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engineering
engineering mechanics statics

Questions and Answers of Engineering Mechanics Statics

A uniform slender rod AB rests on a frictionless horizontal surface, and a force P of magnitude 0.75 lb is applied at A in a direction perpendicular to the rod. Knowing that the rod weighs 2 lb,
A uniform slender bar AB with a mass m is suspended from two springs as shown. If spring 2 breaks, determine at that instant (a) The angular acceleration of the bar, (b) The acceleration of point
The steel roll shown has a mass of 1200 kg, a centroidal radius of gyration of 150 mm, and is lifted by two cables looped around its shaft. Knowing that for each cable TA = 3100 N and TB = 3300 N,
A force P with a magnitude of 3 N is applied to a tape wrapped around the body indicated. Knowing that the body rests on a frictionless horizontal surface, determine the acceleration of (a) Point
A 250-lb satellite has a radius of gyration of 24 in. with respect to the y axis and is symmetrical with respect to the zx plane. Its orientation is changed by firing four small rockets—A, B, C,
The steel roll shown has a mass of 1200 kg, has a centroidal radius of gyration of 150 mm, and is lifted by two cables looped around its shaft. Knowing that at the instant shown the acceleration of
A uniform semicircular plate with a mass of 6 kg is suspended from three vertical wires at points A, B, and C, and a force P with a magnitude of 5 N is applied to point B. Immediately after P is
A drum with a 200-mm radius is attached to a disk with a radius of rA = 150 mm. The disk and drum have a combined mass of 5 kg and a combined radius of gyration of 120 mm and are suspended by two
A thin plate of the shape indicated and of mass m is suspended from two springs as shown. If spring 2 breaks, determine the acceleration at that instant of (a) Point A, (b) Point B. 2 Vood Ø Ø Ø
A drum with a 200-mm radius is attached to a disk with a radius of rA = 140 mm. The disk and drum have a combined mass of 5 kg and are suspended by two cords. Knowing that the acceleration of point B
The rotor of an electric motor has an angular velocity of 3600 rpm when the load and power are cut off. The 120-lb rotor, which has a centroidal radius of gyration of 9 in., then coasts to rest.
A thin plate of the shape indicated and of mass m is suspended from two springs as shown. If spring 2 breaks, determine the acceleration at that instant of (a) Point A, (b) Point B. 1 www A• Fig.
A thin plate of the shape indicated and of mass m is suspended from two springs as shown. If spring 2 breaks, determine the acceleration at that instant of (a) Point A, (b) Point B. 2 A 1 Fig.
A cyclist uses a stationary trainer during the winter to keep in shape. Knowing that she pushes down on her pedal with a velocity of 26 in./s that increases at a rate of 2 in./s2, determine the
At the instant shown, the angular velocity of crank OB is 100 rpm in the counterclockwise direction. Knowing that gear C is fixed, determine (a) The angular velocity of the planetary gear B, (b)
The sprocket wheel and chain shown are initially at rest. If the wheel has a uniform angular acceleration of 90 rad/s2 counterclockwise, determine (a) The acceleration of point A of the chain, (b)
A person walks radially inward on a platform that is rotating counterclockwise about its center. Knowing that the platform has a constant angular velocity ω and the person walks with a constant
The plate shown moves in the xy plane. Knowing that (vA)x = 12 in./s, (vB)x = −4 in./s, and (vC)y = −24 in./s, determine(a) The angular velocity of the plate,(b) The velocity of point B, (c) The
Rod AB can slide freely along the floor and the inclined plane. At the instant shown, the velocity of end A is 1.4 m/s to the left. Determine (a) The angular velocity of the rod, (b) The velocity
The sprocket wheel and chain shown are being operated at a speed of 600 rpm counterclockwise. When the power is turned off, it is observed that the wheel and chain coast to rest in 4s. Assuming
An overhead door is guided by wheels at A and B that roll in horizontal and vertical tracks. Knowing that when θ = 30° the velocity of wheel B is 2 ft/s downward, determine (a) The angular
The test rig shown was developed to perform fatigue testing on fitness trampolines. A motor drives the 9-in.-radius flywheel AB, which is pinned at its center point A, in a counterclockwise
