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engineering
engineering mechanics dynamics

Engineering Mechanics Dynamics 8th Edition James L. Meriam, L. G. Kraige, J. N. Bolton - Solutions

The motor turns the disk at the constant speed p = 30 rad/sec. The motor is also swiveling about the horizontal axis B-O (y-axis) at the constant speed θ˙ = 2 rad/sec. Simultaneously, the entire assembly is rotating about the vertical axis C-C at the constant rate q = 8 rad/sec. For the instant
The collars at the ends of the telescoping link AB slide along the fixed shafts shown. During an interval of motion, vA = 5 in./sec and vB = 2 in./sec. Determine the vector expression for the angular velocity wn of the centerline of the link for the position where yA = 4 in. and yB = 2 in. FYB B UB
The rectangular steel plate of mass 12 kg is welded to the shaft with its plane tilted 15° from the plane (x-y) normal to the shaft axis. The shaft and plate are rotating about the fixed z-axis at the rate N = 300 rev/min. Determine the angular momentum HO of the plate about the given axes and
Each of the two grinding wheels has a diameter of 6 in., a thickness of 3/4 in., and a specific weight of 425 lb/ft3. When switched on, the machine accelerates from rest to its operating speed of 3450 rev/min in 5 sec. When switched off, it comes to rest in 35 sec. Determine the motor torque
The assembly from Prob. 3/219 is repeated here with the following additional information. The 2-kg collar at C has an outer diameter of 80 mm and is press fitted to the light 50-mm-diameter shaft. Each spoke has a mass of 1.5 kg and carries a 3-kg sphere with a radius of 40 mm attached to its end.
Repeat Prob. 6/74, except that the direction of the applied force has been changed as shown in the figure. m B. А
Repeat Prob. 6/80 for the case where the cable configuration has been changed as shown in the figure. T m, E G
The system of Prob. 6/20 is repeated here. If the hoop- and semicylinder-assembly is centered on the top of the stationary cart and the system is released from rest, determine the initial acceleration a of the cart and the angular acceleration a of the hoop and semicylinder. Friction between the
The crank OA rotates in the vertical plane with a constant clockwise angular velocity w0 of 4.5 rad/s. For the position where OA is horizontal, calculate the force under the light roller B of the 10-kg slender bar AB. 0.4 m A 0.8 m 1.0 m (B
The rectangular plate of Prob. 6/94 is repeated here. The cables at A and B are now attached to a 50-lb trolley which is constrained to move in the horizontal guide. If the cable at A suddenly breaks, calculate the tension TB in the cable at B an instant after the break occurs and the acceleration
The robotic device of Prob. 6/68 is repeated here. Member AB is rotating about joint A with a counterclockwise angular velocity of 2 rad/s, and this rate is increasing at 4 rad/s2. Determine the moment MB exerted by arm AB on arm BC if joint B is held in a locked condition. The mass of arm BC is 4
The uniform 12-ft pole is hinged to the truck bed and released from the vertical position as the truck starts from rest with an acceleration of 3 ft/sec2. If the acceleration remains constant during the motion of the pole, calculate the angular velocity w of the pole as it reaches the horizontal
The 20-kg wheel has an eccentric mass which places the center of mass G a distance r̅ = 70 mm away from the geometric center O. A constant couple M = 6 N∙ m is applied to the initially stationary wheel, which rolls without slipping along the horizontal surface and enters the curve of radius R =
The 8-kg crank OA, with mass center at G and radius of gyration about O of 0.22 m, is connected to the 12-kg uniform slender bar AB. If the linkage is released from rest in the position shown, compute the velocity v of end B as OA swings through the vertical. -0.4 m – A G !0.18 m! 1.0 m 0.8 m B
The sheave of 400-mm radius has a mass of 50 kg and a radius of gyration of 300 mm. The sheave and its 100-kg load are suspended by the cable and the spring, which has a stiffness of 1.5 kN/m. If the system is released from rest with the spring initially stretched 100 mm, determine the velocity of
Motive power for the experimental 10-Mg bus comes from the energy stored in a rotating flywheel which it carries. The flywheel has a mass of 1500 kg and a radius of gyration of 500 mm and is brought up to a maximum speed of 4000 rev/min. If the bus starts from rest and acquires a speed of 72 km/h
The homogeneous solid semicylinder is released from rest in the position shown. If friction is sufficient to prevent slipping, determine the maximum angular velocity w reached by the cylinder as it rolls on the horizontal surface.
