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engineering
engineering mechanics statics

Questions and Answers of Engineering Mechanics Statics

The small gear has a mass m and may be treated as a uniform disk. If it is released from rest at θ = 0°, and rolls along the fixed circular gear rack, determine the angular velocity of the radial
The slender rod has a mass of 10 kg and is released from rest when it is in the vertical position. Determine its angular velocity at the instant it becomes horizontal. The attached block at D has a
The uniform rectangular door panel has a mass of 25 kg and is held in equilibrium above the horizontal at the position θ = 60° by rod BC. Determine the required stiffness of the torsional spring at
The arm and seat of the amusement-park ride have a mass of 1.5 Mg, with the center of mass located at point G1. The passenger seated at A has a mass of 125 kg, with the center of mass located at G2.
The uniform bar AB has a mass of 12 kg and is pin connected at A. If the support at B is remove (θ = 90°), determine the velocity of the 5-kg block C at the instant the bar rotates downward to θ =
Pulley A has a weight of 30 lb and a centroidal radius of gyration kB = 0.6 ft. Determine the speed of the 20-lb crate C at the instant s = 10 ft. Initially, the crate is released from rest when s =
The 50-lb wheel has a radius of gyration about its center of gravity G of KG = 0.7 ft. If it rolls without slipping, determine its angular velocity when it has rotated clockwise 90° from the
The system consists of 60-lb and 20-lb blocks A and B, respectively, and 5-lb pulleys C and D that can be treated as thin disks. Determine the speed of block A after block B has risen 5 ft, starting
Gear A has a mass of 0.5 kg and a radius of gyration of kA = 40 mm, and gear B has a mass of 0.8 kg and a radius of gyration of kB = 55 mm. The link is pinned at C and has a mass of 0.35 kg. If the
The gear is pinned at A and has a mass of 0.3 kg and a radius of gyration of kA = 25 mm. The gear rack has mass of 0.5 kg. If has spring is stretched 50 mm and released from rest, determine the
Determine the moment of inertia Iz of the frustum of the cone, which has a conical depression. The material has a density of 200 kg/m3. 200 mm- 800 mm Z 600 mm 400 mm
The pendulum consists of a plate having a weight of 12 lb and a slender rod having a weight of 4 lb. Determine the radius of gyration of the pendulum about an axis perpendicular to the page and
The pendulum consists of a 2-kg disk, and slender rods AB and DC which have a mass per unit length of 2 kg/m. Determine the length L of DC so that the center of mass is at the bearing O. What is the
The jet plane has a mass of 250 Mg and a horizontal velocity of 100 m/s when t = 0. If both engines provide a horizontal thrust which varies as shown in the graph, determine the plane’s velocity in
Determine the moment of inertia Iy for the slender rod. The rod’s density ρ and cross-sectional area A are constant. Express the result in terms of the rod’s total mass m. N
The handcart has a mass of 200 kg and center of mass at G. Determine the normal reactions at each of the wheels at A and B if a force P = 50 N is applied to the handle. Neglect the mass and rolling
The two 3-lb rods EF and HI are fixed (welded) to the link AC at E. Determine the internal axial force Ex shear force Ey, and moment ME, which the bar AC exerts on FE at E if at the instant θ = 30°
The cart and its load have a total mass of 100 kg. Determine the acceleration of the cart and the normal reactions on the pair of wheels at A and B. Neglect the mass of the wheels. 100 N 1.2 m OB 0.3
The solid cylinder has an outer radius R, height h, and is made from a material having a density that varies from its center as ρ = k + ar2, where k and a are constants. Determine the mass of the
The 20-lb link AB is pinned to a moving frame at Aand held in a vertical position by means of a string BC whichcan support a maximum tension of 10 lb. Determine themaximum acceleration of the frame
If the 80-kg cabinet is allowed to roll down theinclined plane, determine the acceleration of the cabinetand the normal reactions on the pair of rollers at A and Bthat have negligible mass. 1.5
Determine the moment of inertia of the thin ring about the z axis.The ring has a mass m. y R -X
A 20-kg roll of paper, originally at rest, is pin supported at its ends to bracket AB. The roll rests against a wall for which the coefficient of kinetic friction at C is μc=0.3. If a force of 40 N
The car has a mass of 1.50 Mg and a mass center at G. Determine the maximum acceleration it can have if power is supplied only to the rear wheels. Neglect the mass of the wheels in the calculation,
At the instant shown both rods of negligible mass swing with a counterclockwise angular velocity of ω = 5 rad/s, while the 50-kg bar is subjected to the 100-N horizontal force. Determine the tension
Determine the maximum acceleration of the truck without causing the 100-kg assembly to move relative to the truck. Also what is the corresponding normal reaction on legs A and B? The assembly has a
The right circular cone is formed by revolving the shaded area around the x axis. Determine the moment of inertia Ix and express the result in terms of the total mass m of the cone. The cone has a
At the instant shown, two forces act on the 30-lb slender rod which is pinned at O. Determine the magnitude of force F and the initial angular acceleration of the rod so that the horizontal reaction
Determine the mass moment of inertia Iz of the cone formed by revolving the shaded area around the z axis. The total density of the material is ρ. Express the results in terms of the mass m of the
The pendulum consists of a 30-lb sphere and a 10-lb slender rod. Compute the reaction at the pin O just after the cord AB is cut. 1 ft B 2 ft
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

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