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engineering
engineering mechanics statics

Questions and Answers of Engineering Mechanics Statics

Two cylinders A and B, having a weight of 10 lb and 5 lb, respectively, are attached to the ends of a cord which passes over a 3-lb pulley (disk). If the cylinders are released from rest, determine
The 50-kg flywheel has a radius of gyration about its center of mass of ko = 250 mm. It rotates with a constant angular velocity of 1200 rev/min before the brake is applied. If the coefficient of
The 20-kg roll of paper has a radius of gyration kA = 120 mm about an axis passing through point A. It is pin supported at both ends by two brackets AB. The roll rests on the floor, for which the
Disk D turns with a constant clockwise angular velocity of 30 rad/s. Disk E has a weight of 60 lb and is initially at rest when it is brought into contact with D. Determine the time required for disk
The 50-kg flywheel has a radius of gyration about its center of mass of ko = 250 mm. It rotates with a constant angular velocity of 1200 rev/min before the brake is applied. If the coefficient of
Determine the angular acceleration of the 25-kg diving board, and the horizontal and vertical components of reaction at the pin A, the instant the man dives off. Assume that the board is uniform and
The turbine consists of a rotor which is powered from a torque applied at its center. At the instant the rotor is horizontal it has an angular velocity of 15 rad/s and a clockwise angular
The bar has a weight per length of w. If it is rotating in the vertical plane at a constant rate ω about point O, determine the internal normal force, shear force, and moment as a function of x and
If the support at B is suddenly removed, determine the initial reactions at the pin A. The plate has a weight of 30 lb. 2 ft B -2 ft
The furnace cover has a mass of 20 kg and a radius of gyration kG = 0.25 m about its mass center G. If an operator applies a force F = 120 N to the handle in order to open the cover, determine the
The 4-kg slender rod is initially supported horizontally by a spring at B and pin at A. Determine the angular acceleration of the rod and the acceleration of the rod’s mass center at the instant
The “Catherine wheel” is a firework that consists of a coiled tube of powder which is pinned at its center. If the powder burns at a constant rate of 20 g/s such that the exhaust gases always
The 4-kg slender rod is supported horizontally by a spring at A and a cord at B. Determine the angular acceleration of the rod and the acceleration of the rod’s mass center at the instant the cord
The uniform rod of length L has a mass of m. If the couple moment M0 is applied to its end, determine the internal normal force and shear force, and the bending moment in the rod as a function of x
If the disk in Fig. 17-19 rolls without slipping, show that when moments are summed about the instantaneous center of zero velocity, IC, it is possible to use the moment equation ∑MIC = lIcα,
The uniform 150-lb beam is initially at rest when the forces are applied to the cables. Determine the magnitude of the acceleration of the mass center and the angular acceleration of the beam at this
The 75-kg wheel has a radius of gyration about the z axis of kz = 150 mm. If the belt of negligible mass is subjected to a force of P = 150 N, determine the acceleration of the mass center and the
The spool has a mass of 100 kg and radius of gyration about its mass center of kG = 0.3 m. Determine its angular acceleration when the force of 250 N is applied to the cable. The spool rolls without
The ship has a weight of 4(166) lb and center of gravity at G. Two tugboats of negligible weight are used to turn it. If each tugboat pushes on it with a force of T = 2000 lb, determine the initial
The spool has a mass of 100 kg and radius of gyration about its mass center of kG = 0.3 m. Determine the smallest coefficient of static friction that will prevent slipping on the rail at A. What is
The 75-kg wheel has a radius of gyration about its mass center of kG = 375 mm. If it is subjected to a torque of M = 100 N · m, determine its angular acceleration. The coefficients of static and
The spool has a mass of 100 kg and a radius of gyration kG = 0.3 m. If the coefficients of static and kinetic friction at A are μs = 0.2 and μk = 0.15, respectively, and P = 600 N, determine the
The 75-kg wheel has a radius of gyration about its mass center of kG = 375 mm. If it is subjected to a torque of M = 150 N · m, determine its angular acceleration. The coefficients of static and
The 15-lb circular plate is suspended from a pin at A. If the pin is connected to a track which is given an acceleration aA = 3 ft/s2, determine the initial horizontal and vertical components of
If the coefficient of static friction at C is μs = 0.3, determine the largest force F that can be applied to the 5-kg ring without causing it to slip. Neglect the thickness of the ring. G 0.4
A force of F = 10 N is applied to the 10-kg ring as shown. If slipping does not occur, determine the ring’s initial angular acceleration, and the acceleration of its mass center, G. Neglect the
The slender, 200-kg beam is suspended by a cable at its end as shown. If a man pushes on its other end with a horizontal force of 30 N, determine the initial acceleration of its mass center G, the