The figure shows the side view of a door to a storage compartment. As the 40-kg uniform door is opened, the light rod slides through the collar at C and compresses the spring of stiffness k. With the door closed (θ = 0), a constant force P = 225 N is applied to the end of the door via a cable. If
Reconsider the door of Prob. 6/144. If the door is in the closed vertical position when a constant input force P = 225 N is applied through the end of the cable, determine the maximum angle θmax reached by the door before it comes to a stop. Plot the angular velocity of the door over this period
A small experimental vehicle has a total mass m of 500 kg including wheels and driver. Each of the four wheels has a mass of 40 kg and a centroidal radius of gyration of 400 mm. Total frictional resistance R to motion is 400 N and is measured by towing the vehicle at a constant speed on a level
The two slender bars each of mass m and length b are pinned together and move in the vertical plane. If the bars are released from rest in the position shown and move together under the action of a couple M of constant magnitude applied to AB, determine the velocity of A as it strikes O. B 0:0 M A
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 dropped a distance b (b) After A has dropped a distance 2b. The small wheels roll without
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. M b. b, OG m т А
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 initial angular acceleration a as they collapse in the vertical plane. A B 9.
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" A 18" B C
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 acceleration a. P 9. m a
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 horizontal slots allow the linkage to unfold as the cargo box is elevated. Determine the upward
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 θ. The torsion spring at O exerts a moment M = kTθ on the pendulum to oppose the angular
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 bars have negligible mass, and the collar slides freely on the shaft. The spring has a stiffness k
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 mass. Without dismembering the system, determine the initial angular acceleration of the links as P
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 mass m, and the mass of the linkage is small and may be neglected. Determine the upward acceleration
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 action of the force P. Neglect any friction in the guide rollers. - P Horizontal 45° Vertical
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 12-oz weights A, which rotate with the shaft. Collar C is fixed to the shaft. Determine the
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 gyration of 30 mm about its center. The spider E has a mass of 1.2 kg and a radius of gyration about O
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 combined mass of the man and the cab is 200 kg and if all other masses are neglected, determine
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. The drum C has a mass of 40 kg and a radius of gyration of 100 mm. The total mass of the vehicle is
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 panel is modeled by a 60-kg uniform rectangular plate which is 1.2 m in length as viewed from above,
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 = 0, determine its angular velocity w at t = 3 s. MY
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 needed information. Comment on the relative contributions of the terms I̅w and mv̅ d. Sunlight
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 along the smooth slots. The roller at A catches in the support at O without rebounding and serves as a
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 running with an angular velocity w0, determine the time t for the speed of the turbine to drop to
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 of 1.5 m/s, and the drum is rotating counterclockwise with an angular velocity of 3 rad/s when a
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 wrapped securely around an inner hub with a radius of 100 mm. Determine the time t required for the
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 embedded in the bar. Determine the final linear and angular velocities of the bar with its embedded
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 center O, determine the angular momenta HG and HO of the system about its center of mass G and about O
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 0.3 m/s, and with the spring stretched 25 mm. Plot the velocity of the block as a function of the
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 is in radians and α is in radians per second squared. Determine the angular position of point A at
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 mm 60 mm
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 value R = 6371 km for the radius of the earth and determine the velocities of points A, B, C, and D,
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. Calculate the speed of point D when in the position shown. Also compute the change ∆x which occurs
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 the velocities of points A and P of the disk. Describe the motion upon contact with the ground. y L--x
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 evolution every 2 seconds. For the position shown, determine the speed at which the box is being shoved
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 guide roller A in the 20° slot and the speed of point C midway between A and B. 10" OB C/20" 40 20°
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 illustrated. Also, fi nd the velocity of the center G of link AB. B G 100 mm 9 rad/s A 80 mm AB = 200 mm
