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engineering
engineering mechanics dynamics

Questions and Answers of Engineering Mechanics Dynamics

Each of the solid circular disk wheels has a mass of 2 kg, and the inner solid cylinder has a mass of 3 kg. The disks and cylinder are mounted on the small central shaft so that each can rotate
The preliminary design of a unit for automatically reducing the speed of a freely rotating assembly is shown. Initially the unit is rotating freely about a vertical axis through O at a speed of 600
The body of mass m = 1.2 kg is lying motionless on the smooth horizontal surface when an impulse ∫P dt = 6 N∙ s is applied as shown. Determine the linear momentum G and the angular momentum HG of
The 5-kg bar is released from rest while in the position shown and its end rollers travel in the vertical-plane slot shown. If the speed of roller A is 3.25 m/s as it passes point C, determine the
The mass m is traveling with speed v when it strikes the corner of the plate of mass M. If the mass sticks to the side of the plate, determine the maximum angle θ reached by the plate. Use the
The 30-kg wheel has a radius of gyration about its center of 75 mm and is rotating clockwise at the rate of 300 rev /min when it is released onto the incline with no velocity of its center O. While
The uniform cylinder is rolling without slip with a velocity v along the horizontal surface when it overtakes a ramp traveling with speed v0. Determine an expression for the speed v′ which the
A frozen-juice can rests on the horizontal rack of a freezer door as shown. With what maximum angular velocity Ω can the door be “slammed” shut against its seal and not dislodge the can? Assume
The gear train shown starts from rest and reaches an output speed of wC = 240 rev/min in 2.25 s. Rotation of the train is resisted by a constant 150 N∙m moment at the output gear C. Determine the
The 8-lb slotted circular disk has a radius of gyration about its center O of 6 in. and initially is rotating freely about a fixed vertical axis through O with a speed N1 = 600 rev /min. The 2-lb
A 55-kg dynamics instructor is demonstrating the principles of angular momentum to her class. She stands on a freely rotating platform with her body aligned with the vertical platform axis. With the
The body of the spacecraft weighs 322 lb on earth and has a radius of gyration about its z-axis of 1.5 ft. Each of the two solar panels may be treated as a uniform flat plate weighing 16.1 lb. If the
The motor at B supplies a constant torque M which is applied to a 375-mm-diameter internal drum around which is wound the cable shown. This cable then wraps around an 80-kg pulley attached to a
In the rotating assembly shown, arm OA and the attached motor housing B together weigh 10 lb and have a radius of gyration about the z-axis of 7 in. The motor armature and attached 5-in.- radius disk
The 165-lb ice skater with arms extended horizontally spins about a vertical axis with a rotational speed of 1 rev/sec. Estimate his rotational speed N if he fully retracts his arms, bringing his
The uniform slender bar of mass m and length l has no angular velocity as end A strikes the ground against the stop with no rebound. If a = 15°, what is the minimum magnitude of the initial velocity
The 100-lb platform rolls without slipping along the 10° incline on two pairs of 16-in.-diameter wheels. Each pair of wheels with attached axle weighs 25 lb and has a centroidal radius of gyration
The homogeneous sphere of Prob. 6/191 is placed on the incline with a clockwise angular velocity w0 but no linear velocity of its center (v0 = 0). Determine the time duration t of the period of
The homogeneous sphere of mass m and radius r is projected along the incline of angle θ with an initial speed v0 and no angular velocity (w0 = 0). If the coefficient of kinetic friction is μk,
The system is initially rotating freely with angular velocity w1 = 10 rad/s when the inner rod A is centered lengthwise within the hollow cylinder B as shown in the figure. Determine the angular
Child A weighs 75 lb and is sitting at rest relative to the merry-go-round which is rotating counterclockwise with an angular velocity Ω = 15 rev /min. Child B, with a weight of 65 lb, runs toward
The slender bar of mass m and length l is released from rest in the horizontal position shown. If point A of the bar becomes attached to the pivot at B upon impact, determine the angular velocity w
The phenomenon of vehicle “tripping” is investigated here. The sport-utility vehicle is sliding sideways with speed v1 and no angular velocity when it strikes a small curb. Assume no rebound of
Each of the two 300-mm uniform rods A has a mass of 1.5 kg and is hinged at its end to the rotating base B. The 4-kg base has a radius of gyration of 40 mm and is initially rotating freely about its
