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engineering
engineering mechanics dynamics

Questions and Answers of Engineering Mechanics Dynamics

The figure shows the cross section AB of a garage door which is a rectangular 2.5-m by 5-m panel of uniform thickness with a mass of 200 kg. The door is supported by the struts of negligible mass and
The uniform 40-lb bar with attached 12-lb wheels is released from rest when θ = 60°. If the wheels roll without slipping on the horizontal and vertical surfaces, determine the angular velocity of
A 1200-kg flywheel with a radius of gyration of 400 mm has its speed reduced from 5000 to 3000 rev/min during a 2-min interval. Calculate the average power supplied by the flywheel. Express your
The wheel consists of a 4-kg rim of 250-mm radius with hub and spokes of negligible mass. The wheel is mounted on the 3-kg yoke OA with mass center at G and with a radius of gyration about O of 350
The uniform slender bar ABC weighs 6 lb and is initially at rest with end A bearing against the stop in the horizontal guide. When a constant couple M = 72 lb-in. is applied to end C, the bar rotates
The torsional spring at A has a stiffness kT = 10 N∙m/rad and is undeformed when the uniform 10-kg bars OA and AB are in the vertical position and overlap. If the system is released from rest with
The system is released from rest when the angle θ = 90°. Determine the angular velocity of the uniform slender bar when θ equals 60°. Use the values m1 = 1 kg, m2 = 1.25 kg, and b = 0.4 m. -2b- C
The homogeneous torus and cylindrical ring are released from rest and roll without slipping down the incline. Determine an expression for the velocity difference vdiff which develops between the two
The uniform 12-lb disk pivots freely about a horizontal axis through O. A 4-lb slender bar is fastened to the disk as shown. If the system is nudged from rest while in the position shown, determine
Under active development is the storage of energy in high-speed rotating disks where friction is effectively eliminated by encasing the rotor in an evacuated enclosure and by using magnetic bearings.
For the pivoted slender rod of length l, determine the distance x for which the angular velocity will be a maximum as the bar passes the vertical position after being released in the horizontal
The wheel has mass m and a centroidal radius of gyration k and rolls without slipping up the incline under the action of a force P. The force is applied to the end of a cord which is wrapped securely
Motion of the bar is controlled by the constrained paths of A and B. If the angular velocity of the bar is 2 rad/s counterclockwise as the position θ = 45° is passed, determine the speeds of points
The shaft of the wheel unit rolls without slipping on the fixed horizontal surface, and point O has a velocity of 3 ft /sec to the right. By the method of this article, determine the velocities of
The center D of the car follows the centerline of the 100-ft skidpad. The speed of point D is v = 45 ft/sec. Determine the angular velocity of the car and the speeds of points A and B of the car. A
The attached wheels roll without slipping on the plates A and B, which are moving in opposite directions as shown. If vA = 60 mm/s to the right and vB = 200 mm/s to the left, determine the speeds of
The mechanism of Prob. 5/78 is repeated here. By the method of this article, determine the angular velocity of link AB and the velocity of collar B for the instant depicted. Assume the quantities w0
At the instant under consideration, the rod of the hydraulic cylinder is extending at the rate vA = 2 m/s. Determine the corresponding angular velocity wOB of link OB. A VA = 2 m/s 60° 180 mm 120 mm
End A of the slender pole is given a velocity vA to the right along the horizontal surface. Show that the magnitude of the velocity of end B equals vA when the midpoint M of the pole comes in contact
The flexible band F is attached at E to the rotating sector and leads over the guide pulley G. Determine the angular velocities of links AB and BD for the position shown if the band has a speed of 2
The rear driving wheel of a car has a diameter of 26 in. and has an angular speed N of 200 rev/min on an icy road. If the instantaneous center of zero velocity is 4 in. above the point of contact of
Link OA has a counterclockwise angular velocity θ˙ = 4 rad/sec during an interval of its motion. Determine the angular velocity of link AB and of sector BD for θ = 45° at which instant AB is
Vertical oscillation of the spring-loaded plunger F is controlled by a periodic change in pressure in the vertical hydraulic cylinder E. For the position θ = 60°, determine the angular velocity of
Motion of the roller A against its restraining spring is controlled by the downward motion of the plunger E. For an interval of motion the velocity of E is v = 0.2 m/s. Determine the velocity of A
A device which tests the resistance to wear of two materials A and B is shown. If the link EO has a velocity of 4 ft/sec to the right when θ = 45°, determine the rubbing velocity vA. D -5"→ 12" E
In the design of the mechanism shown, collar A is to slide along the fixed shaft as angle θ increases. When θ = 30°, the control link at D is to have a downward component of velocity of 0.60 m/s.
