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engineering
engineering mechanics dynamics

Questions and Answers of Engineering Mechanics Dynamics

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
The drive mechanism imparts to the semicircular plate simple harmonic motion of the form θ = θ0 sin ω0t, where θ0 is the amplitude of the oscillation and ω0 is its circular frequency. Determine
The cylinder rotates about the fixed z-axis in the direction indicated. If the speed of point A is vA = 2 ft/sec and the magnitude of its acceleration is aA = 12 ft/sec2, determine the angular
The angular acceleration of a body which is rotating about a fixed axis is given by α = −kw2, where the constant k = 0.1 (no units). Determine the angular displacement and time elapsed when the
The device shown rotates about the fixed z-axis with angular velocity ω = 20 rad /s and angular acceleration α = 40 rad/s2 in the directions indicated. Determine the instantaneous velocity and
The circular disk rotates with a constant angular velocity ω = 40 rad /sec about its axis, which is inclined in the y-z plane at the angle θ = tan−1 3/4. Determine the vector expressions for
The T-shaped body rotates about a horizontal axis through point O. At the instant represented, its angular velocity is ω = 5 rad/sec and its angular acceleration is α = 10 rad/sec2 in the
In order to test an intentionally weak adhesive, the bottom of the small 0.3-kg block is coated with adhesive and then the block is pressed onto the turntable with a known force. The turntable starts
The two attached pulleys are driven by the belt with increasing speed. When the belt reaches a speed v = 2 ft/sec, the total acceleration of point P is 26 ft/sec2. For this instant determine the
The bent flat bar rotates about a fixed axis through point O with the instantaneous angular properties indicated in the figure. Determine the velocity and acceleration of point A. o = 2 rad/s a = 5
At time t = 0, the arm is rotating about the fixed z-axis with an angular velocity ω = 200 rad/s in the direction shown. At that time, a constant angular deceleration begins and the arm comes to a
A variable torque is applied to a rotating wheel at time t = 0 and causes the clockwise angular acceleration to increase linearly with the clockwise angular displacement θ of the wheel during the
Develop general expressions for the instantaneous velocity and acceleration of point A of the square plate, which rotates about a fixed axis through point O. Take all variables to be positive. Then
The motor A accelerates uniformly from zero to 3600 rev/min in 8 seconds after it is turned on at time t = 0. It drives a fan (not shown) which is attached to drum B. The effective pulley radii are
During its final spin cycle, a front-loading washing machine has a spin rate of 1200 rev/min. Once power is removed, the drum is observed to uniformly decelerate to rest in 25 s. Determine the number
The design characteristics of a gear-reduction unit are under review. Gear B is rotating clockwise with a speed of 300 rev/min when a torque is applied to gear A at time t = 2 s to give gear A a
A V-belt speed-reduction drive is shown where pulley A drives the two integral pulleys B which in turn drive pulley C. If A starts from rest at time t = 0 and is given a constant angular acceleration
Slider A moves in the horizontal slot with a constant speed v for a short interval of motion. Determine the angular velocity ω of bar AB in terms of the displacement xA. 40° A XA-
The concrete pier P is being lowered by the pulley and cable arrangement shown. If points A and B have velocities of 0.4 m/s and 0.2 m/s, respectively, compute the velocity of P, the velocity of
At the instant under consideration, the hydraulic cylinder AB has a length L = 0.75 m, and this length is momentarily increasing at a constant rate of 0.2 m /s. If vA = 0.6 m /s and θ = 35°,
The hydraulic cylinder D is causing the distance OA to increase at the rate of 2 in./sec. Calculate the velocity of the pin at C in its horizontal guide for the instant when θ = 50o. AO 6". 6". B D
The Scotch-yoke mechanism converts rotational motion of the disk to oscillatory translation of the shaft. For given values of θ, ω, α, r, and d, determine the velocity and acceleration of point P
The Scotch-yoke mechanism of Prob. 5/34 is modified as shown in the figure. For given values of ω, α, r, θ, d, and β, determine the velocity and acceleration of point P of the shaft. at P d- B
At a bulk loading station, gravel leaves the hopper at the rate of 220 lb/sec with a velocity of 10 ft/sec in the direction shown and is deposited on the moving flatbed truck. The tractive force
A railroad coal car weighs 54,600 lb empty and carries a total load of 180,000 lb of coal. The bins are equipped with bottom doors which permit discharging coal through an opening between the rails.
