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engineering
engineering mechanics dynamics

Questions and Answers of Engineering Mechanics Dynamics

The open square frame is constructed of four identical slender rods, each of length b. If the frame is released from rest in the position shown, determine the speed of corner A (a) After A has
The load of mass m is supported by the light parallel links and the fixed stop A. Determine the initial angular acceleration a of the links due to the application of the couple M to one end as shown.
The uniform slender bar of mass m is shown in its equilibrium configuration before the force P is applied. Compute the initial angular acceleration of the bar upon application of P. A k B
The two uniform slender bars are hinged at O and supported on the horizontal surface by their end rollers of negligible mass. If the bars are released from rest in the position shown, determine their
Links A and B each weigh 8 lb, and bar C weighs 12 lb. Calculate the angle θ assumed by the links if the body to which they are pinned is given a steady horizontal acceleration a of 4 ft/sec2. a 18"
The load of mass m is given an upward acceleration a from its supported rest position by the application of the forces P. Neglect the mass of the links compared with m and determine the initial
The cargo box of the food-delivery truck for aircraft servicing has a loaded mass m and is elevated by the application of a couple M on the lower end of the link which is hinged to the truck frame.
The sliding block is given a horizontal acceleration to the right that is slowly increased to a steady value a. The attached pendulum of mass m and mass center G assumes a steady angular deflection
Each of the uniform bars OA and OB has a mass of 2 kg and is freely hinged at O to the vertical shaft, which is given an upward acceleration a = g/2. The links which connect the light collar C to the
The linkage consists of the two slender bars and moves in the horizontal plane under the influence of force P. Link OC has a mass m and link AC has a mass 2m. The sliding block at B has negligible
The portable work platform is elevated by means of the two hydraulic cylinders articulated at points C. The pressure in each cylinder produces a force F. The platform, man, and load have a combined
Each of the three identical uniform panels of a segmented industrial door has mass m and is guided in the tracks (one shown dashed). Determine the horizontal acceleration a of the upper panel under
The mechanical tachometer measures the rotational speed N of the shaft by the horizontal motion of the collar B along the rotating shaft. This movement is caused by the centrifugal action of the two
A planetary gear system is shown, where the gear teeth are omitted from the figure. Each of the three identical planet gears A, B, and C has a mass of 0.8 kg, a radius r = 50 mm, and a radius of
The aerial tower shown is designed to elevate a workman in a vertical direction. An internal mechanism at B maintains the angle between AB and BC at twice the angle θ between BC and the ground. If
The vehicle is used to transport supplies to and from the bottom of the 25-percent grade. Each pair of wheels, one at A and the other at B, has a mass of 140 kg with a radius of gyration of 150 mm.
A person who walks through the revolving door exerts a 90-N horizontal force on one of the four door panels and keeps the 15° angle constant relative to a line which is normal to the panel. If each
The 75-kg flywheel has a radius of gyration about its shaft axis of k̅ = 0.50 m and is subjected to the torque M = 10(1 − e−t) N∙m, where t is in seconds. If the flywheel is at rest at time t
Determine the angular momentum of the earth about the center of the sun. Assume a homogeneous earth and a circular earth orbit of radius 149.6(106) km. Consult Table D/2 of Appendix D for other
The frame of mass m is welded together from uniform slender rods. The frame is released from rest in the upper position shown and constrained to fall vertically by two light rollers which travel
The frictional moment Mƒ acting on a rotating turbine disk and its shaft is given by Mƒ = kw2 where w is the angular velocity of the turbine. If the source of power is cut off while the turbine is
The cable drum has a mass of 800 kg with radius of gyration of 480 mm about its center O and is mounted in bearings on the 1200-kg carriage. The carriage is initially moving to the left with a speed
The 15-kg wheel with 150-mm outer radius and 115-mm centroidial radius of gyration is rolling without slipping down the 15° incline at a speed of 2 m/s when a tension T = 30 N is applied to a cable
A uniform slender bar of mass M and length L is translating on the smooth horizontal x-y plane with a velocity vM when a particle of mass m traveling with a velocity vm as shown strikes and becomes
The homogeneous circular cylinder of mass m and radius R carries a slender rod of mass m/2 attached to it as shown. If the cylinder rolls on the surface without slipping with a velocity vO of its
The system of Prob. 3/166 is repeated here. The system is released from rest at position x = 0 with the cable taut at time t = 0, with the 10-kg block moving down the rough incline with a speed of
The disk of Prob. 5/22 is at the angular position θ = 0 at time t = 0. Its angular velocity at t = 0 is ω0 = 0.1 rad /s, and then it experiences an angular acceleration given by α = 2θ, where θ
The two gears form an integral unit and roll on the fixed rack. The large gear has 48 teeth, and the worm turns with a speed of 120 rev/min. Find the velocity vO of the center O of the gear. 150
The speed of the center of the earth as it orbits the sun is v = 107 257 km/h, and the absolute angular velocity of the earth about its north–south spin axis is ω = 7.292(10−5) rad/s. Use the
The center C of the smaller wheel has a velocity vC = 0.4 m/s in the direction shown. The cord which connects the two wheels is securely wrapped around the respective peripheries and does not slip.