Determine the angular velocity w of the ram head AE of the rock crusher in the position for which θ = 60°. The crank OB has an angular speed of 60 rev/min. When B is at the bottom of its circle, D
For the instant represented, corner C of the rectangular plate has an acceleration of 5 m/s2 in the negative y-direction, and the plate has a clockwise angular velocity of 4 rad/s which is decreasing
The two rotor blades of 800-mm radius rotate counterclockwise with a constant angular velocity w = θ˙ = 2 rad/s about the shaft at O mounted in the sliding block. The acceleration of the block is
A container for waste materials is dumped by the hydraulically-activated linkage shown. If the piston rod starts from rest in the position indicated and has an acceleration of 1.5 ft/sec2 in the
Determine the angular velocity and angular acceleration of the slender bar AB just after roller B passes point C and enters the circular portion of the support surface. R A В C L-
The wheel of radius R rolls without slipping, and its center O has an acceleration aO. A point P on the wheel is a distance r from O. For given values of aO, R, and r, determine the angle θ and the
The 9-m steel beam is being hoisted from its horizontal position by the two cables attached at A and B. If the initial angular accelerations of the hoisting drums are a1 = 0.5 rad/s2 and a2 = 0.2
For a short interval, collars A and B are sliding along the fixed vertical shaft with velocities vA = 2 m/s and vB = 3 m/s in the directions shown. Determine the magnitude of the velocity of point C
The right-angle link has a counterclockwise angular velocity of 3 rad /s at the instant represented, and point B has a velocity vB = 2i − 0.3j m/s. Determine the velocity of A using vector
The two pulleys are riveted together to form a single rigid unit, and each of the two cables is securely wrapped around its respective pulley. If point A on the hoisting cable has a velocity v = 3
The rider of the bicycle shown pumps steadily to maintain a constant speed of 16 km/h against a slight head wind. Calculate the maximum and minimum magnitudes of the absolute velocity of the pedal A.
Determine the angular velocity of bar AB just after roller B has begun moving up the 15° incline. At the instant under consideration, the velocity of roller A is vA. VA L 15° A
The spoked wheel of radius r is made to roll up the incline by the cord wrapped securely around a shallow groove on its outer rim. For a given cord speed v at point P, determine the velocities of
At the instant represented, the velocity of point A of the 1.2-m bar is 3 m/s to the right. Determine the speed vB of point B and the angular velocity w of the bar. The diameter of the small end
Determine the angular velocity of link BC for the instant indicated. In case (a), the center O of the disk is a fixed pivot, while in case (b), the disk rolls without slipping on the horizontal
The elements of a switching device are shown. 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.
Determine the angular velocity wAB of link AB and the velocity vB of collar B for the instant represented. Assume the quantities w0 and r to be known. A 2r 45° B
Determine the angular velocity wAB of link AB and the velocity vB of collar B for the instant represented. Assume the quantities w0 and r to be known. A 2r B 45° 30°
The rotation of the gear is controlled by the horizontal motion of end A of the rack AB. If the piston rod has a constant velocity x˙ = 300 mm/s during a short interval of motion, determine the
Motion of the rectangular plate P is controlled by the two links which cross without touching. For the instant represented where the links are perpendicular to each other, the plate has a
The elements of a simplified clam-shell bucket for a dredge are shown. The cable which opens and closes the bucket passes through the block at O. With O as a fixed point, determine the angular
In the design of a produce-processing plant, roller trays of produce are to be oscillated under water spray by the action of the connecting link AB and crank OB. For the instant when θ = 15°, the
The vertical rod has a downward velocity v = 0.8 m/s when link AB is in the 30° position shown. Determine the corresponding angular velocity of AB and the speed of roller B if R = 0.4 m. 1.25R R
Pin P on the end of the horizontal rod slides freely in the slotted gear. The gear engages the moving rack A and the fixed rack B (teeth not shown) so it rolls without slipping. If A has a velocity
A four-bar linkage is shown in the figure (the ground “link” OC is considered the fourth bar). If the drive link OA has a counterclockwise angular velocity w0 = 10 rad/s, determine the angular
The mechanism is part of a latching device where rotation of link AOB is controlled by the rotation of slotted link D about C. If member D has a clockwise angular velocity of 1.5 rad /s when the slot
The elements of the mechanism for deployment of a spacecraft magnetometer boom are shown. Determine the angular velocity of the boom when the driving link OB crosses the y-axis with an angular
The wheel rolls without slipping. For the instant portrayed, when O is directly under point C, link OA has a velocity v = 1.5 m/s to the right and θ = 30°. Determine the angular velocity w of the
The slender bar is moving in general plane motion with the indicated linear and angular properties. Locate the instantaneous center of zero velocity and determine the speeds of points A and B. 4
The slender bar is moving in general plane motion with the indicated linear and angular properties. Locate the instantaneous center of zero velocity and determine the velocities of points A and B.