A coil of heavy flexible cable with a total length of 100 m and a mass of 1.2 kg/m is to be laid along a straight horizontal line. The end is secured to a post at A, and the cable peels off the coil
By lowering a scoop as it skims the surface of a body of water, the aircraft (nicknamed the “Super Scooper”) is able to ingest 4.5 m3 of fresh water during a 12-second run. The plane then flies
A small rocket-propelled vehicle weighs 125 lb, including 20 lb of fuel. Fuel is burned at the constant rate of 2 lb/sec with an exhaust velocity relative to the nozzle of 400 ft/sec. Upon ignition
The end of a pile of loose-link chain of mass ρ per unit length is being pulled horizontally along the surface by a constant force P. If the coefficient of kinetic friction between the chain and the
A coal car with an empty mass of 25 Mg is moving freely with a speed of 1.2 m/s under a hopper which opens and releases coal into the moving car at the constant rate of 4 Mg per second. Determine the
Sand is released from the hopper H with negligible velocity and then falls a distance h to the conveyor belt. The mass flow rate from the hopper is m′. Develop an expression for the steady-state
The open-link chain of length L and mass ρ per unit length is released from rest in the position shown, where the bottom link is almost touching the platform and the horizontal section is supported
In the figure is shown a system used to arrest the motion of an airplane landing on a field of restricted length. The plane of mass m rolling freely with a velocity v0 engages a hook which pulls the
The free end of the flexible and inextensible rope of mass ρ per unit length and total length L is given a constant upward velocity v. Write expressions for P, the force R supporting the fixed end,
The system of three particles has the indicated particle masses, velocities, and external forces. Determine r̅, r̅̇, r̅̈ , T, HO, and H˙ O for this three-dimensional system. 4m 1.5d F 3v d 2d m
Each of the identical steel balls weighs 4 lb and is fastened to the other two by connecting bars of negligible weight and unequal length. In the absence of friction at the supporting horizontal
A 2-oz bullet is fired horizontally with a velocity v = 1000 ft/sec into the slender bar of a 3-lb pendulum initially at rest. If the bullet embeds itself in the bar, compute the resulting angular
A large rocket ready for vertical launch has a total mass of 2.7(103) Mg. At launch, fuel is burned at the rate of 13 Mg/s with an exhaust velocity of 2400 m/s. Determine the initial acceleration a
In an operational design test of the equipment of the fire truck, the water cannon is delivering fresh water through its 2-in.-diameter nozzle at the rate of 1400 gal/min at the 20° angle. Calculate
The rocket shown is designed to test the operation of a new guidance system. When it has reached a certain altitude beyond the effective influence of the earth’s atmosphere, its mass has decreased
When only the air of a sand-blasting gun is turned on, the force of the air on a flat surface normal to the stream and close to the nozzle is 20 N. With the nozzle in the same position, the force
A two-stage rocket is fired vertically up and is above the atmosphere when the first stage burns out and the second stage separates and ignites. The second stage carries 1200 kg of fuel and has an
Water of density ρ issues from the nozzle of area A and impinges upon the block of mass m, which is at rest on the rough horizontal surface. If the block is on the verge of tipping rightward,
The block of Prob. 4 /102 is now fitted with two small rollers. Determine the normal force under each roller and the initial rightward acceleration of the block if the exit velocity of the water
A jet of fresh water under pressure issues from the 3/4-in.-diameter fixed nozzle with a velocity v = 120 ft/sec and is diverted into the two equal streams. Neglect any energy loss in the streams and
The flexible nonextensible rope of length πr/2 and mass ρ per unit length is attached at A to the fixed quarter-circular guide and allowed to fall from rest in the horizontal position. When the
In the static test of a jet engine and exhaust nozzle assembly, air is sucked into the engine at the rate of 30 kg /s and fuel is burned at the rate of 1.6 kg/s. The flow area, static pressure, and
The upper end of the open-link chain of length L and mass ρ per unit length is released from rest with the lower end just touching the platform of the scale. Determine the expression for the force F
The chain of length L and mass ρ per unit length is released from rest on the smooth horizontal surface with a negligibly small overhang x to initiate motion. Determine (a) The acceleration a
A vertical force P acting on the 2.5-lb cylindrical valve A, shown in section, serves to limit the flow of fresh water from the top of the vertical pipe B of 3-in. inside diameter. Water is fed
The chain of mass ρ per unit length passes over the small freely turning pulley and is released from rest with only a small imbalance h to initiate motion. Determine the acceleration a and velocity
The centrifugal pump handles 20 m3 of fresh water per minute with inlet and outlet velocities of 18 m/s. The impeller is turned clockwise through the shaft at O by a motor which delivers 40 kW at a
A rope or hinged-link bicycle-type chain of length L and mass ρ per unit length is released from rest with x = 0. Determine the expression for the total force R exerted on the fixed platform by the