The circular disk of radius 8 in. is released very near the horizontal surface with a velocity of its center vO = 27 in./sec to the right and a clockwise angular velocity ω = 2 rad/sec. Determine
A mechanism for pushing small boxes from an assembly line onto a conveyor belt is shown with arm OD and crank CB in their vertical positions. The crank revolves clockwise at a constant rate of 1
At the instant represented, crank OB has a clockwise angular velocity ω = 0.8 rad/sec and is passing the horizontal position. By the method of this article, determine the corresponding speed of the
Crank OA rotates with a counterclockwise angular velocity of 9 rad/s. By the method of this article, determine the angular velocity w of link AB and the velocity of roller B for the position
The mechanism of Prob. 5/100 is now shown in a different position, with the crank OA 30° below the horizontal as illustrated. Determine the angular velocity w of link AB and the velocity of roller
If link OA has a clockwise angular velocity of 2 rad/s in the position for which x = 75 mm, determine the velocity of the slider at B by the method of this article. A 300 mm 300 mm B 100 mm -X-
The switching device of Prob. 5/76 is repeated here. If the vertical control rod has a downward velocity v = 2 ft/sec when the device is in the position shown, determine the corresponding speed of
The mechanism of Prob. 5/77 is repeated here. By the method of this article, determine the angular velocity of link AB and the velocity of collar B for the position shown. Assume the quantities ω0
The bar of Prob. 5/82 is repeated here. The ends of the 0.4-m bar remain in contact with their respective support surfaces. End B has a velocity of 0.5 m/s and an acceleration of 0.3 m/s2 in the
Determine the acceleration of point B on the equator of the earth, repeated here from Prob. 5/63. Use the data given with that problem and assume that the earth’s orbital path is circular,
The spoked wheel of Prob. 5/73 is repeated here with additional information supplied. For a given cord speed v and acceleration a at point P and wheel radius r, determine the acceleration of point B
Calculate the angular acceleration of the plate in the position shown, where control link AO has a constant angular velocity wOA = 4 rad/sec and θ = 60° for both links. D B. --- 12"- 5" C 10" WOA
The bar AB of Prob. 5/71 is repeated here. At the instant under consideration, roller B has just begun moving on the 15° incline, and the velocity and acceleration of roller A are given. Determine
Determine the angular acceleration aAB of AB for the position shown if link OB has a constant angular velocity w. В rv2 To A r-
Determine the angular acceleration of AB and the linear acceleration of A for the position θ = 90° if θ˙ = 4 rad/s and θ¨ = 0 at that position. А 500 mm 400 mm y | OB -- х TO 400 mm
The two connected wheels of Prob. 5/64 are shown again here. Determine the magnitude of the acceleration of point D in the position shown if the center C of the smaller wheel has an acceleration to
The end rollers of bar AB are constrained to the slot shown. If roller A has a downward velocity of 1.2 m/s and this speed is constant over a small motion interval, determine the tangential
If the wheel in each case rolls on the circular surface without slipping, determine the acceleration of point C on the wheel momentarily in contact with the circular surface. The wheel has an angular
The system of Prob. 5/100 is repeated here. Crank OA rotates with a constant counterclockwise angular velocity of 9 rad/s. Determine the angular acceleration aAB of link AB for the position shown. G
The system of Prob. 5/101 is repeated here. Crank OA is rotating at a counterclockwise angular rate of 9 rad /s, and this rate is decreasing at 5 rad/s2. Determine the angular acceleration aAB of
The triangular plate ABD has a clockwise angular velocity of 3 rad/sec and link OA has zero angular acceleration for the instant represented. Determine the angular accelerations of plate ABD and link
The mechanism of Prob. 5/77 is repeated here. The angular velocity w0 of the disk is constant. For the instant represented, determine the angular acceleration aAB of link AB and the acceleration
The system of Prob. 5/84 is repeated here. If the vertical rod has a downward velocity v = 0.8 m/s and an upward acceleration a = 1.2 m/s2 when the device is in the position shown, determine the
The shaft of the wheel unit rolls without slipping on the fixed horizontal surface. If the velocity and acceleration of point O are 3 ft/sec to the right and 4 ft/sec2 to the left, respectively,
