65651. The block has a weight of 1.5 lb and slides along the smooth chute AB. It is released from rest at A, which has coordinates of A(5 ft, 0, 10 ft). Determine the speed at which it slides off at B, which has coordinates of B(0, 8 ft, 0).
65652. Determine the radius of gyration ky of the parabolic area.
65653. Determine the inertia of the parabolic area about the x axis.
65654. The composite cross section for the column consists of two cover plates riveted to two channels. Determine the radius of gyration k with respect to the centroidal axis. Each channel has a cross-sectional area of Ac = 11.8 in.2 and moment of inertia (I )c = 349 in.4.
65655. The irregular area has a moment of inertia about the AA axis of 35 (106) mm4. If the total area is 12.0(103) mm2, determine the moment of inertia if the area about the BB axis. The DD axis passes through the centroid C of the area.
65656. The scaffold S is raised hydraulically by moving the roller at A towards the pin at B. If A is approaching B with a speed of 1.5 ft/s, determine the speed at which the platform is rising as a function of . Each link is pin-connected at its midpoint and end points and has a length of 4 ft.
65657. If rod CD has a downward velocity of 6in/s at the instant shown, determine the velocity of the gear rack A at this instant. The rod is pinned at C to gear B.
65658. As the cord unravels from the wheel's inner hub, the wheel is rotating at = 2 rad/s at the instant shown. Determine the magnitudes of the velocities of point A and B.
65659. The rotation of link AB creates an oscillating movement of gear F. If AB has an angular velocity of AB = 8 rad/s, determine the angular velocity of gear F at the instant shown. Gear E is a part of arm CD and pinned at D to a fixed point.
65660. The mechanism is used to convert the constant circular motion of rod AB into translating motion of rod CD. Compute the velocity and acceleration of CD for any angle of AB.
65661. If the block at C is moving downward at 4 ft/s, determine the angular velocity of bar AB at the instant shown.
65662. The sphere starts from rest at = 0 and rotates with an angular acceleration of = (4) rad/s2, where is measured in radians. Determine the magnitudes of the velocity and acceleration of point P on the sphere at the instant = 6 rad.
65663. Due to an engine failure, the missile is rotating at = 3 rad/s, while its mass center G is moving upward at 200 ft/s. Determine the magnitude of the velocity of its nose B at this instant.
65664. Arm ABCD is printed at B and undergoes reciprocating motion such that = (0.3 sin 4t) rad, where t is measured in seconds and the argument for the sine is in radiaus. Determine the largest speed of point A during the motion and the magnitude of the acceleration of point D at this instant.
65665. At the instant shown, gear A is rotating with a constant angular velocity of A = 6 rad/s. Determine the largest angular velocity of gear B and the maximum speed of point C.
65666. The disk rolls without slipping such that it has an angular acceleration of = 4 rad/s2 and angular velocity of = 2 rad/s at the instant shown. Determine the accelerations of points A and B on the link and the link's angular acceleration at this instant. Assume point A lies on the periphery of the disk, 150 mm from C.
65667. Knowing the angular velocity of link CD is CD = 4 rad/s, determine the angular velocities of links BC and AB at the instant shown.
65668. The safe is transported on a platform which rests on rollers, each having a radius r. If the rollers do not slip, determine their angular velocity if the safe moves forward with a velocity v.
65669. The oil pumping unit consists of a walking beam AB, connecting rod BC, and crank CD. If the crank rotates at a constant rate of 6 rad/s, determine the speed of the rod hanger H at the instant shown.
65670. Rod CD presses against AB, giving it an angular velocity. If the angular velocity of AB is maintained at = 5 rad/s, determine the required speed v of CD for any angle of rod AB.
65671. Gear C is rotating with a constant angular velocity of c = 3 rad/s. Determine the acceleration of the piston A and the angular acceleration of rod AB at the instant = 90°. Set rc = 0.2 ft and rd = 0.3 ft.
