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- The cranks and connecting rods of a four cylinder in-line engine running at 2000 rpm are 60mm and 240mm each respectively. The cylinders are spaced 150 mm apart. If the cylinders are numbered 1 to 4 in sequence from one end, the cranks appear at intervals of 90º in an end view in the order 1-4-2-3.The reciprocating mass for each cylinder is 15 kg. Determine (i) unbalanced primary and secondary forces, (ii) unbalanced primary and secondary couples with reference to central plane of the engineAt the top A of the vehicle moving along line AC in the figureIts speed is 30 m / sec and its weight is 9 kN.Tool radius of curvature 40The reaction force to the tires when reaching point B, which is m,and so that the tires do not separate from the asphalt when it reaches point CWhat should be the radius of curvature of point C? (hA = 6 m andhC = 9 m)Referring to Prob. 18.143, (a) prove that the Poinsot ellipsoid is tangent to the invariable plane, (b) show that the motion of the rigid body must be such that the Poinsot ellipsoid appears to roll on the invariable plane. [Hint: In part a, show that the normal to the Poinsot ellipsoid at the tip of w is parallel to HO. It is recalled that the direction of the normal to a surface of equation F (x,y,z), ) = constant at a point is the same as that of grad F at point P.J
- The figure below is a system consisting of two masses MA = 1.82 kg and MB = 3.6 kg, whose distance from the pore axis is R₁ = R₂ = 15 cm, while the angular positions are 0₁ = 30° and 0 = 150° . Determine the weight and position of the balancing mass placed on planes C and D if the distance from the axis RC = RD = 15 cm.A bar weighing 2 lb per ft is bent at right angles into segments 26 in. and 13 in long. It takes to the position shown in Fig. P-1086 when the frame F to which it is pinned at A is accelerated horizontally. Determine this acceleration and the components of the reaction at A. Please show solution clearly. Answer is given but I don't get it.Thank youa rotating shaft carries four unbalanced masses 18 kg, 14 kg, 16 kg and 12 kg at radii 50 mm, 60 mm, 70 mm and 60 mm respectively. the 2nd, 3rd and 4th masses revolve in planes 80 mm, 160 mm and 280 mm respectively measured from the plane of the first mass and are angularly located at 60°, 135° and 270° respectively measured clockwise from the first mass looking from this mass end of the shaft. the shaft is dynamically balanced by two masses, both located at 50 mm radii and revolving in planes mid-way between those of 1st and 2nd masses and midway between those of 3rd and 4th masses. determine, graphically or otherwise, the magnitudes of the masses and their respective angular positions.
- 5) In ice figure skating, a couple execute a “top” (see picture). The centre of mass of the woman (58 kg) is situated 1.3 m from the axis of rotation which is vertical and passes through the centre of mass of the man (85 kg). They are spinning at a constant angular velocity equal to 3.1415 rad/s and the man and woman have moments of inertia, about their own centres of mass, equal to 1.6 and 2.5 kg.m2 respectively. Then the woman grabs the neck of the man. At this point, her moment of inertia decreases to 1.4 kg.m2 and her body centre of gravity is 0.9 m from the axis of rotation. Determine the new angular velocity. Hints: This is a conservation of angular momentum problem, and needs the parallel axis theorem to determine moments of inertia about the axis of rotation. The skaters are moving as one body with one angular velocity, but they each have their own moments of inertia given relative to their own CoMs. For the man, that’s fine…the axis they’re rotating about passes through his…While the system shown is in equilibrium, a counter-clockwise torque T =T0sin(ωt) N-m(with T0 = 226.6 and ω=7) is applied to teh disk. What is the disk angular speed ω0 = ? in rad/s at time t = 4.2 sec? ( I = 0.2 kg.m2, b = 7.8 N-m-s/r, k = 1,504 N/m, r = 0.52m )Consider the system of two blocks. Thereis no friction between block A and the tabletop. The mass of block B is5.00 kg. The pulley rotates about a frictionless axle, and the light ropedoesn’t slip on the pulley surface. The pulley has radius 0.200 m andmoment of inertia 1.30 kg . m2. If the pulley is rotating with an angularspeed of 8.00 rad/s after the block has descended 1.20 m, what is themass of block A?
- A shaft with 3 meters span between two bearings carries two masses of 10 kg and 20 kg acting at the extremities of the arms 0.45 m and 0.6 m long respectively. The planes in which these masses rotate are 1.2 m and 2.4 m respectively from the left end bearing supporting the shaft. The angle between the arms is 60°. The speed of rotation of the shaft is 200 r.p.m. If the masses are balanced by two counter-masses rotating with the shaft acting at radii of 0.3 m and placed at 0.3 m from each bearing centers, estimate the magnitude of the two balance masses and their orientation with respect to the X-axis, i.e. mass of 10 kg Note: It must be solved using the graphic method, not the equations method.A shaft with 3 meters span between two bearings carries two masses of 10 kg and 20 kg acting at the extremities of the arms 0.45 m and 0.6 m long respectively. The planes in which these masses rotate are 1.2 m and 2.4 m respectively from the left end bearing supporting the shaft. The angle between the arms is 60°. The speed of rotation of the shaft is 200 r.p.m. If the masses are balanced by two counter-masses rotating with the shaft acting at radii of 0.3 m and placed at 0.3 m from each bearing centers, estimate the magnitude of the two balance masses and their orientation with respect to the X-axis, i.e. mass of 10 kg.19-31 The 75 kg gymnast lets go of the horizontal bar in a fully stretched position A, rotating with an angular velocity of = 3 rad/s. estimate his angular velocity when he assumes a tucked position B. assume the gymnast at position A and B as a uniform slender rod and a uniform circular disk, respectively.