Plane motion of the triangular plate ABC is controlled by crank OA and link DB. For the instant represented, when OA and DB are vertical, OA has a clockwise angular velocity of 3 rad/s and a
The system of Prob. 5/110 is repeated here. At the instant under consideration, the rod of the hydraulic cylinder is extending at the constant rate vA = 2 m/s. Determine the angular acceleration
The velocity of roller A is vA = 0.5 m/s to the right as shown, and this velocity is momentarily decreasing at a rate of 2 m/s2. Determine the corresponding value of the angular acceleration a of bar
In the design of this linkage, motion of the square plate is controlled by the two pivoted links. Link OA has a constant angular velocity w = 4 rad/s during a short interval of motion. For the
If the piston rod of the hydraulic cylinder C has a constant upward velocity of 0.5 m/s, calculate the acceleration of point D for the position where θ is 45°. D y A C BO 300 mm 100 mm
Motion of link ABC is controlled by the horizontal movement of the piston rod of the hydraulic cylinder D and by the vertical guide for the pinned slider at B. For the instant when θ = 45°, the
The deployment mechanism for the spacecraft magnetometer boom of Prob. 5/88 is shown again here. The driving link OB has a constant clockwise angular velocity wOB of 0.5 rad/sec as it crosses the
The four-bar linkage of Prob. 5/86 is repeated here. If the angular velocity and angular acceleration of drive link OA are 10 rad/s and 5 rad/s2, respectively, both counterclockwise, determine the
The elements of a power hacksaw are shown in the figure. The saw blade is mounted in a frame which slides along the horizontal guide. If the motor turns the flywheel at a constant counterclockwise
An intermittent-drive mechanism for perforated tape F consists of the link DAB driven by the crank OB. The trace of the motion of the finger at D is shown by the dashed line. Determine the magnitude
The disk rotates about a fixed axis through O with angular velocity w = 5 rad/s and angular acceleration a = 3 rad/s2 at the instant represented, in the directions shown. The slider A moves in the
The sector rotates with the indicated angular quantities about a fixed axis through point B. Simultaneously, the particle A moves in the curved slot with constant speed u relative to the sector.
The slotted wheel rolls to the right without slipping, with a constant speed v = 2 ft/sec of its center O. Simultaneously, motion of the sliding block A is controlled by a mechanism not shown so that
The disk rolls without slipping on the horizontal surface, and at the instant represented, the center O has the velocity and acceleration shown in the figure. For this instant, the particle A has the
The cars of the roller coaster have a speed v = 25 ft/sec at the instant under consideration. As rider B passes the topmost point, she observes a stationary friend A. What velocity of A does she
An experimental vehicle A travels with constant speed v relative to the earth along a north–south track. Determine the Coriolis acceleration aCor as a function of the latitude θ. Assume an
Car B is rounding the curve with a constant speed of 54 km/h, and car A is approaching car B in the intersection with a constant speed of 72 km/ h. Determine the velocity which car A appears to have
The small collar A is sliding on the bent bar with speed u relative to the bar as shown. Simultaneously, the bar is rotating with angular velocity w about the fixed pivot B. Take the x-y axes to be
A train traveling at a constant speed v = 25 mi/hr has entered a circular portion of track with a radius R = 200 ft. Determine the velocity and acceleration of point A of the train as observed by the
Vehicle A travels west at high speed on a perfectly straight road B which is tangent to the surface of the earth at the equator. The road has no curvature whatsoever in the vertical plane. Determine
Aircraft B has a constant speed of 540 km/h at the bottom of a circular loop of 400-m radius. Aircraft A flying horizontally in the plane of the loop passes 100 m directly under B at a constant speed
Bar OC rotates with a clockwise angular velocity wOC = 2 rad/s. The pin A attached to bar OC engages the straight slot of the sector. Determine the angular velocity w of the sector and the velocity
A smooth bowling alley is oriented north–south as shown. A ball A is released with speed v along the lane as shown. Because of the Coriolis effect, it will deflect a distance δ as shown. Develop a
