The figure shows a trolley of mass 10 kg that can move freely along a smooth fixed horizontal rail driven by a horizontal applied force, F. Pivoted to the trolley at A is a rigid link AB of mass 2 kg, length 1.5 m and inertia 0.38 kgm2 about the centre of gravity of the link, which is located at the midpoint. The link is driven by a motor mounted on the trolley which applies an anticlockwise torque T to the link. When the link is at 30° to the horizontal and the mechanism is undergoing the motion shown in the figure determine the magnitude of the reaction force acting on the link at point A in the x and y directions. The positive sense for x and y is given in the figure, and gravity can be assumed to be 10 m/s2. y+ O O O O F X Rail B Rx = 6.94 N Ry= 21.7 N Rx = 14.29 N Ry = 10.15 N Rx = 19.62 N Ry= 22.48 N Rx = 32.05 N Ry = 45.00 N 30⁰ w = 2 rad/s a = 1 rad/s² v = 0.5 m/s a = 0.5 m/s²

The figure shows a trolley of mass 10 kg that can move freely along a smooth fixed horizontal rail driven by a horizontal applied force, F. Pivoted to the trolley at A is a rigid link AB of mass 2 kg, length 1.5 m and inertia 0.38 kgm2 about the centre of gravity of the link, which is located at the midpoint. The link is driven by a motor mounted on the trolley which applies an anticlockwise torque T to the link. When the link is at 30° to the horizontal and the mechanism is undergoing the motion shown in the figure determine the magnitude of the reaction force acting on the link at point A in the x and y directions. The positive sense for x and y is given in the figure, and gravity can be assumed to be 10 m/s2. y+ O O O O F X Rail B Rx = 6.94 N Ry= 21.7 N Rx = 14.29 N Ry = 10.15 N Rx = 19.62 N Ry= 22.48 N Rx = 32.05 N Ry = 45.00 N 30⁰ w = 2 rad/s a = 1 rad/s² v = 0.5 m/s a = 0.5 m/s²

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

A 1.6-kg tube AB can slide freely on rod DE which in turn can rotate freely in a horizontal plane. Initially the assembly is rotating with an angular velocity of magnitude w = 5 rad/s and the tube is held in position by a cord. The moment of inertia of the rod and bracket about the vertical axis of rotation is 0.30 kg.m2 and the centroidal moment of inertia of the tube about a vertical axis is 0.0025 kg.m2If the cord suddenly breaks, determine (a) the angular velocity of the assembly after the tube has moved to end E, (b) the energy lost during the plastic impact at E.
A load of mass 230 kg is lifted by means of a rope which is wound several times round a drum and which then supports a balance mass of 140 kg. As the load rises, the balance mass falls. The drum has a diameter of 1.2 m and a radius of gyration of 530 mm and its mass is 70 kg. The frictional resistance to the movement of the load is 110 N. and that to the movement of the balance mass 90 N. The frictional torque on the drum shaft is 80 N-m. 2. Find the torque required on the drum, and also the power required, at the instant when the load has an upward velocity of 2.5 m/s and an upward acceleration of 1.2 m/s?. [Ans. 916.2 N-m ; 4.32 kW]
A truck with four wheels, each 750 mm diameter, travels on rails round a curve of 75 m at a speed of 50 km/h. The total mass of the truck is 5 t and its centre of gravity is midway between the axles, 1.05 m above the rails and midway between them. Each pair of wheels is driven by a motor rotating in the opposite direction to the wheels and at four times the speed. The moment of inertia of each pair of wheels is 15 Kgm2. The rails lie on a horizontal plane and 1.45 m apart. Determine the load on each rail.
A shaft carries four masses, B, C, and D of magnitude 200 kg, 300 kg, 400 kg, and 200 kg respectively and revolving at radii 80 mm, 70 mm, 60 mm, and 80 mm in planes measured from A at 300 mm, 400 mm and 700 mm. The angles between the cranks measured anticlockwise are A to B 45º, B to C 70º, and C to D 120º. the balancing masses are to be placed in planes X and Y. The distance between the planes A and X is 100 mm, between X and Y is 400 mm and between Y and D is 200 mm. If the balancing masses revolve at a radius of 100 mm, find their magnitude and angular positions.
In order to determine the mass moment of inertia of a flywheel of radius 600 mm, a 12-kg block is attached to a wire that is wrapped around the flywheel. The block is released and is observed to fall 3 m in 4.6 s. To eliminate bearing friction from the computation, a second block of mass 24 kg is used and is observed to fall 3 m in 3.1 s. Assuming that the moment of the couple due to friction remains constant, determine the mass moment of inertia of the flywheel.
3.32). As shown in Figure 3, a yo-yo toy is formed by wrapping a massless cord around adisk of radius R= 0.2 m and mass M=3 kg. The cord is vertical and its top end is fixed and the disk isinitially stationary. The cord remains vertical for the entire motion and does not slide on the disk.When the disk is released from rest, it falls down by a distance H=0.8 m, The moment of inertia ofthe disk around its center is I disk=1/2mdiskR^2a . Find the angular acceleration of the disk when it is lowered by a distance H.b . Find the angular velocity of the disk when it is lowered by a distance H.
A flywheel of mass 0.9 ton is fitted to a multi cylinder engine, which runs at a mean speed of 380 r.p.m. If the speed varies from 9 % above the mean to 6 % below it and the fluctuation energy is 1100 kN-cm, find (i) mass moment of inertia of the wheel and (ii) radius of Gyration.
A uniform disc of diameter 315mm and of mass 14 kg is mounted on one end of an arm of length 600 mm.Then the couple will _________________N-m
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?
A caravan weighs 28 kN. It has a wheel base of 2 m, track width 1m and height ofC.G. 300 mm above the ground level and lies midway between the front andrear axle. The engine flywheel rotates at 2950 rpm clockwise when viewed from thefront. The moment of inertia of the flywheel is 4 kg-m 2 and moment of inertia ofeach wheel is 3 kg-m 2 . Find the reactions between the wheels and the ground whenthe car takes a curve of 15 m radius towards right at 30 km/h, taking intoconsideration the gyroscopic and the centrifugal effects. Each wheel radius is 400 mm.
A four wheeled trolley car has a total mass 3000kg. Each axle with its two wheels and gears has a total moment of inertia of 32kgm2. Each wheel is of 400mm radius. The centre distance between the two wheels on an axle is 1.4m. Each axle is driven by a motor with a speed ratio of 1.3. Each along with it gear has a moment of inertia of 16kgm2 and rotates in the opposite direction to that of the axle. The centre of mass of the car is 1m above the rails. Calculate the limiting speed of the car when it has to travel around a curve of 250m radius without the wheels leaving the road.
A flywheel connected to a punching machine has to supply energy of 400 Nm while running at a mean angular speed of 20 radians/s. If the total fluctuation of speed is not to exceed ±2%, the mass moment of inertia of the flywheel in kg – m2 is