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engineering
engineering mechanics dynamics

Questions and Answers of Engineering Mechanics Dynamics

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
The solid right-circular cone of base radius r and height h rolls on a flat surface without slipping. The center B of the circular base moves in a circular path around the z-axis with a constant
The solid cylinder has a body cone with a semi-vertex angle of 20°. Momentarily the angular velocity w has a magnitude of 30 rad/s and lies in the y-z plane. Determine the rate p at which the
The helicopter is nosing over at the constant rate q rad/s. If the rotor blades revolve at the constant speed p rad/s, write the expression for the angular acceleration a of the rotor. Take the
The collar at O and attached shaft OC rotate about the fixed x0-axis at the constant rate Ω = 4 rad/s. Simultaneously, the circular disk rotates about OC at the constant rate p = 10 rad/s. Determine
If the angular rate p of the disk in Prob. 7/31 is increasing at the rate of 6 rad/s per second and if Ω remains constant at 4 rad/s, determine the angular acceleration a of the disk at the instant
For the conditions of Prob. 7/31, determine the velocity vA and acceleration aA of point A on the disk as it passes the position shown. Reference axes x-y-z are attached to the collar at O and its
An unmanned radar-radio controlled aircraft with tilt-rotor propulsion is being designed for reconnaissance purposes. Vertical rise begins with θ = 0 and is followed by horizontal flight as θ
End A of the rigid link is confined to move in the −x-direction while end B is confined to move along the z-axis. Determine the component wn normal to AB of the angular velocity of the link as it
The small motor M is pivoted about the x-axis through O and gives its shaft OA a constant speed p rad/s in the direction shown relative to its housing. The entire unit is then set into rotation about
The flight simulator is mounted on six hydraulic actuators connected in pairs to their attachment points on the underside of the simulator. By programming the actions of the actuators, a variety of
The robot of Prob. 7/16 is shown again here, where the coordinate system x-y-z with origin at O2 rotates about the X-axis at the rate θ˙. Nonrotating axes X-Y-Z oriented as shown have their origin
For the instant represented collar B is moving along the fixed shaft in the X-direction with a constant velocity vB = 4 m/s. Also at this instant X = 0.3 m and Y = 0.2 m. Calculate the velocity of
The spacecraft is revolving about its z-axis, which has a fixed space orientation, at the constant rate p = 1/10 rad/s. Simultaneously, its solar panels are unfolding at the rate β˙ which is
The disk has a constant angular velocity p about its z-axis, and the yoke A has a constant angular velocity w2 about its shaft as shown. Simultaneously, the entire assembly revolves about the fixed
The collar and clevis A are given a constant upward velocity of 8 in./sec for an interval of motion and cause the ball end of the bar to slide in the radial slot in the rotating disk. Determine the
The circular disk of 100-mm radius rotates about its z-axis at the constant speed p = 240 rev/min, and arm OCB rotates about the Y-axis at the constant speed N = 30 rev/min. Determine the velocity v
Solve Prob. 7/43 by attaching the reference axes x-y-z to the rotating disk. 180 mm p -100 mm B D Y 100 mm Problem 7/43
For the conditions described in Prob. 7/36, determine the velocity v and acceleration a of the center A of the ball tool in terms of β. R. M/ Problem 7/36
The circular disk is spinning about its own axis (y-axis) at the constant rate p = 10π rad/s. Simultaneously, the frame is rotating about the Z-axis at the constant rate Ω = 4π rad/s. Calculate
The center O of the spacecraft is moving through space with a constant velocity. During the period of motion prior to stabilization, the spacecraft has a constant rotational rate Ω = 0.5 rad/sec
The thin circular disk of mass m and radius r is rotating about its z-axis with a constant angular velocity p, and the yoke in which it is mounted rotates about the x-axis through OB with a constant

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