A uniform cylinder of mass m₁ and radius R is pivoted on frictionless bearings. A massless string wrapped around the cylinder is connected to a block of mass m2 that is on a frictionless incline of angle e as shown below. The system is released from rest when the block is at a vertical distance h above the bottom of the incline. (Use any variable or symbol stated above along with the following as necessary: g.) (a) What is the acceleration of the block? gsin 1+ m1 2m2 (b) What is the tension in the string? T = (c) What is the speed of the block as it reaches the bottom of the incline? v =

A uniform cylinder of mass m₁ and radius R is pivoted on frictionless bearings. A massless string wrapped around the cylinder is connected to a block of mass m2 that is on a frictionless incline of angle e as shown below. The system is released from rest when the block is at a vertical distance h above the bottom of the incline. (Use any variable or symbol stated above along with the following as necessary: g.) (a) What is the acceleration of the block? gsin 1+ m1 2m2 (b) What is the tension in the string? T = (c) What is the speed of the block as it reaches the bottom of the incline? v =

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

bucket of mass m is hanging from the free end of a rope whose other end is wrapped around a drum (radius R, mass M) that can rotate with negligible friction about a stationary horizontal axis. The drum is not a uniform cylinder and has unknown moment of inertia. When you release the bucket from rest, you find that it has a downward acceleration of magnitude a. What are (a) the tension in the cable between the drum and the bucket and (b) the moment of inertia of the drum about its rotation axis?
A spool of mass 60 kg is supported on two rollers at A and B as shown in FigureQ1(c). Neglect the mass of the inelastic cable, friction and the mass of therollers at A and B. Knowing that a constant pulling force P is applied in order tounwind 6 m of cable in 3 s starting from rest. The radius of gyration for the spoolis (604) mm, Appendix Ashows the examples of identifying the radius of gyration using student ID.(i) Determine the angular acceleration of the spool. (ii) Determine the pulling force P. (iii) Explain with calculation on ways to increase the acceleration of cablebeing pulled. [
The 2.00-kg slender rod shown is hanging in a vertical position and is pin-supported at point A. The slender rod is initially at rest until a 1.000-kg block C, strikes it at its end at point B.The block slides on a frictionless surface with a velocity of 3.50 m/s to the right. After the impact, it slides with a velocity of 1.250 m/s to the right, and the bar rotates with an angular velocity, ω'. 1. What gives the correct kinematic relationship relating the final velocity of the center of the rod, v' , and its angular velocity, ω'? 2. What is the coefficient of restitution, e, between the block and the slender rod? 3. What is the magnitude of the horizontal impulse at the support at point A?
The follower is attached to the end of a light telescopic rod that is pivoted at O. The follower is pressed against a frictionless spiral surface by a spring of stiffness and the free length . The equation of spiral, which lies in the horizontal plane, is , where and in radians. Immediately after the rod is released from rest in position OA, determine (a) the angular acceleration of the rod; and (b) the contact force between the follower and the spiral surface.
A spool of mass 60 kg is supported on two rollers at A and B as shown in Figure Q1(c). Neglect the mass of the inelastic cable, friction and the mass of the rollers at A and B. Knowing that a constant pulling force P is applied in order to unwind 6 m of cable in 3 s starting from rest. The radius of gyration for the spool is (600+a) mm, where a = 8. Appendix A shows the examples of identifying the radius of gyration using student ID. Determine the pulling force P.
The pulley in Fig has radius R and a moment of inertia I. The rope does not slip over the pulley, and the pulley spins on a frictionless axle. The coefficient of kinetic friction between block A and the tabletop is mk . The system is released from rest, and block B descends. Block A has mass mA and block B has mass mB . Use energy methods to calculate the speed of block B as a function of the distance d that it has descended.
A Mine cage of mass 4t is to be raised with an acceleration of 1.5 m/s by a rope passing over a hoist drum of 1.5 m diameter. What is the power required when the load has reached a velocity of 6 m/s, neglecting the inertia of of the drum and the weight of the rope, but allowing for a bearing friction torque of 3kN m at the drum. What is the power required at a uniform velocity of 6 m/s
The gear train shown operates in a horizontal plane and is used to transmit motion to the rack D of mass mD = 4.9 kg. If an input torque M = 63 N●m is applied to gear A, what will be the magnitude of the resulting acceleration a of the unloaded rack? (The mechanism which it normally drives has been disengaged.) Gear C is keyed to the same shaft as gear B. Gears A, B, and C have pitch diameters dA = 185 mm, dB = 355 mm, and dC = 185 mm, and centroidal mass moments of inertia IA = 0.45 kg●m2, IB = 3.38 kg●m2, and IC = 0.45 kg●m2, respectively. All friction is negligible.
A drum A, of mass 200 kg, external diameter 380 mm and radius of gyration 150 mm, rotates on frictionless bearings at 250 rev/min. A stationary drum, B, of mass 50 kg, external diameter 200 mm and radius of gyration 80 mm, mounted on a frictionless axis parallel to that of A, is pressed into contact with A with a force of 90 N. The coefficient of friction is 0·25. Determine: The final speeds of A and B. (b) The time of slipping. (c) The time of slipping if a torque is applied to A, to maintain the speed of A as a constant 250 rev/min.
If either a simple or a compound pendulum is used to determine experimentally the acceleration of gravity g, difficulties are encountered. In the case of the simple pendulum, the string is not truly weightless, while in the case of the compound pendulum, the exact location of the mass center is difficult to establish. In the case of a compound pendulum, the difficulty can be eliminated by using a reversible, or Kater, pendulum. Two knife edges A and B are placed so that they are obviously not at the same distance from the mass center G, and the distance l is measured with great precision. The position of a counterweight D is then adjusted so that the period of oscillation τ obtained is equal to that of a true simple pendulum of length l and that g 4π2 l/τ.
a porter governor has two balls each of mass 3 Kg and a central load of mass 15 Kg. The arms are all 200 mm long, pivoted on the axis. If the maximum and minimum radii of rotation of the balls are 160 mm and 120 mm respectively find the range of speed
A torque T of 100 N-m is applied to a wheel D having a mass of 50 kg. a diame- ter of 600 mm, and a radius of gyration of 280 mm. The wheel D is attached by a light member AB to a slider C having a mass of 30 kg. If the system is at rest at the instant shown, what is the acceleration of slider C? What is the axial force in member AB? Neglect friction everywhere, and neglect the inertia of the memberAB. (Draw FBDs)