The body composed of slender rods of mass p per unit length is lying motionless on the smooth horizontal surface when a linear impluse ∫P dt is applied as shown. Determine the velocity vB of corner
Two small variable-thrust jets are actuated to keep the spacecraft angular velocity about the z-axis constant at w0 = 1.25 rad/s as the two telescoping booms are extended from r1 = 1.2 m to r2 = 4.5
The uniform concrete block, which weighs 171 lb and falls from rest in the horizontal position shown, strikes the fixed corner A and pivots around it with no rebound. Calculate the angular velocity w
The device shown is a simplified model of an amusement-park ride in which passengers are rotated about the vertical axis of the central post at an angular speed Ω while sitting in a pod which is
Just after leaving the platform, the diver’s fully extended 80-kg body has a rotational speed of 0.3 rev/s about an axis normal to the plane of the trajectory. Estimate the angular velocity N later
The plate of Prob. 6/179 is repeated here where the coordinates of corner C are established. The plate is falling freely in the x-y vertical plane. What is the linear momentum of the plate and its
The 30-lb uniform plate has the indicated velocities at corners A and B. What is the angular momentum of the plate about the mass center G? 10 ft/sec A 4' y L--x G. 2' YUB
The wad of clay of mass m is initially moving with a horizontal velocity v1 when it strikes and sticks to the initially stationary uniform slender bar of mass M and length L. Determine the final
The grooved pulley of mass m is acted on by a constant force F through a cable which is wrapped securely around the exterior of the pulley. The pulley supports a cylinder of mass M which is attached
The man is walking with speed v1 = 1.2 m/s to the right when he trips over a small floor discontinuity. Estimate his angular velocity ω just after the impact. His mass is 76 kg with center-of-mass
The uniform arm OA has a mass of 4 kg, and the gear D has a mass of 5 kg with a radius of gyration about its center of 64 mm. The large gear B is fixed and cannot rotate. If the arm and small gear
The sector and attached wheels are released from rest in the position shown in the vertical plane. Each wheel is a solid circular disk weighing 12 lb and rolls on the fixed circular path without
The mechanism shown moves in the vertical plane. The vertical bar AB weighs 10 lb, and each of the two links weighs 6 lb with mass center at G and with a radius of gyration of 10 in. about its
Repeat Prob. 5/22, except now the angular acceleration of the disk is given by α = 2t, where t is in seconds and α is in radians per second squared. Determine the velocity and acceleration of point
An air table is used to study the elastic motion of flexible spacecraft models. Pressurized air escaping from numerous small holes in the horizontal surface provides a supporting air cushion which
The figure illustrates a commonly used quick-return mechanism which produces a slow cutting stroke of the tool (attached to D) and a rapid return stroke. If the driving crank OA is turning at the
The satellite of Sample Problem 3/31 has a perigee velocity of 26 140 km/h at the perigee altitude of 2000 km. What is the minimum increase Δv in velocity required of its rocket motor at this
Repeat the previous problem, only now the mass of puck B is twice that of puck A. y A B - x 30° VA = 10 m/s UB = 6 m/s
For the particle system of Prob. 4/1, determine HG and H˙G. y 2m | 20 4m F m 2d (stationary) Problem 4/1
For the particle system of Prob. 4/3, determine HG and H˙G. 3F Зт 20 1.5b 5m 2.56 2F 40 --y 60° 3b 30° 26 m 56 Problem 4/3
Repeat the previous problem, but now let h ≠ 0. Then evaluate your expression for the conditions h = 2 m, L = 10 m, and θ = 25°. H, h A B L. Problem 4/87
Replace the rope of Prob. 4/91 by an open-link chain with the same mass ρ per unit length. The free end is given a constant upward velocity v. Write expressions for P, the tension T1 at the bottom
For the particle system of Prob. 4/93, determine HG and H˙G. 4m 1.5d F 3v d 2d m 20 -y 2m Problem 4/93 20-- -
The binary star system consists of stars A and B, both of which orbit about the system mass center. Compare the orbital period τƒ calculated with the assumption of a fixed star A with the period
Fresh water issues from the two 30-mm-diameter holes in the bucket with a velocity of 2.5 m/s in the directions shown. Calculate the force P required to give the bucket an upward acceleration of 0.5
Repeat the previous problem, but now express your results in terms of components along the n- and t-axes. 9" 30° n A 3" PB 3" t Problem 5/13