Under the action of its stern and starboard bow thrusters, the cruise ship has the velocity vB = 1 m/s of its mass center B and angular velocity w = 1 deg/s about a vertical axis. The velocity of B
The air transport B is flying with a constant speed of 480 mi/hr in a horizontal arc of 9-mi radius. When B reaches the position shown, aircraft A, flying southwest at a constant speed of 360 mi/hr,
Car A is traveling along the straightaway with constant speed v. Car B is moving along the circular on-ramp with constant speed v/2. Determine the velocity and acceleration of car A as seen by an
For the instant represented, link CB is rotating counterclockwise at a constant rate N = 4 rad/s, and its pin A causes a clockwise rotation of the slotted member ODE. Determine the angular velocity w
The disk rotates about a fixed axis through point O with a clockwise angular velocity w0 = 20 rad/s and a counterclockwise angular acceleration a0 = 5 rad/s2 at the instant under consideration. The
All conditions of the previous problem remain the same, except now, rather than rotating about a fixed center, the disk rolls without slipping on the horizontal surface. If the disk has a clockwise
The space shuttle A is in an equatorial circular orbit of 240-km altitude and is moving from west to east. Determine the velocity and acceleration which it appears to have to an observer B fixed to
Determine the angular acceleration of link EC in the position shown, where w = β˙ = 2 rad/sec and β¨ = 6 rad/sec2 when θ = β = 60°. Pin A is fixed to link EC. The circular slot in link DO has
One wheel of an experimental vehicle F, which has a constant velocity v = 36 km / h, is shown. The wheel rolls without slipping and causes an oscillation of the slotted arm through the action of its
The circular disk of radius r rotates about a fixed axis through point O with the angular properties indicated in the figure. Determine the instantaneous velocity and acceleration of point A. Take
The circular disk rotates about its z-axis with an angular velocity w = 2 rad/s. A point P located on the rim has a velocity given by v = −0.8i − 0.6j m/s. Determine the coordinates of P and the
The frictional resistance to the rotation of a flywheel consists of a retardation due to air friction which varies as the square of the angular velocity and a constant frictional retardation in the
What angular velocity w of bar AC will result in point B having zero velocity? What would be the corresponding velocity of point C? Take the length L of the bar and the velocity v of the collar as
The rectangular plate rotates about its fixed z-axis. At the instant considered its angular velocity is w = 3 rad/s and is decreasing at the rate of 6 rad/s per second. For this instant write the
Roller B of the linkage has a velocity of 0.75 m/s to the right as the angle θ passes 60° and bar AB also makes an angle of 60° with the horizontal. Locate the instantaneous center of zero
Rotation of the slotted bar OA is controlled by the lead screw that imparts a horizontal velocity v to collar C. Pin P is attached to the collar. Determine the angular velocity w of bar OA in terms
The helicopter is flying in the horizontal x-direction with a velocity v = 120 mi/hr, and the plane of rotation of the 26-ft-diameter rotor is tilted 10° from the horizontal x-y plane. The rotor
The large power-cable reel is rolled up the incline by the vehicle as shown. The vehicle starts from rest with x = 0 for the reel and accelerates at the constant rate of 2 ft/sec2. For the instant
The isosceles triangular plate is guided by the two vertex rollers A and B which are confined to move in the perpendicular slots. The control rod gives A a constant velocity vA to the left for an
The right-angle bar with equal legs weighs 6 lb and is freely hinged to the vertical plate at C. The bar is prevented from rotating by the two pegs A and B fixed to the plate. Determine the
The driver of a pickup truck accelerates from rest to a speed of 45 mi / hr over a horizontal distance of 225 ft with constant acceleration. The truck is hauling an empty 500-lb trailer with a
A passenger car of an overhead monorail system is driven by one of its two small wheels A or B. Select the one for which the car can be given the greater acceleration without slipping the driving
The uniform box of mass m slides down the rough incline. Determine the location d of the effective normal force N. The effective normal force is located at the centroid of the nonuniform pressure

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