3. A slender, rigid bar of mass 20 kg and length 4 m is rotating about its pin joint at Point A as shown in the figure below. A 50-N force is applied to the end of the rod in the vertical direction. Determine the reactions at the pin joint as well as the change in angular rotation rate at the instant shown. Use 0 = 30° and 8 = 2 rad/s. e P
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- The tensional pendulum shown in the figure consists of a horizontal circular disk of a mass M = 60 kg suspended by a vertical steel wire (G = SOGPa) of a length L = 2 m and diameter d = 4 mm. Calculate the maximum permissible angle of rotation <£m:ls of the disk (that is, the maximum amplitude of torsional vibrations) so that the stresses in the wire do not exceed 100 MPa in tension or 50 MPa in shear.A frame ABC travels horizontally with an acceleration a0(see figure). Obtain a formula for the maximum stress emax in the vertical arm AB, which has length thickness t, and mass density p.The centrifuge shown in the figure rotates in a horizontal plane (the x-y plane) on a smooth surface about the z axis (which is vertical) with an angular acceleration a. Each of the two arms has a weight w per unit length and supports a weight W = 2B/L at its end. Derive formulas for the maximum shear force and maximum bending moment in the arms, assuming b = L/9 and c = L/10.
- The inclined ladder AB supports a house painter (85 kg) at C and the weight iq = 40 K/m} of the ladder itself. Each ladder rail (t5= 4 mm) is supported by a shoe (ts= 5 mm) that is attached to the ladder rail by a bolt of diameter d = 8 mmA homogeneous cylindrical wooden beam, with diameter of 48 cm, length of 3 m and mass of 100 kg, is hung horizontally by means of two 2 m ropes, as shown in the figure. The beam is released from rest in the position where each rope makes an angle of 60° with the horizontal. Determine the tension and angular acceleration of each rope at the exact moment the beam is released from rest. Please answer it only right someone give me incorrect answer. Answer is 2.45 rad/s^2. TA is 153.4N TB is 695.3NThe disk shown in the figure rolls without slipping on the slope with an inclination angle of alpha = 28 degrees. The mass of the disk is 43 kg, its radius is R = 1.4 m, the arm of the rolling resistance is 0.012 m, and its instantaneous angular velocity is omega = 7 rad/s in the direction indicated in the figure. The disc is acted upon by a system of forces Fx = 79 N, Fy = 115 N, MO = 22 Nm, their direction is given in the figure. The disc starts up the slope, then stops and continues its downward movement. Determine the elapsed time (in seconds) from the examined moment to the stop.
- A flywheel of mass 120 kg and radius of gyration 450 mm is rotating at 760 r.p.m. It is brought to rest by means of block brake system as shown in the figure. The mass of the brake drum assembly is 5 kg. The brake drum is made of cast iron having specific heat 470 J / kg°C. and the brake system provides a braking torque of 380 N-m. If the diameter of brake drum is 300 mm, the coefficient of friction is 0.35. find 1. The force (P) to be applied at the end of the lever for the clockwise rotation of drum. 2. Assuming that the total heat generated is absorbed by the brake drum only, calculate the temperature riseAn oversized yo-yo is made from two identical solid disks each of mass M = 1.90 kgand radius R = 10.9 cm.The two disks are joined by a solid cylinder of radius r = 4.00 cm and mass m = 1.00 kg as in the figure below. Take the center of the cylinder as the axis of the system, with positive torques directed to the left along this axis. All torques and angular variables are to be calculated around this axis. Light string is wrapped around the cylinder, and the system is then allowed to drop from rest. Answer these parts: (g) Eliminate ? from the rotational second law with the expression found in part (d) and find a symbolic expression for the acceleration a in terms of m, M, g, r and R. a = (h) What is the numeric value for the system's acceleration? m/s2(i) What is the tension in the string? N(j) How long does it take the system to drop 1.17 m from rest? sA shaft turning at a uniform speed carries two uniform discs A and B of masses 10kg and 8kg respectively. The centres of the mass of the discs are each 2.5mm from the axis of rotation. The radii to the centres of mass are at right angles. The shaft is carried in bearings C and D between A and B such that AC = 0.3m, AD = 0.9m and AB = 1.2m. It is required to make dynamic loading on the bearings equal and a minimum for any given shaft speed by adding a mass at a radius 25mm in a plane E. Determine: (a) The magnitude of the mass in plane E and its angular position relative to the mass in plane A (b) The distance of the plane E from plane A (c) The dynamic loading on each bearing when the mass in plane E has been attached and the shaft rotates at 200 rev/min. For the bearing loads in the opposite direction determine all the unknown values. For the bearing loads in the same direction, show the diagrams and equations only to use for a possible solution.
- A shaft turning at a uniform speed carries two uniform discs A and B of masses 10kg and 8kg respectively. The centres of the mass of the discs are each 2.5mm from the axis of rotation. The radii to the centres of mass are at right angles. The shaft is carried in bearings C and D between A and B such that AC = 0.3m, AD = 0.9m and AB = 1.2m. It is required to make dynamic loading on the bearings equal and a minimum for any given shaft speed by adding a mass at a radius 25mm in a plane E. USING THE METHOD OF DRAWING m*r and m*r*l diagram Determine: The magnitude of the mass in plane E and its angular position relative to the mass in plane A The distance of the plane E from plane A The dynamic loading on each bearing when the mass in plane E has been attached and the shaft rotates at 200 rev/min. For the bearing loads in the opposite direction determine all the unknown values. For the bearing loads in the same direction, show the diagrams and equations only to use for a possible…A shaft turning at a uniform speed carries two uniform discs A and B of masses 10kg and 8kg respectively. The centres of the mass of the discs are each 2.5mm from the axis of rotation. The radii to the centres of mass are at right angles. The shaft is carried in bearings C and D between A and B such that AC = 0.3m, AD = 0.9m and AB = 1.2m. It is required to make dynamic loading on the bearings equal and a minimum for any given shaft speed by adding a mass at a radius 25mm in a plane E. Determine: The magnitude of the mass in plane E and its angular position relative to the mass in plane A The distance of the plane E from plane A PS – Use graphical methods to solve the balancing problemA shaft turning at a uniform speed carries two uniform discs A and B of masses 10kg and 8kg respectively. The centres of the mass of the discs are each 2.5mm from the axis of rotation. The radii to the centres of mass are at right angles. The shaft is carried in bearings C and D between A and B such that AC = 0.3m, AD = 0.9m and AB = 1.2m. It is required to make dynamic loading on the bearings equal and a minimum for any given shaft speed by adding a mass at a radius 25mm in a plane E. Determine: The dynamic loading on each bearing when the mass in plane E has been attached and the shaft rotates at 200 rev/min. For the bearing loads in the opposite direction determine all the unknown values. For the bearing loads in the same direction, show the diagrams and equations only to use for a possible solution. PS – Use graphical methods to solve the balancing problem