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 B. B 100 mm 9 rad/s 30° 80 mm A AB = 200 mm
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 point A by the method of this article. Roller C is in continuous contact with the inclined surface. A
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 and r to be known. A 2r 45° В
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 directions shown. Determine the angular acceleration of the bar and the acceleration of end A. A 30°
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, consulting Table D/2 as necessary. Consider the center of the sun fixed and neglect the tilt of the axis of
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 with respect to point A. P r y B A L--x
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 the angular acceleration of bar AB and the acceleration of roller B. VA B 15° А
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 right of 0.8 m /s2 and has reached a velocity of 0.4 m/s at this instant. B A 200 mm 100 mm- 150
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 acceleration of roller B as it passes the topmost position. The value of R is 0.5 m. B R VA 1.5R
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 velocity w and an angular acceleration a. y y R a OK | (a) (b) R
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 100 mm 9 rad/s A 80 mm AB = 200 mm
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 link AB for the position shown. B 100 mm 9 rad/s G. 30° 80 mm A AB = 200 mm
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 BC for this instant. D 5" B 5" 3" 5" 3" C A - 7" –
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 aB of collar B. Assume the quantities w0 and r to be known. A 2r 45° В
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 corresponding angular acceleration a of bar AB and the magnitude of the acceleration of roller B.
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, determine the accelerations of points A and D. A y | L-- x 10" ao = 2" vo = 4 ft/sec2 3 ft/sec C D
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 counterclockwise angular acceleration of 10 rad/s2. Determine the angular acceleration of DB for this
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 aOB of link OB. A VA = 2 m/s 60° 180 mm 120 mm В 15°
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 AB as well as the tangential acceleration of roller B along the circular guide. The value of R is
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 instant represented, θ = tan−1 4/3 and AB is parallel to the x-axis. For this instant, determine 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 piston rod is retracting at the constant rate vC = 0.6 ft/sec. Determine the acceleration of point A
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 vertical position. Determine the angular acceleration CA of the boom for the position shown where tan
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 angular accelerations of bars AB and BC for the instant represented. В 15° 240 mm 80 mm 200 @0, doy
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 speed of 60 rev/min, determine the acceleration of the blade for the position where θ = 90°, and fi
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 of the acceleration of D at the instant represented when both OB and CA are horizontal if OB has a
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 straight slot. Determine the absolute velocity and acceleration of A for the same instant, when x = 36
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. Determine the absolute velocity and acceleration of particle A, and identify the Coriolis acceleration.
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 x˙ = 1.5 ft/sec with x¨ = 0. Determine the magnitude of the acceleration of A for the instant
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 indicated speed u and time rate of change of speed u˙, both relative to the disk. Determine 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 observe? At the position under consideration, the center of curvature of the path of rider B is point C.
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 earth-fixed rotating frame Bxyz and a spherical earth. If the vehicle speed is v = 500 km/h, determine the
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 to an observer riding in and turning with car B. The x-y axes are attached to car B. Is this
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 fixed to the bar and determine the Coriolis acceleration of the slider for the instant represented.
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 engineer B, who is fixed to the locomotive. Use the axes given in the figure. R/2 A y R B L--x 20°
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 the necessary speed vrel of the vehicle relative to the road which will give rise to zero
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 of 360 km/ h. With coordinate axes attached to B as shown, determine the acceleration which A
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 of pin A relative to the sector for the instant represented. y 400 mm B A 30° OA = 500 mm
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 general expression for δ. The bowling alley is located at a latitude θ in the northern
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 is constant, but the angular rate w is decreasing at 0.5 deg/s2. Person A is stationary on the dock.
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, crosses the radial line from B to the center of curvature C of its path. Write the vector

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