The spool has a mass of 75 kg and a radius of gyration kG = 0.380 m. It rests on the inclined surface for which the coefficient of kinetic friction is μk = 0.15. If the spool is released from rest
If P = 30 lb, determine the angular acceleration of the 50-lb roller. Assume the roller to be a uniform cylinder and that no slipping occurs. P 30° 1.5 ft
If the coefficient of static friction between the 50-lb roller and the ground is μs = 0.25, determine the maximum force P that can be applied to the handle, so that the roller rolls on the ground
The truck carries the spool which has a weight of 500 lb and a radius of gyration of kG = 2 ft. Determine the angular acceleration of the spool if it is not tied down on the truck and the truck
The truck carries the spool which has a weight of 200 lb and a radius of gyration of kG = 2 ft. Determine the angular acceleration of the spool if it is not tied down on the truck and the truck
The semicircular disk having a mass of 10 kg is rotating at ω = 4 rad/s at the instant θ = 60°. If the coefficient ofstatic friction at A is μs = 0.5, determine if the disk slips at this instant.
The 10-lb hoop or thin ring is given an initial angular velocity of 6 rad/s when it is placed on the surface. If the coefficient of kinetic friction between the hoop and the surface μk = 0.3, is
Wheel C has a mass of 60 kg and a radius of gyration of 0.4 m, whereas wheel D has a mass of 40 kg and a radius of gyration of 0.35 m. Determine the angular acceleration of each wheel at the instant
The uniform bar of mass m and length L is balanced in the vertical position when the horizontal force P is applied to the roller at A. Determine the bar’s initial angular acceleration and the
The circular concrete culvert rolls with an angular velocity of ω = 0.5 rad/s when the man is at the position shown. Atthis instant the center of gravity of the culvert and the man islocated at
The uniform disk of mass m is rotating with an angular velocity of ω0 when it is placed on the floor. Determine the initial angular acceleration of the disk and the acceleration of its mass
The uniform disk of mass m is rotating with an angular velocity of ω0 when it is placed on the floor. Determine the time before it starts to roll without slipping. What is the angular velocity
The uniform plate weighs 40lb and is supported by a roller at A. If a horizontal force of F = 70 lb is applied to the roller, determine the acceleration of the center of the roller at the instant the
The cylinder A has a weight of 15 lb and is attached to the 20-lb block B using the cord and pulley system shown. Determine the acceleration of the block when it is released. The coefficients of
The uniform beam has a weight W. If it is originally at rest while being supported at A and B by cables, determine the tension in cable A if cable B suddenly fails. Assume the beam is a slender rod.
The 500-lb beam is supported at A and B when it is subjected to a force of 1000 lb as shown. If the pin support at A suddenly fails, determine the beam’s initial angular acceleration and the force
The 0.5-kg ball strikes the rough ground and rebounds with the velocities shown. Determine the magnitude of the impulse the ground exerts on the ball. Assume that the ball does not slip when it
A hammer head H having a weight of 0.3 lb is moving downwards at 40 ft/s when it strikes the head of a nail of negligible mass and drives it into a block of wood. Find the impulse on the nail if it
The 50-kg block is hoisted up the incline using the cable and motor arrangement shown. The coefficient of kinetic friction between the block and the surface is μk = 0.4. If the block is initially
The motor exerts a force of F = (20t2) N on the cable, where t is in seconds. Determine the speed of the 25-kg crate when t = 4 s. The coefficients of static and kinetic friction between the crate
A 20-kg block is originally at rest on a horizontal surface for which the coefficient of static friction is µs = 0.6 and the coefficient of kinetic friction is µk = 0.5. If a horizontal force F is
A 20-lb block slides down a 30° inclined plane with an initial velocity of 2 ft/s. Determine the velocity of the block in 3 s if the coefficient of kinetic friction between the block and the plane
Each of the cables can sustain a maximum tension of 5000 lb. If the uniform beam has a weight of 5000 lb, determine the shortest time possible to lift the beam with a speed of 10 ft/s starting from
The wheels of the 1.5-Mg car generate the traction force F described by the graph. If the car starts from rest, determine its speed when t = 6 s. F (KN) 6 kN 2 6 F -t(s)
The 200-g projectile is fired with a velocity of 900 m/s towards the center of the 15-kg wooden block, which rests on a rough surface. If the projectile penetrates and emerges from the block with a
The 2.5-Mg four-wheel-drive SUV tows the 1.5-Mg trailer. The traction force developed at the wheels is FD = 9 kN. Determine the speed of the truck in 20 s, starting from rest. Also, determine the
The 10-lb block A attains a velocity of 1 ft/s in 5 seconds, starting from rest. Determine the tension in the cord and the coefficient of kinetic friction between block A and the horizontal plane.
The 60-lb hoisting block is operated by a motor M. Starting from rest, the supporting cable can be wound up by the motor so that it is wound into the motor with a relative velocity of 3 ft/s in 5 s.
The freight cars A and B have a mass of 20 Mg and 15 Mg, respectively. Determine the velocity of A after collision if the cars collide and rebound, such that B moves to the right with a speed of 2
Crates A and B weigh 100 lb and 50 lb, respectively. If they start from rest, determine their speed when t = 5s . Also, find the force exerted by crate A on crate B during the motion. The coefficient
The automobile has a weight of 2700 lb and is traveling forward at 4 ft/s when it crashes into the wall. If the impact occurs in 0.06 s, determine the average impulsive force acting on the car.
The 200-kg crate rests on the ground for which the coefficients of static and kinetic friction are μs = 0.5 and μk = 0.4, respectively. The winch delivers a horizontal towing force T to its cable
The 5-kg block A has an initial speed of 5 m/s as it slides down the smooth ramp, after which it collides with the stationary 8-kg block B. If the two blocks couple together after collision,
The spring is fixed to block A and block B is pressed against the spring. If the spring is compressed s = 200 mm and then the blocks are released, determine their velocity at the instant block B
The force acting on a projectile having a mass m as it passes horizontally through the barrel of the cannon is F = C sin (πt/t′). Determine the projectile’s velocity when t = t′. If the
Blocks A and B have a mass of 15 kg and 10 kg, respectively. If A is stationary and B has a velocity of 15 m/s just before collision, and the blocks couple together after impact, determine the
During operation the jack hammer strikes the concrete surface with a force which is indicated in the graph. To achieve this the 2-kg spike S is fired into the surface at 90 m/s. Determine the speed
For a short period of time, the frictional driving force acting on the wheels of the 2.5-Mg van is FD = (600 t2) N, where t is in seconds. If the van has a speed of 20 km/h when , determine its speed
The cannon and support without a projectile have a mass of 250 kg. If a 20-kg projectile is fired from the cannon with a velocity of 400 m/s, measured relative to the cannon, determine the speed of
Determine the coefficient of restitution e between ball A and ball B. The velocities of A and B before and after the collision are shown. 8 m/s A Before collision 1 m/s A After collision 2 m/s 9
The 15-Mg tank car A and 25-Mg freight car B travel toward each other with the velocities shown. If the coefficient of restitution between the bumpers is e = 0.6, determine the velocity of each car
The 2.5-Mg van is traveling with a speed of 100 km/h when the brakes are applied and all four wheels lock. If the speed decreases to 40 km/h in 5 s, determine the coefficient of kinetic friction
A tankcar has a mass of 20 Mg and is freely rolling to the right with a speed of 0.75 m/s. If it strikes the barrier, determine the horizontal impulse needed to stop the car if the spring in the
The 30-lb package A has a speed of 5 ft/s when it enters the smooth ramp. As it slides down the ramp, it strikes the 80-lb package B which is initially at rest. If the coefficient of restitution
The 10-lb slider block is moving to the right with a velocity of 10 ft/s when it is acted upon by the forces F1 and F2. If the loading vary in the manner shown in the graph, determine the velocity of
The ball strikes the smooth wall with a velocity of (vb)₁= 20 m/s. If the coefficient of restitution between the ball and the wall is e = 0.75, determine the velocity of the ball just after the
The 180-lb iron worker is secured by a fall-arrest system consisting of a harness and lanyard AB, which is fixed to the beam. If the lanyard has a slack of 4 ft, determine the average impulsive force
The towing force acting on the 400-kg safe varies as shown in the graph. Determine its speed, starting from rest, when t = 8 s. How far has it traveled during this time? -0.0 F
The motor exerts a force F on the 40-kg crate as shown in the graph. Determine the speed of the crate when t = 3 s and when t = 6 s. When t = 0, the crate is moving downward at 10 m/s. B F F
The 30-kg slider block is moving to the left with a speed of 5 m/s when it is acted upon by the forces F1 and F2. If these loadings vary in the manner shown on the graph, determine the speed of the
Two disks A and B each have a mass of 1 kg and the initial velocities shown just before they collide. If the coefficient of restitution is e = 0.5, determine their speeds just after impact. (VB)1 = 3
The 2-kg particle A has the velocity shown. Determine its angular momentum Ho about point O. 3 m 0 -4 m- 2 kg | A X 10 m/s
Determine the maximum speed attained by the 1.5-Mg rocket sled if the rockets provide the thrust shown in the graph. Initially, the sled is at rest. Neglect friction and the loss of mass due to fuel
The motor pulls on the cable at A with a force F = (30 + t2) lb, where t is in seconds. If the 34-lb crate is originally on the ground at t = 0, determine its speed in t = 4 s. Neglect the mass of
If it takes 35 s for the 50-Mg tugboat to increase its speed uniformly to 25 km/h, starting from rest, determine the force of the rope on the tugboat. The propeller provides the propulsion force F on
The 2-kg sphere is attached to the rod, which rotates in the horizontal plane centered at O. If the system is subjected to a couple moment M = (0.9t2) N · m, where t is in seconds, determine the
The tanker has a mass of 130 Gg. If it is originally at rest, determine its speed when t = 10 s. The horizontal thrust provided by its propeller varies with time as shown in the graph. Neglect the
Two identical 10-kg spheres are attached to the rod, which rotates in the horizontal plane centered at pin O. If the spheres are subjected to tangential forces of P = 10 N, and the rod is subjected
The small 20-lb block is placed on the inclined plane and subjected to 6-lb and 15-lb forces that act parallel with edges AB and AC, respectively. If the block is initially at rest, determine its
The balloon has a total mass of 400 kg including the passengers and ballast. The balloon is rising at a constant velocity of 18 km/h when h = 10 m. If the man drops the 40-kg sand bag, determine the
A jet plane having a mass of 7 Mg takes off from an aircraft carrier such that the engine thrust varies as shown by the graph. If the carrier is traveling forward with a speed of 40 km/h, determine
The 100-kg crate is hoisted by the motor M. If the velocity of the crate increases uniformly from 1.5m/s to 4.5m/s in 5 s, determine the tension developed in the cable during the motion. M
The 100-kg crate is hoisted by the motor M.The motor exerts a force on the cable of T = (200t1/2 + 150) N, where t is in seconds. If the crate starts from rest at the ground, determine the speed of
If the force T exerted on the cable by the motor M is indicated by the graph, determine the speed of the 500-lb crate when t = 4 s, starting from rest. The coefficients of static and kinetic friction
The inclined plate moves to the left with a constant velocity v. Determine the angular velocity and angular acceleration of the slender rod of length ∫.The rod pivots about the step at C as it
The 5-Mg bus B is traveling to the right at 20 m/s. Meanwhile a 2-Mg car A is traveling at 15 m/s to the right. If the vehicles crash and become entangled, determine their common velocity just after
A cake and plate weighing 1.5 lb rest at the center of a circular table. Without touching the cake a boy attempts to remove the 2-ft-radius tablecloth by quickly pulling on it horizontally. If
The 2.5-Mg pickup truck is towing the 1.5-Mg car using a cable as shown. If the car is initially at rest and the truck is coasting with a velocity of 30 km/h when the cable is slack, determine the
The 5-kg spring-loaded gun rests on the smooth surface. It fires a ball having a mass of 1 kg with a velocity of v' = 6 m/s relative to the gun in the direction shown. If the gun is originally at
The 5-kg spring-loaded gun rests on the smooth surface. It fires a ball having a mass of 1 kg with a velocity of v' = 6 m/s relative to the gun in the direction shown. If the gun is originally at
The 20-g bullet is traveling at 400 m/s when it becomes embedded in the 2-kg stationary block. Determine the distance the block will slide before it stops. The coefficient of kinetic friction between
A ballistic pendulum consists of a 4-kg wooden block originally at rest, θ = 0°. When a 2-g bullet strikes and becomes embedded in it, it is observed that the block swings upward to a maximum angle
The boy B jumps off the canoe at A with a velocity of 5 m/s relative to the canoe as shown. If he lands in the second canoe C, determine the final speed of both canoes after the motion. Each canoe

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