For the instant represented, corner A of the rectangular plate has a velocity vA = 2.8 m/s and the plate has a clockwise angular velocity w = 12 rad/s. Determine the magnitude of the corresponding
Roller B of the quarter-circular link has a velocity vB = 3 ft /sec directed down the 15° incline. The link has a counterclockwise angular velocity w = 2 rad /sec. By the method of this article,
The bar AB has a counterclockwise angular velocity of 6 rad/sec. Construct the velocity vectors for points A and G of the bar and specify their magnitudes if the instantaneous center of zero velocity
A car mechanic “walks” two wheel/tire units across a horizontal floor as shown. He walks with constant speed v and keeps the tires in the configuration shown with the same position relative to
At a certain instant vertex B of the right-triangular plate has a velocity of 200 mm/s in the direction shown. If the instantaneous center of zero velocity for the plate is 40 mm from point B and if
End A of the 2-ft link has a velocity of 5 ft/sec in the direction shown. At the same instant, end B has a velocity whose magnitude is 7 ft/sec as indicated. Find the angular velocity ω of the link
The cart has a velocity of 4 ft/sec to the right. Determine the angular speed N of the wheel so that point A on the top of the rim has a velocity (a) Equal to 4 ft/sec to the left, (b) Equal to
The uniform rectangular plate moves on the horizontal surface. Its mass center has a velocity vG = 3 m/s directed parallel to the x-axis and the plate has a counterclockwise (as seen from above)
The right-angle link AB has a clockwise angular velocity ω = 2 rad/sec when in the position shown. Determine the velocity of B with respect to A for this instant. A y 30° 12" Lーーズ 5" B の
The punch is operated by a simple harmonic oscillation of the pivoted sector given by θ = θ0 sin 2πt where the amplitude is θ0 = π/12 rad (15°) and the time for one complete oscillation is 1
The Geneva wheel is a mechanism for producing intermittent rotation. Pin P in the integral unit of wheel A and locking plate B engages the radial slots in wheel C, thus turning wheel C one-fourth of
One of the most common mechanisms is the slider-crank. Express the angular velocity ωAB and angular acceleration αAB of the connecting rod AB in terms of the crank angle θ for a given constant
Angular oscillation of the slotted link is achieved by the crank OA, which rotates clockwise at the steady speed N = 120 rev/min. Determine an expression for the angular velocity β˙ of the slotted
A variable-speed belt drive consists of the two pulleys, each of which is constructed of two cones which turn as a unit but are capable of being drawn together or separated so as to change the
The rotation of link AO is controlled by the piston rod of hydraulic cylinder BC, which is elongating at the constant rate s˙ = k for an interval of motion. Write the vector expression for the
Show that the expressions v = rω and at = rα hold for the motion of the center O of the wheel which rolls on the concave or convex circular arc, where ω and α are the absolute angular velocity
It is desired to design a system for controlling the rate of extension x˙ of the fire-truck ladder during elevation of the ladder so that the bucket B will have vertical motion only. Determine x˙
Derive an expression for the upward velocity v of the car hoist in terms of θ. The piston rod of the hydraulic cylinder is extending at the rate s˙. b. 26 b. L
Link OA is given a clockwise angular velocity ω = 2 rad/sec as indicated. Determine the velocity v of point C for the position θ = 30° if b = 8 in. А b 26 B
Motion of the wheel as it rolls up the fixed rack on its geared hub is controlled through the peripheral cable by the driving wheel D, which turns counterclockwise at the constant rate ω0 = 4 rad/s
A roadway speed bump is being installed on a level road to remind motorists of the existing speed limit. If the driver of the car experiences at G a vertical acceleration of as much as g, up or down,
The rod OB slides through the collar pivoted to the rotating link at A. If CA has an angular velocity ω = 3 rad/s for an interval of motion, calculate the angular velocity of OB when θ = 45°. CA =
