Determine the moment of inertia I about axis O-M for the uniform slender rod bent into the shape shown. Plot I versus θ from θ = 0 to θ = 90° and determine the minimum value of I and the angle a which its axis makes with the x-direction. (Note: Because the analysis does not […]
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The uniform sector of Prob. 8/77 is repeated here with m = 4 kg, r = 325 mm, and β = 45°. If the sector is released from rest with θ0 = 90°, plot the value of for the time period 0 ≤ t ≤ 6 s. Friction in the pivot at O results in […]
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Shown in the figure are the elements of a displacement meter used to study the motion yB = b sin wt of the base. The motion of the mass relative to the frame is recorded on the rotating drum. If l1 = 1.2 ft, l2 = 1.6 ft, l3 = 2 ft, W = 2 […]
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The assembly shown consists of two sheaves of mass m1 = 35 kg and m2 = 15 kg, outer groove radii r1 = 525 mm and r2 = 250 mm, and centroidal radii of gyration (kO)1 = 350 mm and (kO)2 = 150 mm. The sheaves are fitted to a central shaft at O with […]
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Determine the amplitude of vertical vibration of the car as it travels at a velocity v = 40 km/h over the wavy road whose contour may be expressed as a sine or cosine function with a double amplitude 2b = 50 mm. The mass of the car is 1800 kg and the stiffness of each […]
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The elements of the “swing-axle” type of independent rear suspension for automobiles are depicted in the figure. The differential D is rigidly attached to the car frame. The half-axles are pivoted at their inboard ends (point O for the half-axle shown) and are rigidly attached to the wheels. Suspension elements not shown constrain the wheel […]
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The assembly of Prob. 8/40 is repeated here with the additional information that body ABC now has mass m4 and a radius of gyration kO about its pivot at O, about which it is balanced. If a harmonic torque M = M0 cos wt is applied to body ABC, determine the equation of motion for […]
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The owner of a 3400-lb pickup truck tests the action of his rear-wheel shock absorbers by applying a steady 100-lb force to the rear bumper and measuring a static deflection of 3 in. Upon sudden release of the force, the bumper rises and then falls to a maximum of 12 in. below the unloaded equilibrium […]
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For a short interval of motion, collar A moves along its fixed shaft with a velocity vA = 2 m/s in the Y-direction. Collar B, in turn, slides along its fixed vertical shaft. Link AB is 700 mm in length and can turn within the clevis at A to allow for the angular change between […]
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The elements of a reaction-wheel attitude-control system for a spacecraft are shown in the figure. Point G is the center of mass for the system of the spacecraft and wheels, and x, y, z are principal axes for the system. Each wheel has a mass m and a moment of inertia I about its own […]
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