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ENGINEERING MECH DYNAMICS W/MASTREV
- A yoyo is constructed by attaching three uniform, solid disks along their central axes as shown. The two outer disks are identical, each with mass M = 58 g, radius R = 3.3 cm, and moment of inertia 1/2MR2. The central, smaller disk has mass M/2 and radius R/2. A light, flexible string of negligible mass is wrapped counterclockwise around the central disk of the yoyo. The yoyo is then placed on a horizontal tabletop and the string is gently pulled with a constant force F = 0.25 N. The tension in the string is not sufficient to cause the yoyo to leave the tabletop. In this problem consider the two cases show. In Case 1 the string is pulled straight up, perpendicular to the tabletop. In Case 2 the string is pulled horizontally, parallel to the tabletop. In both cases the yoyo rolls without slipping. In both the cases shown what is the magnitude of the tourqe t excerted by the string about the contact point of the yo-yo wiith the table in N*m. What is the moment of intertia of the yo-yo…arrow_forwardIn the multi-rotor system shown below, m1=2 kg, m2=5 kg, r1=36 mm, r2=65 mm, z1=119 mm, z2=414 mm, θ1=118o, θ2=252o. We have 2 kg masses to balance the multi-rotor shaft. Answer questions a, b, c, and d accordingly. 1/ Determine the radius at which the 2 kg mass will be placed on the R plane (mm). a.35,763 b.268,220 c.53,644 D.107,288 2/Determine the angle (degrees) at which the 2 kg mass will be placed on the R plane. a.69,256 b.83,107 c.90,033 D.55,405 3/ Determine the radius at which the 2 kg mass will be placed on the L plane (mm). a.105,006 b.12,251 c.36,752 D.18,376 4/Determine the angle (degrees) at which the 2 kg mass will be placed on the L plane. a.30,085 b.37,607 c.43,248 D.45,128 solve the question by using the rules of Machine Dynamicsarrow_forwardOne end of cable AB is fixed, whereas the other end passes over a smooth pulley at B. If the mass of the cable is 1.2 kg/m and the sag is H = 1.6 m, determine the mass M that is attached to the free end of. the cable.arrow_forward
- A cylinder shown has a weight of 100lb Assuming the cylinder to be solid indetermining the moment of inertiaa.Determine the velocity of the cylinder after it has rolled 10ft from restif the horizontal force P applied at A is 10lbb.Determine the velocity of the cylinder after it has rolled 10 ft fromrest if the horizontal force P=10lb is applied at Bc.Determine the velocity of the cylinder after it has rolled 10 ft fromrest if the horizontal force P=10lb is applied at Carrow_forwardA cylinder shown has a weight of 100lb Assuming the cylinder to be solid indetermining the moment of inertiaa.Determine the velocity of the cylinder after it has rolled 10ft from restif the horizontal force P applied at A is 10lbb.Determine the velocity of the cylinder after it has rolled 10 ft fromrest if the horizontal force P=10lb is applied at Bc.Determine the velocity of the cylinder after it has rolled 10 ft fromrest if the horizontal force P=10lb is applied atarrow_forwardA 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.arrow_forward
- A cord 3.0 m long is coiled around the axle of a wheel. The cord is pulled with a constant force of 40 N. When the cord leaves the axle, the wheel is rotating at 2.0 rev/s. Determine the moment of inertia of the wheel and axle. Neglect friction.arrow_forward3) The force F, is applied to a rope which wraps around a hip with a radius of 200 mm. The disk has a mass of 30 kg. The disk moves in a vertical plane and has a radius of gyration of mass of 0.5 m with respect to a horizontal axis through the mass centre perpendicular to the plane of motion. The magnitude of the force F, in newtons is given by the ex- pression F, = 100+ 30^2, where t is in seconds. The sys- tem is released from rest when t is zero. When t = 4 s, determine(a) The angular velocity of the disk.(b) The velocity of point A on the rope.arrow_forwardA 7.5-kg disk A radius 0.6 m initially rotating clockwise at 300 rev/min is engaged with an 8.5-kg disk B radius 0.4 m initially rotating counter-clockwise at 700 rev/min, where the moment of inertia of a disk is given as I=1/2mr^2. Determine their combined angular speed (in rpm) and direction of rotation after the meshing of the two disk.arrow_forward
- A stepped cylinder has the dimensions R₁ = 0.30 m, R₂ = 0.65 m, and the radius of gyration, k, is 0.35 m. The mass of the stepped cylinder is 100 kg. Weights A and B are connected to the cylinder. If weight B has a mass of 80 kg, and weight A has a mass of 50 kg, how far does A move in 5 seconds? In which direction does it move? (Draw all FBDs)arrow_forwardA shaft carries four masses A, B, C and D of magnitude 10 kg, 20 kg, 15 kg and 25 kg respectively and revolving at radii 100 mm, 50 mm, 80 mm and 120mm in planes measured from A at 100 mm, 300 mm and 500 mm. The angles between the cranks measured anticlockwise are A to B = 40°, B to C = 50° and C to D = 150°. The balancing masses are to be placed in planes X and Y. The distance between the planes A and X is 50 mm, between X and Y is 350 mm. If the balancing masses revolve at a radius of 50 mm, find the magnitude for mass on plane X (consider plane X as the refernce plane).arrow_forward3.32). 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.arrow_forward
- International Edition---engineering Mechanics: St...Mechanical EngineeringISBN:9781305501607Author:Andrew Pytel And Jaan KiusalaasPublisher:CENGAGE L