65672. The automobile with wheels 2.5 ft in diameter is traveling in a straight path at a rate of 60 ft/s. If no slipping occurs, determine the angular velocity of one of the rear wheels and the velocity of the fastest moving point on the wheel.
65673. If the rim of the wheel and its hub maintain contact with the three stationary tracks as the wheel rolls, it is neccessary that slipping occurs at the hub A if no slipping occurs at B. Under these conditions, what is the speed at A if the wheel has an angular velocity ?
65674. Gear A is in mesh with gear B as shown. If A starts from rest and has a constant angular acceleration of A = 2 rad/s2, determine the tome needed for B to attain an angular velocity of B = 50 rad/s.
65675. The 2-m-long bar is confined to move in the horizontal and vertical slots A and B. If the velocity of the slider block at A is 6 m/s, determine the bar's angular velocity and the velocity of block B at the instant = 60°.
65676. Determine the angular acceleration of link BC at the instant = 90° if the collar C has an instantaneous velocity of vc = 4 ft/s and deceleration of ac = 3 ft/s2 as shown.
65677. During a gust of wind, the blades of the windmill are given an angular acceleration of = (0.2 ) rad/s2, where is measured in radians. If initially the blades have an angular velocity of 5 rad/s, determine the speed of point P located at the tip of one of the blades just after the blade has turned two revolutions.
65678. The pulley os pin-connected to block B at A. As cord CF unwinds from the inner hub with the motion shown, cord DE unwinds from the outer rim. Determine the angular acceleration of the pulley at the instant shown.
65679. The 10-kg block rests on the platform for which = 0.4. If at the instant shown link AB has an angular velocity = 2 rad/s, determine the greatest angular acceleration of the link so that the block doesn't slip.
65680. If the cable CB is horizontal and the beam is at rest in the position shown, determine the tension in the cable at the instant the towing force F = 1500 N is applied. The coefficient of friction between the beam and the floor at A is A = 0.3. For the calculation, assume that the beam is a uniform slender rod having a mass of 100 kg.
65681. The 15-lb rod is pinned and has an angular velocity of = 5 rad/s when it is in the horizontal position shown. Determine the rod's angular acceleration and the pin reactions at this instant.
65682. Bar AB has a weight of 10 lb and is fixed to the carriage at A. Determine the internal axial force Ay, shear force V, and moment MA at A if the carriage is descending the plane with an acceleration of 4 ft/s2.
65683. A cord wrapped around the inner core of a spool. If the cord is pulled with a constant tension of 30 lb and the spool is originally at rest, determine the spool's angular Velocity when s = 8 ft of cord have unraveled. Neglect the weight of the cord. The spool and cord have a total weight of 400 lb and the radius of gyration about the axle A is kA = 1.30 ft.
65684. If the support at B is suddenly removed, determine the initial reactions at the pin A. The plate has a weight of 30 lb.
65685. A woman sits in a rigid position on her rocking chair by keeping her feet on the bottom rungs at B. At the instant shown, she has reached an extreme backward position and has zero angular velocity. Determine her forward angular acceleration and the frictional force at A necessary to prevent the rocker from slipping. The woman and the rocker have a combined weight of 180 lb and a raduis of gyration about G of kG = 2.2 ft.
65686. The wheel has a weight of 30 lb, a radius of r = 0.5 ft, and a radius of gyration of kG = 0.23 ft. If the coefficient if friction between the wheel and the plane is = 0.2, determine the wheel's angular acceleration as it rolls down the incline. Set = 12°.
65687. The slender 200-kg beam is suspended by a cable at its end as shown. If a man pushes on its other end with a horizontal force of 30 N, determine the initial acceleration of its mass center G, the beam's angular acceleration, and the tension in the cable AB.
65688. A clown, mounted on stilts, loses his balance and falls backward from the position, where it is assumed the = 0 when = 07deg;. Paralyzed with fear, he remains rigid as he falls. His mass including the stilts is 80 kg, the mass center is at G, and the radius of gyration about G is kG = 1.2 m. Determine the coefficient of friction between his shoes and the ground at A if it is observed that slipping occurs when = 30°.