Repeat Prob. 5/22, except now the angular acceleration of the disk is given by α = 2ω, where ω is in radians per second and α is in radians per second squared. Determine the velocity and
Determine the acceleration of point C of the previous problem if the clockwise angular velocity of link OA is constant at ω = 2 rad/sec. b 26 B C Problem 5/47
The magnitude of the absolute velocity of point A on the automobile tire is 12 m/s when A is in the position shown. What are the corresponding velocity vO of the car and the angular velocity ω of
The bar of Prob. 5/82 is repeated here. By the method of this article, determine the velocity of end A. Both ends remain in contact with their respective support surfaces. A 30° 0.4 m 105° B VB =
Solve for the speed of point D in Prob. 5/64 by the method of Art. 5/5. B A 200 mm- 100 mm- C D -150 mm Problem 5/64
If the bar OC of the previous problem rotates with a clockwise angular velocity wOC = 2 rad/s and a counterclockwise angular acceleration aOC = 4 rad/s2, determine the angular acceleration a of the
The switching device of Prob. 5/76 is repeated here. If the vertical control rod has a downward velocity v = 2 ft/sec and an upward acceleration a = 1.2 ft/sec2 when the device is in the position
The mechanism of Prob. 5/112 is repeated here. If the band has a constant speed of 2 m/s as indicated in the figure, determine the angular acceleration aAB of link AB. D 2 m/s 0.18 m 15°. 0.3 m 0.4
The bar AB from Prob. 5/74 is repeated here. If the velocity of point A is 3 m/s to the right and is constant for an interval including the position shown, determine the tangential acceleration of
A mechanism for pushing small boxes from an assembly line onto a conveyor belt, repeated from Prob. 5/89, is shown with arm OD and crank CB in their vertical positions. For the configuration shown,
For the cars of Prob. 5/163 traveling with constant speed, determine the acceleration which car A appears to have to an observer riding in and turning with car B. A 100 m Problem 5/163
The fire truck is moving forward at a speed of 35 mi/hr and is decelerating at the rate of 10 ft/sec2. Simultaneously, the ladder is being raised and extended. At the instant considered the angle θ
For the conditions of Prob. 5/175, obtain the vector expression for the acceleration which aircraft A appears to have to an observer in and turning with aircraft B, to which axes x-y are attached. N
The system of Prob. 5/170 is modified in that OC is now a slotted member which accommodates the pin A attached to the sector. If bar OC rotates with a clockwise angular velocity wOC = 2 rad/s and a
Refer to the figure for Prob. 5/177. Car A is traveling along the straightaway with speed v, and this speed is decreasing at a rate a. Car C is moving along the circular off-ramp with speed v/2, and
Consider the system of the previous problem. If the speed of collar C is decreasing at the rate a for the instant represented, determine the angular acceleration a of bar OA in terms of a, v, and x.
The pin A in the bell crank AOD is guided by the flanges of the collar B, which slides with a constant velocity vB of 3 ft/sec along the fixed shaft for an interval of motion. For the position θ =
The oscillating produce tray of Prob. 5/83 is shown again here. If the crank OB has a constant counterclockwise angular velocity of 0.944 rad /s, determine the angular velocity of AB when θ = 20°.
The load L is being elevated by the downward velocities of ends A and B of the cable. Determine the magnitude of the acceleration of point P on the top of the sheave for the instant when vA = 2 ft
The hydraulic cylinder C imparts a velocity v to pin B in the direction shown. The collar slips freely on rod OA. Determine the resulting angular velocity of rod OA in terms of v, the displacement s
The end rollers of the bent bar ADB are confined to the slots shown. If vB = 0.3 m/s, determine the velocity of roller A and the angular velocity of the bar. А 90 mm 30° B D 90 mm UB В B = 15°
For the position shown where θ = 30°, point A on the sliding collar has a constant velocity v = 0.3 m/s with corresponding lengthening of the hydraulic cylinder AC. For this same position BD is
A radar station B situated at the equator observes a satellite A in a circular equatorial orbit of 200-km altitude and moving from west to east. For the instant when the satellite is 30° above the
Slotted arm OB oscillates about the vertical by the action of the rotating crank CA of 5-in. length, where the pin A engages the slot. For a constant speed N = 120 rev/min of crank CA, determine and
The disk rotates about a fixed axis with a constant angular velocity w0 = 10 rad/s. Pin A is fixed to the disk. Determine and plot the magnitudes of the velocity and acceleration of pin A relative to
