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A flight simulator is used to train pilots on how to recognize spatial disorientation. It has four degrees of freedom and can rotate around a planetary axis, as well as in yaw, pitch, and roll The pilot is seated so that her head B is located at
Fig. P15.220 and P15.221
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Chapter 15 Solutions
Vector Mechanics For Engineers
- Lever is attached to a gear of radius R_1 = 0.50 in and moment of inertia I_1 = 1.0 kg m^2. This gear meshes with a second gear of radius R_2 = 1.0 m and moment of inertia I_2 = 16.0 kgm^2. Each gear rotates about a fixed axis running through its center. Force F = 2.0 N is applied on the lever at a distance of 1.0 m from the center of the gear. What is the angular acceleration of each gear?arrow_forwardFind the magnitude and position of the balancing mass at a radius of 13cm by using the analytical method. Three masses m1, m2, m3, are attached to a shaft and revolve in the same plane. The masses are 12kg, 10kg, and 15kg respectively and their radii of rotations are 5cm, 6cm, 7cm respectively. The angular position of the masses m2, m3 are 45° and 145° from the mass m1.arrow_forwardThe connecting rod of a horizontal reciprocating engine is 400 mm and length of the stroke is 200mm. The mass of the reciprocating parts is 125 kg and that the connecting rod is 100 kg. The radius of gyration of the connecting rod about an axis through the centre of gravity is 120 mm and the distance of centre of gravity of the connecting rod from big end centre is 160 mm. The engine runs at750 r.p.m. Determine graphically the torque exerted on the crankshaft when the crank has turned 30° from the inner dead centre.arrow_forward
- A, B, C and D are the four masses carried by a shaft in this order. Radii of rotation of the masses are 20cm, 25 cm, 10 cm and 15 cm respectively. The masses of B, C and D are 3 kg, 5 kg and 4 kg respectively.The planes containing B and C are 25 cm apart. Angle between B and C is 90o and between B and D is220o measured in anticlockwise direction. For complete dynamic balance, find (i) The mass and angularposition of A, (ii) The position of planes A and D.arrow_forwardA coin is tossed into the air. It is observed to spin at the rate of 600 rpm about an axis GC perpendicular to the coin and to precess about the vertical direction GD Knowing that GC forms an angle of 15° with GD, determine (a) the angle that the angular velocity w of the coin forms with G (b) the rate of precession of the coin about GD.arrow_forwardThe upper and lower ends of the arms are pivoted on the axis of the governor has equal arms of length 44cm. The extension arms of the lower links are each 10cm long and parallel to the axis.When the governor at minimum and maximum position, the radii of rotation of the balls are 17cm and 24cm respectively. The mass of each ball is 10 kg and the mass of the central load is 102 kg. Determine : 1.The range of angular speed of the governor and identify the type of governor 2.Draw the line diagram when the governor at minimum and maximum positionarrow_forward
- To be able to develop an equation relating the linear distance between moving bodies to the angular position and velocity of the first or driving body and to use this relationship to derive the function for absolute velocity and acceleration of the second body. A circular cam is in contact with a rectangular lifter and used to intermittently operate a piece of equipment at the end of a lifter arm. The lifter is in contact with the highest point of the cam at the instant shown and the lifter is constrained to move only in the vertical direction. The cam has a radius of r = 5.0 in and is rotating about point O, which is offset from the center by a distance c = 2.7 in. The cam’s angular position is measured from the positive x axis and is positive clockwise. The angular velocity and acceleration are positive clockwise. Find the linear velocity of the lifter with respect to point O when the cam has an angular position of θ = 25 ∘ and is rotating with an angular velocity of ω = 3.4 rad/s…arrow_forwardQ2: The turbine rotor of a ship has a mass of 2.2 tones and rotates at 1800 rpm clockwise when viewed from the aft (rear). The radius of gyration of the rotor is 320 mm. Determine the gyroscopic couple and its effect when the (i) ship turns right at a radius of 250 m with a speed 25 km/h (ii) ship pitches with the bow rising at an angular velocity of 0.8 rad/s (iii) ship rolls at an angular velocity of 0.1 rad/s.arrow_forwardTo be able to develop an equation relating the linear distance between moving bodies to the angular position and velocity of the first or driving body and to use this relationship to derive the function for absolute velocity and acceleration of the second body. A circular cam is in contact with a rectangular lifter and used to intermittently operate a piece of equipment at the end of a lifter arm. The lifter is in contact with the highest point of the cam at the instant shown and the lifter is constrained to move only in the vertical direction. The cam has a radius of r = 5.0 in and is rotating about point O, which is offset from the center by a distance c = 2.7 in. The cam’s angular position is measured from the positive x axis and is positive clockwise. The angular velocity and acceleration are positive clockwise. The lifter with respect to point O when the angle is θ = 25 ∘, the angular velocity is ω = 3.4 rad/s, and the angular acceleration is α = 3.0 rad/s2 . Find the range of…arrow_forward
- The bar AB of 3.62kg is attached to the collar A of negligible mass and a wheel of mass 15.81kg with a turning radius of 0.16m. If at the position shown the angular velocity of the wheel is 67rpm clockwise, determine the velocity of the wheel in RPM when point B is located just below C. The angle of the bar with respect to Y is 19.47°. The answer is 93.89arrow_forwardThe system shown is composed of equal-length bars (L=0.20m). At the instant shown, the velocity of the midpoint of bar DC is 2m/s directed to the right. A. Identify the type of motion of each bar. B. Determine the angular velocities of each bar.arrow_forwardA 7.5 kg disk A radius of 0.6 m initially rotating clockwise at 300 rev/min is engaged with an 8.5 kg disk B of 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 after the meshing of the two disks.arrow_forward
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