4) At the instant shown the tensions in the vertical ropes AB and DE are 300 N and 200 N, respectively. A T 1.2 mi 0.4 m B Knowing that the mass of the uniform bar BE is 5 kg, determine: (a) The force P (b) The magnitude of the angular velocity of rope (c) The angular acceleration of each rope ANS. D 0.4 m E 30° A) acy = 90.2 m/s². P=173.2 N aGx = 34.64 m/s². B),C) AB =ED = 15.0k r/s AB =ED=86.6k r/s²
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- An uniform W=14 kg rod is supported by a ball-and-socket joint at A, and by the cord CG that attached to the midpoint G of the rod and by the frictionless wall at B. Given, x=562 mm, d=132 mm and g=9.81 m/s². What is the magnitude of z-component of reaction force at B? Put your answer up to 2 decimal points. 'd' mm 150 mm B 400 mm 'x' mm 22The two identical springs below are holding up the mass D. The springs each have a stiffness of 895 N/m. The mass of D is 18.8 kg. What was the unstretched length of the springs in m? A 45° D 45 C B 0.3 mQ.5) A weightless Collar C is attached to the cable CD and can freely slide on the cylindrical bar AB. If the tension in the cable CD is 200 N, determine the components of this tension parallel and perpendicular bar AB. Also find the angle between bar AB and cable CD. The coordinate of point C (80 mm, 220 mm, 80 mm). 60 mm 120 mm D 240 mm 240 mm 280 mm SC 120 mm 300 mm
- GROUP A Q1) A shaft carries five masses A, B, C, D and E which revolve at the same radius in planes which are equidistant from one another. The magnitude of the masses in planes A, C and D are 50 kg, 40 kg and 80 kg, respectively. The angle between 4 and C is 90° and that between C and D is 135º. Determine the magnitude of the masses in planes B and E and their positions to put the shaft in complete rotating balance, Q2)R - m 130° A hollow wheel of mass given by m 50 kg rolls down an incline of 30° without slipping. The inner radius of the wheel is given by R = 50 mm and its thickness is given by d = 5 mm. Gravity acts down. (a) Show that the moment of inertia of the wheel is given by Ī = 138 125 kg mm². (b) Show that the linear acceleration of the wheel's centre of gravity ā is related to the angular acceleration of the wheel a via a (55 mm)a. = (c) Analyse an appropriate free-body diagram to determine the linear acceleration of the wheel's centre of gravity ā.A. A motorcycle and rider have a combined mass of 350kg. The wheels each have a mass of 20kg, diameter of 500mm and radius of gyration of 200mm. The rider accelerates uniformly from 5m/s to 25m/s over a distance of 100m, whilst climbing a hill of slope 1 in 20. The average resistance to motion, including drag, is 105 N. 1. Determine the total work done as the motorcycle ascends the incline. 2. Calculate the amount of power developed during the climb. B. At another point in its journey, the motorcycle and rider travel at 80 km/h around a left-hand bend of radius 30m. Calculate: 1. The angular velocity of each of the wheels. 2. The moment of inertia of each wheel. 3. The magnitude and effect of the gyroscopic torque produced on the bike.
- Consider a ball rolling around in a circular path on the inner surface of a cone. The weight of the ball is shown by the vector W. Without friction, only one other force acts on the ball—a normal force, (a) Draw in the vector for the normal force. (The length of the vector depends on the next step, b.) (b) Using the parallelogram rule, show that the resultant of the two vectors is along the radial direction of the ball’s circular path. (Yes, the normal is appreciably larger than the weight!)Q3: A frozen-juice can rests on the horizontal rack of a freezer door as shown. With what maximum angu- lar velocity a can the door be "slammed" shut against its seal and not dislodge the can? Assume that the can rolls without slipping on the corner of the rack, and neglect the dimension d compared with the 500-mm distance. Ans. 1.135 rad/s 500 mm 35 mm 7 mm10. Find the magnitude of the force F acting from D toward A that will have a component of 100 lb along DB. (а) 134.3 1b (b) 125.4 lb (c) 124.3 lb (d) 144.3 1b (e) 145.4 lb
- 25 in. 25 in.. 5 in. 5 in. Cord B' Two solid spheres (radius = 3 in., W=2 lb) are mounted on a spinning horizontal rod (IR = 0.25 lb · ft s, @ =6 rad/sec) as shown. The balls are held together by a string which is suddenly cut. Determine a) angular velocity of the rod after the balls have moved to A' and B', and b) the energy lost due to the plastic impact of the spheres and stops. 2 RQ4/ Two identical spheres of radius 8 in. and weighing 2 lb on the surface of the earth are placed in contact. Find the gravitational attraction between them. Q5/ A person weighs 30 lb on the moon, where g = 5.32 ft/s2. Determine (a) the mass of the person and (b) the weight of the person on earth. Q6/ What is the weight in newtons of an object that has a mass of (a) 9 kg, (b) 0.06 kg.A 1904 Ib car starts from rest at point 1 and moves without friction down the track shown. Determine the force (Ib) exerted by the track on the car at point 2 if a = 47 ft, b = 13 ft and r= 23 ft. Round off only on the final answer expressed in 3 decimal places. WE exercise3(1).png