Vertical motion of the work platform is controlled by the horizontal motion of pin A. If A has a velocity v0 to the left, determine the vertical velocity v of the platform for any value of θ. L/2
The hydraulic cylinder imparts a constant upward velocity vA = 0.2 m/s to corner A of the rectangular container during an interval of its motion. For the instant when θ = 20°, determine the
Boom OA is being elevated by the rope-and-pulley arrangement shown. If point B on the rope is given a constant velocity vB = 9 ft/sec, determine the angular velocity and angular acceleration ω of
The collar C moves to the left on the fixed guide with speed v. Determine the angular velocity ωOA as a function of v, the collar position s, and the height h. A, В h C U-
Link OA rotates with a counterclockwise angular velocity ω = 3 rad/s. Determine the angular velocity of bar BC when θ = 20°. A b. В 26-
Determine the acceleration of the shaft B for θ = 60° if the crank OA has an angular acceleration θ¨ = 8 rad/s2 and an angular velocity θ˙ = 4 rad/s at this position. The spring maintains
Link OA rotates with a clockwise angular velocity ω = 7 rad/s. Determine the velocity of point B for the position θ = 30°. Use the values b = 80 mm, d = 100 mm, and h = 30 mm. A d h B
The wheel of radius r rolls without slipping, and its center O has a constant velocity vO to the right. Determine expressions for the magnitudes of the velocity v and acceleration a of point A on the
A rocket stage designed for deep-space missions consists of 200 kg of fuel and 300 kg of structure and payload combined. In terms of burnout velocity, what would be the advantage of reducing the
The upper end of the open-link chain of length L and mass ρ per unit length is lowered at a constant speed v by the force P. Determine the reading R of the platform scale in terms of x. P A L
The magnetometer boom for a spacecraft consists of a large number of triangular-shaped units which spring into their deployed configuration upon release from the canister in which they were folded
A model rocket weighs 1.5 lb just before its vertical launch. Its experimental solid-fuel motor carries 0.1 lb of fuel, has an escape velocity of 3000 ft/sec, and burns the fuel for 0.9 sec.
A tank truck for washing down streets has a total weight of 20,000 lb when its tank is full. With the spray turned on, 80 lb of water per second issue from the nozzle with a velocity of 60 ft/sec
The mass m of a raindrop increases as it picks up moisture during its vertical descent through still air. If the air resistance to motion of the drop is R and its downward velocity is v, write the
A small rocket of initial mass m0 is fired vertically upward near the surface of the earth (g constant). If air resistance is neglected, determine the manner in which the mass m of the rocket must
The space shuttle, together with its central fuel tank and two booster rockets, has a total mass of 2.04(106) kg at liftoff. Each of the two booster rockets produces a thrust of 11.80(106) N, and
One of the functions of the space shuttle is to release communications satellites at low altitude. A booster rocket is fi red at B, placing the satellite in an elliptical transfer orbit, the apogee
The angular velocity of a gear is controlled according to ω = 12 − 3t2 where ω, in radians per second, is positive in the clockwise sense and where t is the time in seconds. Find the net angular
Magnetic tape is fed over and around the light pulleys mounted in a computer frame. If the speed v of the tape is constant and if the ratio of the magnitudes of the acceleration of points A and B is
When switched on, the grinding machine accelerates from rest to its operating speed of 3450 rev/min in 6 seconds. When switched off, it coasts to rest in 32 seconds. Determine the number of
The small cart is released from rest in position 1 and requires 0.638 seconds to reach position 2 at the bottom of the path, where its center G has a velocity of 14.20 ft/sec. Determine the angular
The flywheel has a diameter of 600 mm and rotates with increasing speed about its z-axis shaft. When point P on the rim crosses the y-axis with θ = 90°, it has an acceleration given by a = −1.8i

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