The circular sector rotates about a fixed axis through point O with angular velocity ω = 2 rad/s and angular acceleration α = 4 rad/s2 with directions as indicated in the figure. Determine the
The total linear momentum of a system of five particles at time t = 2.2 s is given by G2.2 = 3.4i − 2.6j + 4.6k kg∙m/s. At time t = 2.4 s, the linear momentum has changed to G2.4 = 3.7i − 2.2j
Three monkeys A, B, and C weighing 20, 25, and 15 lb, respectively, are climbing up and down the rope suspended from D. At the instant represented, A is descending the rope with an acceleration of 5
A department-store escalator makes an angle of 30° with the horizontal and takes 40 seconds to transport a person from the first to the second floor with a vertical rise of 20 ft. At a certain
The 50,000-lb flatcar supports a 15,000-lb vehicle on a 5° ramp built on the flatcar. If the vehicle is released from rest with the flatcar also at rest, determine the velocity v of the flatcar when
A 60-kg rocket is fired from O with an initial velocity v0 = 125 m/s along the indicated trajectory. The rocket explodes 7 seconds after launch and breaks into three pieces A, B, and C having masses
A horizontal bar of mass m1 and small diameter is suspended by two wires of length l from a carriage of mass m2 which is free to roll along the horizontal rails. If the bar and carriage are released
In the unstretched position the coils of the 3-lb spring are just touching one another, as shown in part a of the figure. In the stretched position the force P, proportional to x, equals 200 lb when
The experimental race car is propelled by a rocket motor and is designed to reach a maximum speed v = 300 mi/hr under the thrust T of its motor. Prior wind-tunnel tests disclose that the wind
The jet aircraft has a mass of 4.6 Mg and a drag (air resistance) of 32 kN at a speed of 1000 km/h at a particular altitude. The aircraft consumes air at the rate of 106 kg /s through its intake
Fresh water issues from the nozzle with a velocity of 30 m/s at the rate of 0.05 m3/s and is split into two equal streams by the fixed vane and deflected through 60° as shown. Calculate the force F
In an unwise effort to remove debris, a homeowner directs the nozzle of his backpack blower directly toward the garage door. The nozzle velocity is 130 mi/hr and the flow rate is 410 ft3/min.
The jet water ski has reached its maximum velocity of 70 km/h when operating in salt water. The water intake is in the horizontal tunnel in the bottom of the hull, so the water enters the intake at
The 25-mm steel slab 1.2 m wide enters the rolls at the speed of 0.4 m /s and is reduced in thickness to 19 mm. Calculate the small horizontal thrust T on the bearings of each of the two rolls. 19 mm
The fire tug discharges a stream of salt water (density 1030 kg/m3) with a nozzle velocity of 40 m/s at the rate of 0.080 m3/s. Calculate the propeller thrust T which must be developed by the tug to
The pump shown draws air with a density ρ through the fixed duct A of diameter d with a velocity u and discharges it at high velocity v through the two outlets B. The pressure in the airstreams at A
A jet-engine noise suppressor consists of a movable duct which is secured directly behind the jet exhaust by cable A and deflects the blast directly upward. During a ground test, the engine sucks in
The 90° vane moves to the left with a constant velocity of 10 m/s against a stream of fresh water issuing with a velocity of 20 m/s from the 25-mmdiameter nozzle. Calculate the forces Fx and Fy on
The pipe bend shown has a cross-sectional area A and is supported in its plane by the tension T applied to its flanges by the adjacent connecting pipes (not shown). If the velocity of the liquid is
A jet of fluid with cross-sectional area A and mass density ρ issues from the nozzle with a velocity v and impinges on the inclined trough shown in section. Some of the fluid is diverted in each of
The 8-oz ball is supported by the vertical stream of fresh water which issues from the 1/2-in.-diameter nozzle with a velocity of 35 ft /sec. Calculate the height h of the ball above the nozzle.
A jet-engine thrust reverser to reduce an aircraft speed of 200 km/h after landing employs folding vanes which deflect the exhaust gases in the direction indicated. If the engine is consuming 50 kg
Water issues from a nozzle with an initial velocity v and supports a thin plate of mass m at a height h above the nozzle exit. A hole in the center of the plate allows some of the water to travel
The axial-flow fan C pumps air through the duct of circular cross section and exhausts it with a velocity v at B. The air densities at A and B are ρA and ρB, respectively, and the corresponding
Air is pumped through the stationary duct A with a velocity of 50 ft/sec and exhausted through an experimental nozzle section BC. The average static pressure across section B is 150 lb/in.2 gage, and
Air enters the pipe at A at the rate of 6 kg/s under a pressure of 1400 kPa gage and leaves the whistle at atmospheric pressure through the opening at B. The entering velocity of the air at A is 45
The sump pump has a net mass of 310 kg and pumps fresh water against a 6-m head at the rate of 0.125 m3/s. Determine the vertical force R between the supporting base and the pump flange at A during
The experimental ground-effect machine has a total weight of 4200 lb. It hovers 1 or 2 ft off the ground by pumping air at atmospheric pressure through the circular intake duct at B and discharging

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