A constant torque M exceeds the moment about O due to the force F on the plunger, and an angular acceleration θ¨ = 100(1 − cos θ) rad/s2 results. If the crank OA is released from rest at B,
The crank OA of the four-bar linkage is driven at a constant counterclockwise angular velocity w0 = 10 rad/s. Determine and plot as functions of the crank angle θ the angular velocities of bars AB
If all conditions in the previous problem remain the same, determine and plot as functions of the crank angle θ the angular accelerations of bars AB and BC over the range 0 ≤ θ ≤ 360°. State
All conditions of Prob. 5/207 remain the same, except the counterclockwise angular velocity of crank OA is 10 rad/s when θ = 0 and the constant counterclockwise angular acceleration of the
Bar OA rotates about the fixed pivot O with constant angular velocity β˙ = 0.8 rad/s. Pin A is fixed to bar OA and is engaged in the slot of member BD, which rotates about a fixed axis through
For the slider-crank configuration shown, derive the expression for the velocity vA of the piston (taken positive to the right) as a function of θ. Substitute the numerical data of Sample Problem 5
For the slider-crank of Prob. 5/211, derive the expression for the acceleration aA of the piston (taken positive to the right) as a function of θ for w = θ˙ = constant. Substitute the numerical
In Prob. 6/1, if the plate is given a horizontal acceleration a = 2g, calculate the force exerted on the bar by either peg A or B. 8" C a 8" A B Problem 6/1
If the collar P of the pendulum of Prob. 6/12 is given a constant acceleration a = 5g, what will be the steady-state deflection of the pendulum from the vertical? Use the value kT = 7mgL. P kT L т
The uniform 225-lb crate is supported by the thin homogeneous 40-lb platform BF and light support links whose motion is controlled by the hydraulic cylinder CD. If the cylinder is extending at a
The uniform 100-kg beam is freely hinged about its upper end A and is initially at rest in the vertical position with θ = 0. Determine the initial angular acceleration α of the beam and the
A momentum wheel for dynamics-class demonstrations is shown. It is basically a bicycle wheel modified with rim band-weighting, handles, and a pulley for cord startup. The heavy rim band causes the
The uniform quarter-circular sector of mass m is released from rest with one straight edge vertical as shown. Determine the initial angular acceleration and the horizontal and vertical components of
For the rotating and oscillating control arm OA of Prob. 7/22, determine the velocity v and acceleration a of the ball tip A for the condition when t = 1/2 s. Distance b = 120 mm, s = 100 mm, and θ
For the robot of Prob. 7/16, determine the angular velocity w and angular acceleration a of the jaws A if θ = 60° and β = 30°, both constant, and if w1 = 2 rad/s, w2 = w3 = w4 = 0, and w5 = 0.8
Determine expressions for the velocity v and acceleration a of point A on the wheel of Prob. 7/18 for the position shown, where A crosses the horizontal line through the center of the wheel. y R- A
The robot shown has five degrees of rotational freedom. The x-y-z axes are attached to the base ring, which rotates about the z-axis at the rate w1. The arm O1O2 rotates about the x-axis at the rate
The wheel rolls without slipping in a circular arc of radius R and makes one complete turn about the vertical y-axis with constant speed in time τ. Determine the vector expression for the angular
The circular disk of 120-mm radius rotates about the z-axis at the constant rate wz = 20 rad/s, and the entire assembly rotates about the fixed x-axis at the constant rate wx = 10 rad/s. Calculate
The crane has a boom of length OP = 24 m and is revolving about the vertical axis at the constant rate of 2 rev/min in the direction shown. Simultaneously, the boom is being lowered at the constant
The design of the rotating arm OA of a control mechanism requires that it rotate about the vertical Z-axis at the constant rate Ω = β˙ = π rad/s. Simultaneously, OA oscillates according to θ =
If the angular velocity w0 = −4j − 3k rad/s of the rotor in Prob. 7/5 is constant in magnitude, determine the angular acceleration a of the rotor for (a) Ω = 0 and θ˙ = 2 rad/s (both constant)
The vertical shaft and attached clevis rotate about the z-axis at the constant rate Ω = 4 rad/s. Simultaneously, the shaft B revolves about its axis OA at the constant rate w0 = 3 rad/s, and the
The right-circular cone A rolls on the fixed right-circular cone B at a constant rate and makes one complete trip around B every 4 seconds. Compute the magnitude of the angular acceleration a of cone
The pendulum oscillates about the x-axis according to θ = π/6 sin 3πt radians, where t is the time in seconds. Simultaneously, the shaft OA revolves about the vertical z-axis at the constant rate

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