65689. The dragster has a mass of 1.3 Mg and a center of mass at G. If a braking parachute is attached at C and provides a horizontal braking force FD, determine the maximum deceleration the dragster can have upon releasing the parachute without tipping the dragster over backwards (i.e., the normal force under the wheels and assume that the engine is disengaged so that the wheels are freely rolling.
65690. The sports car has a mass of 1.5 Mg and a center of mass at G. Determine the shortest time it takes for it to reach a speed of 80 km/h, starting from rest, if the engine only drives the rear wheels, whereas the front wheels are free rolling. The coefficient of friction between the wheels and road is = 0.2. Neglect the mass of the wheels for the calculation.
65691. The disk has a mass of 20 kg and is originally spinning at the end of the massless strut with an angular velocity of = 60 rad/s. If it is then placed against the wall, for which A = 0.3, determine the time required for the motion to stop. What is the force in strut BC during this time?
65692. A constant torque or twist of M = 0.4N • m is applied to the center gear A. If the system starts from rest, determine the angular velocity of each of the three (equal) smaller gears in 3 s. The smaller gears (B) are pinned at their centers, and the mass and centroidal radii of gyration of the gears are given in the figure.
65693. The square plate, where a = 0.75 ft, has a weight of 4 lb and is rotating on the smooth surface with a constant angular velocity of 1 = 10 rad/s. Determine the new angular velocity of the plate just after its corner strikes the peg P and the plate to rotate about P without rebounding.
65694. The flywheel A has a mass of 30 kg and a radius of gyration of kc = 95 mm. Disk B has a mass of 25 kg, is pinned at D, and is coupled to the flywheel using a belt which is subjected to a tension such that it does not slip at its contacting surfaces. If a motor supplies a counter-clockwise torque or twist to the flywheel, having a magnitude of M = (12t) N • m, where t is measured in seconds, determine the angular velocity of the disk 3 s after the motor is turned on. Initially, the flywheel is at rest.
65695. A cord of negligible mass is wrapped around the outer surface of the 50-lb cylinder and its end is subjected to a constant horizontal force of P = 2 lb. If the cylinder rolls without slipping at A, determine its angular velocity in 4 s starting from rest. Neglect the thickness of the cord.
65696. A horizontal circular platform has a weight of 300 lb and a radius of gyration about the z axis passing through its center O of kz = 8 ft. The platform is free to rotate about the z axis and is initially at rest. A man, having a weight of 150 lb, begins to run along the edge in a circular path of radius 10 ft. If he has a speed of 4 ft/s and maintains this speed relative to the platform, compute the angular velocity of the platform.
65697. A cord of negligible mass is wrapped around the outer surface of the 2-kg disk. If the disk is released from rest, determine its angular velocity in 3 s.
65698. The uniform rod AB has a weight of 3 lb and is released from rest without rotating from the position shown. As it falls, the end A strikes a hook S, which provides a permanent connection. Determine the speed at which the other end B strikes the wall at C.
65699. Gear A has a weight of 1.5 lb, a radius of 0.2 ft, and a radius of gyration of ko = 0.13ft. The coefficient of friction between the gear rack B and the horizontal surface is = 0.3. If the rack has a weight of 0.8 lb and is initially sliding to the left with a velocity of (vB)2 = 8 ft/s to the left. Neglect friction between the rack and the gear and assume that the gear exerts only a horizontal force on the rack.
65700. The 50-kg cylinder has an angular velocity of 30 rad/s when it is brought into contact with the horizontal surface at C. If the coefficient of friction is c = 0.2, determine how long it takes for the cylinder to stop spinning. What force is developed at the pin A during this time? The axis of the cylinder is connected to two symmetrical links. (Only AB is shown.) For the computation, neglect the weight of the links.