, m2=2; k1=1, k2=2, k3=2 Find the resulting motion of the system. x1(t) = x2(t) = (Type exact answers, using radicals as needed.)
Determine the following : (a) Tension in each cable when at the bottom (b) the minimum angular velocity in rpm to sustain themotion (refer to the image below)
7. Consider the system shown below. The spring is connected via a cable to the non-rotating shaft of the roller with mass m₂ and radius R. A second cable connected to the shaft passes through the two pulleys. k ww χ M₁ Use conservation of energy to derive the equations of motion. The equilibrium position corresponds to x = 0. Neglect the masses of the pulleys and assume the cable is inextensivle.
!
A drum can rotate about a fixed-point O. The A block is attached to a cord wrapping around the drum. The mass of the drum is md = 100kg and the radius is r = 0.5 m. The radius of gyration of the drum about point O is ko=0.3 m. The mass of the block is mb= 20kg. The block is released from rest. The acceleration due to gravity is g=9.81 m/s2. (1) Calculate the mass moment of inertia of the drum about the point O, IO_______(kgm2) (two decimal places)
A ball governor of the vertical compression spring type runs at a mean speed of N = 189.228 rev/min. The bell crank lever arms are a = 0.158 m and b = 0.063 m and the rotating balls have a mass of m = 2.793 kg each, and the ball radius is r = 0.114 m at the mean speed. Part A: If the speed range of the governor at the mean speed is A = 1.287 rev/min, determine the friction force Fu at the sleeve (neglect the effect of gravity on the balls). Part B: Determine the spring stiffness S that would be required to make the governor isochronous if the sleeve lift is y = 0.013 m from the mean position (assume the ball arm is vertical at the mean position).
For the same question what stiffnessk needed so the rod will stop smoothly on horizontal position 3 Answer: