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engineering
engineering mechanics statics
Questions and Answers of
Engineering Mechanics Statics
At the instant shown, rod CD rotates with an angular velocity of ω = 6 rad/s. If it is subjected to a couplemoment M = 450 N · m, determine the force developed inrod AB, the horizontal and vertical
Determine the backspin ω which should be given to the 20-lb ball so that when its center is given an initial horizontal velocity vG = 20 ft/s it stops spinning and translating at the same instant.
Determine the moment of inertia of the assembly about an axis which is perpendicular to the page and passes through point O. The material has a specific weight of γ = 90 lb>ft3. 0.5 ft 1 ft G 2
The 50-kg disk is subjected to the couple moment of M = (91) N·m, where t is in seconds. Determine theangular velocity of the disk when t = 4 s starting from rest. 0.3 m - M = (9t) N-m
The spool and wire wrapped around its core have a mass of 20 kg and a centroidal radius of gyration KG = 250 mm. If the coefficient of kinetic friction at the ground is μB = 0.1, determine the
Determine the moment of inertia Iz of the torus.The mass of the torus is m and the density is constant. N R.
Determine the moment of inertia of the semi ellipsoid with respect to the x axis and express the result in terms of the mass m of the semi ellipsoid. The material has a constant density ρ. + 1 b X
The wheel consists of a thin ring having a mass of 10 kg and four spokes made from slender rods and each having a mass of 2 kg. Determine the wheel’s moment of inertia about an axis perpendicular
Determine the moment of inertia of the solid steel assembly about the x axis. Steel has a specific weight of γst = 490 lb/ft3. 0.25 ft -2 ft- -3 ft- 0.5 ft X
Determine the location ȳ of the center of mass G of the assembly, and then calculate the moment of inertia about an axis perpendicular to the page and passing through G. The block has a mass of 3
Determine the moment of inertia of the assembly about an axis perpendicular to the page and passing through point O. The block has a mass of 3 kg, and the semicylinder has a mass of 5 kg. y 400
Determine the moment of inertia of the center crank about the x axis. The material is steel having a specific weight of γst = 490 lb/ft3. 0.5 in.- ↓ 1 0.5 in. 0.5 in. 1 in. -0.5 in. 1 in. 0.5
Determine the moment of inertia of the wheel about an axis which is perpendicular to the page and passes through the center of mass G. The material has a specific weight γ = 90 lb/ft3. /0.25 ft/ 0.5
Determine the mass moment of inertia of the thin plate about an axis perpendicular to the page and passing through point O. The material has a mass per unit area of 20 kg/m2. 200 mm 200 mm 200 mm
The slender rods have a weight of 3 lb/ft Determine the moment of inertia of the assembly about an axis perpendicular to the page and passing through point A. A -1.5 ft 1.5 ft 2 ft 1 ft
Determine the moment of inertia of the overhung crank about the x axis. The material is steel having a destiny of ρ = 7.85 Mg/m3. 20 mm 50 mm 20 mm- 90 mm 20 mm ↓ 50 mm -X 30 mm/ 30 mm 180 mm T 30
Determine the moment of inertia of the overhung crank about the x′ axis. The material is steel having a destiny of ρ = 7.85 Mg/m3. 20 mm 50 mm 20 mm- 90 mm 20 mm 50 mm -X 30 mm 30 mm 180 mm 30 mm
Determine the moment of inertia of the wheel about an axis which is perpendicular to the page and passes through point O. The material has a specific weight γ = 90 lb/ft3. 0.5 ft 0.25 ft/1 ft 2
The door has a weight of 200 lb and a center of gravity at G. Determine how far the door moves in 2 s, starting from rest, if a man pushes on it at C with a horizontal force F = 30 lb. Also, find the
The bicycle and rider have a mass of 80 kg with center of mass located at G. If the coefficient of kinetic friction at the rear tire is μB = 0.8, determine the normal reactions at the tires A and B,
The door has a weight of 200 lb and a center of gravity at G. Determine the constant force F that must be applied to the door to push it open 12 ft to the right in 5 s, starting from rest. Also, find
The bicycle and rider have a mass of 80 kg with center of mass located at G. Determine the minimum coefficient of kinetic friction between the road and the wheels so that the rear wheel B starts to
The jet aircraft has a total mass of 22 Mg and a center of mass at G. Initially at take-off the engines provide a thrust 2T = 4 kN and T′ = 1.5 kN Determine the acceleration of the plane and the
The sports car has a weight of 4500 lb and center of gravity at G. If it starts from rest it causes the rear wheels to slip as it accelerates. Determine how long it takes for it to reach a speed of
Block A weighs 50 lb and the platform weighs 10 lb. If P = 100 lb, determine the normal force exerted by block A on B. Neglect the weight of the pulleys and bars of the triangular frame. A P O A B
The motorcycle and rider have a total mass of 900 kg and mass center at G. If it is traveling up the slope with a constant acceleration of 3 m/s2, determine the normal reactions on the front and rear
The motorcycle and rider have a total mass of 900 kg and mass center at G. Determine the minimum coefficient of static friction between the rear wheel and the slope in order for the rider to perform
At the start of takeoff, the propeller on the 2-Mg plane exerts a horizontal thrust of 600 N on the plane. Determine the plane’s acceleration and the vertical reactions at the nose wheel A and each
The sports car has been designed so that the 260-kg engine E 165-kg transmission T have been placed over the front and rear wheels, respectively. Their mass centers are located at GE and GT. The mass
The dresser has a weight of 80 lb and is pushed along the floor. If the coefficient of static friction at A and B is μs = 0.3 and the coefficient of kinetic friction is μk = 0.2, determine the
The bar has a weight per length w and is supported by the smooth collar. If it is released from rest, determine the internal normal force, shear force, and bending moment in the bar as a function of
The dresser has a weight of 80 lb and is pushed along the floor. If the coefficient of static friction at A and B is μs = 0.3 and the coefficient of kinetic friction is μk = 0.2, determine the
The smooth 180-lb pipe has a length of 20 ft and a negligible diameter. It is carried on a truck as shown. If the truck accelerates at a = 5 ft/s2, determine the normal reaction at A and the
The crate of mass m is supported on a cart of negligible mass. Determine the maximum force P that can be applied a distance d from the cart bottom without causing the crate to tip on the cart.
A 75-kg man and 40-kg girl sit on the seesaw, which has negligible mass. At the instant the man lifts his feet from the ground, determine their acceleration if each sits upright, i.e., they do not
The smooth 180-lb pipe has a length of 20 ft and a negligible diameter. It is carried on a truck as shown. Determine the maximum acceleration which the truck can have without causing the normal
The uniform bar of mass m is pin connected to the collar, which slides along the smooth horizontal rod. If the collar is given a constant acceleration of a, determine the bar’s inclination angle
Determine the greatest possible acceleration of the 975-kg race car so that its front tires do not leave the ground or the tires slip on the track. The coefficients of static and kinetic friction are
The truck carries the 1200-lb safe, which has a center of mass at G. Determine the largest acceleration of the truck so that the safe will not slip or tip on the truck bed. The coefficient of static
A man stands in the aisle of a moving train. If the coefficient of static friction between his shoes and the floor is μs = 0.5, and he has a mass of 85 kg, with center of mass at G, determine the
Determine the greatest possible acceleration of the 975-kg race car so that its front wheels do not leave the ground and none of the tires slip on the track. The coefficients of static and kinetic
The four-wheeler has a weight of 335 lb and a center of gravity at G1, whereas the rider has a weight of 150 lb and a center of gravity at G2. If the coefficient of static friction between the rear
The four-wheeler has a weight of 335 lb and a center of gravity at G1, whereas the rider has a weight of 150 lb and a center of gravity at G2. If the engine can develop enough torque to cause the
The forklift travels forward with a constant speed of 9ft/s. Determine the shortest stopping distance without causing any of the wheels to leave the ground. The forklift has a weight of 2000 lb with
If the cart’s mass is 30 kg and it is subjected to a horizontal A force of P = 90 N, determine the tension in cord AB and the horizontal and vertical components of reaction on end C of the uniform
If the cart’s mass is 30 kg, determine the horizontal force P that should be applied to the cart so that the cord AB just becomes slack.The uniform rod BC has a mass of 15 kg. 1
A uniform plate has a weight of 50 lb. Link AB is subjected to a couple moment of M = 10 lb · ft and has a clockwiseangular velocity of 2 rad/s at the instant θ = 30°. Determinethe force developed
If the forklift's rear wheels supply a combined traction force of FA = 300 lb, determine its acceleration and the normal reactions on the pairs of rear wheels and front wheels. The forklift has a
The crate C has a weight of 150 lb and rests on the truck elevator for which the coefficient of static friction is μs = 0.4. Determine the largest initial angular acceleration a, starting from rest,
The 10-kg wheel has a radius of gyration KA = 200 mm. If the wheel is subjected to a moment M = (5t) N · m, where t is in seconds, determine its angular velocity when t = 3 s starting from rest.
The crate C has a weight of 150 lb and rests on the truck elevator. Determine the initial friction and normal force of the elevator on the crate if the parallel links are given an angular
The uniform slender rod has a mass m. If it is released from rest when θ = 0°, determine the magnitude of the reactive force exerted on it by pin B when θ = 90°. A -5. B Te 룩
If the hydraulic cylinder BE exerts a vertical force of F = 1.5 kN on the platform, determine the force developed in links AB and CD at the instant θ = 90°. The platform is at rest when θ = 45°.
The bent rod has a mass of 2 kg/m. If it is released from rest in the position shown, determine its initial angular acceleration and the horizontal and vertical components of reaction at A. 1.5
The uniform slender rod has a mass of 5 kg. If the cord at A is cut, determine the reaction at the pin O, (a) When the rod is still in the horizontal position, and (b) When the rod swings
The uniform 24-kg plate is released from rest at the position shown. Determine its initial angular acceleration and the horizontal and vertical reactions at the pin A. A -0.5 m- 0.5 m
A motor supplies a constant torque M = 2 N · m to a 50-mm- diameter shaft O connected to the center of the 30-kg flywheel. The resultant bearing friction F, which the bearing exerts on the shaft,
If the motor of Prob. 17-62 is disengaged from the shaft once the flywheel is rotating at 15 rad/s, so that M = 0, determine how long it will take before the resultant bearing friction F = 50 N stops
The kinetic diagram representing the general rotational motion of a rigid body about a fixed axis passing through O is shown in the figure. Show that IGα may be eliminated by moving the vectors
In order to experimentally determine the moment of inertia IG of a 4-kg connecting rod, the rod is suspended horizontally at A by a cord and at B by a bearing and piezoelectric sensor, an
Disk A has a weight of 5 lb and disk B has a weight of 10 lb. If no slipping occurs between them, determine the couple moment M which must be applied to disk A to give it an angular acceleration of 4
The disk has a mass M and a radius R. If the block of mass m is attached to the cord, determine the angular velocity of the disk when the block is released from rest and falls a distance h. R h
The rod has a length L and mass m. If it is released from rest when θ ≈ 0°, determine its angular velocity as a function of θ. Also, express the horizontal and vertical components of reaction at
The reel of cable has a mass of 400 kg and a radius of gyration of kA = 0.75 m. Determine its angular velocity when t = 2 s, starting from rest, if the force P = (20t2 + 80) N is applied, where t is
The passengers, the gondola, and its swing frame have a total mass of 50 Mg, a mass center at G, and a radius of gyration kB = 3.5 m. Additionally, the 3-Mg steel block at A can be considered as a
The 30-kg disk is originally spinning at ω = 125 rad/s. If it is placed on the ground, for which the coefficient of kinetic friction is μC = 0.5, determine the time required for the motion to stop.
The passengers, the gondola, and its swing frame have a total mass of 50 Mg, a mass center at G, and a radius of gyration kB = 3.5 m. Additionally, the 3-Mg steel block at A can be considered as a
Cable is unwound from a spool supported on small rollers at A and B by exerting a force T = 300 N on the cable. Determine the time needed to unravel 5 m of cable from the spool if the spool and cable
The man pulls up on the cord with a force of 80 N. Determine the angular acceleration of the spool if there is no slipping at A. The spool has a mass of 60 kg and a radius of gyration about its mass
The 5-kg cylinder is initially at rest when it is placed in contact with the wall B and the rotor at A. If the rotor always maintains a constant clockwise angular velocity ω= 6 rad/s, determine the
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
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