In the position shown, bar AB has an angular velocity of 10 rad/s counterclockwise. Determine the angular velocity of bars BD and DE. B 200 mm 75 mm D Fig. P15.64 - 175 mm → 100 mm A E
As steam is slowly injected into a turbine, the angular acceleration of the rotor is observed to increase linearly with the time t. Knowing that the rotor starts from rest at t = 0 and that after 10
Linkage DBEF is part of a windshield wiper mechanism, where points O, F, and D are fixed pin connections. At the position shown, θ = 30° and link EB is horizontal. Knowing that link EF has a
For the oil pump rig shown, link AB causes the beam BCE to oscillate as the crank OA revolves. Knowing that OA has a radius of 0.6 m and at the instant shown the velocity of point D is 1.5 m/s down,
A rear wheel drive car starts from rest and accelerates to the left so that the tires do not slip on the road. What is the direction of the acceleration of the point on the tire in contact with the
The right leg of an athlete on a rowing machine can be modeled as a linkage as shown, where A represents the ankle (which is stationary), K the knee, and H the hip. At the instant when θ = 75°, the
Knowing that at the instant shown bar AB has a constant angular velocity of 10 rad/s clockwise, determine the angular acceleration of (a) Bar BD, (b) Bar DE. B A E -20 in.. Fig. P15.131 and
Knowing that the angular velocity of rod DE is a constant 20 rad/s clockwise, determine in the position shown (a) The angular acceleration of bar BD, (b) The angular acceleration of bar AB. 8
In the two-cylinder air compressor shown, the connecting rods BD and BE are each 190 mm long and crank AB rotates about the fixed point A with a constant angular velocity of 1500 rpm clockwise.
A 3-in.-radius drum is rigidly attached to a 5-in.- radius drum as shown. One of the drums rolls without sliding on the surface shown, and a cord is wound around the other drum. Knowing that at the
Pin P is attached to the wheel shown and slides in a slot cut in bar BD. The wheel rolls to the right without slipping with a constant angular velocity of 20 rad/s. Knowing that x = 480 mm when θ =
Knowing that at the instant shown bar DE has an angular velocity of 20 rad/s clockwise and an angular acceleration of 5 rad/s2 counterclockwise, determine in the position shown (a) The angular
Knowing that at the instant shown bar AB has a constant angular velocity of 10 rad/s clockwise, determine the angular acceleration of (a) Bar BD, (b) Bar DE. 200 mm B 75 mm D 175 mm 100 mm A Fig.
The motion of pin P is guided by slots cut in rods AE and BD. Knowing that the rods rotate with the constant angular velocities ωA = 4 rad/s clockwise and ωB = 5 rad/s counterclockwise, determine
Two rotating rods are connected by slider block P. The rod attached at A rotates with a constant clockwise angular velocity ωA. For the given data, determine for the position shown (a) The angular
A 3-in.-radius drum is rigidly attached to a 5-in.- radius drum as shown. One of the drums rolls without sliding on the surface shown, and a cord is wound around the other drum. Knowing that at the
In order to uncoil electrical wire from a spool fixed to a truck, a worker drives to the left with a speed of vA = 4 m/s. At the same time, a second worker holds the cable as he walks to the right.
In order to uncoil electrical wire from a 0.6-m-radius spool fixed to a truck, a worker drives to the left with a speed of vA = 5 m/s. At the same time, a second worker holds the cable as he walks to
Rod ABD is guided by wheels at A and B that roll in horizontal and vertical tracks. Knowing that at the instant β = 60° and the velocity of wheel B is 40 in./s downward, determine (a) The angular
Two 500-mm rods are pin-connected at D as shown. Knowing that B moves to the left with a constant velocity of 360 mm/s, determine at the instant shown (a) The angular velocity of each rod, (b) The
An automobile travels to the left at a constant speed of 90 km/h. Knowing that the diameter of the wheel is 650 mm, determine the acceleration of (a) Point B, (b) Point C, (c) Point D. D Fig.
Knowing that at the instant shown block B has a velocity of 2 ft/s to the right and an acceleration of 3 ft/s2 to the left, determine (a) The velocity of block A, (b) The acceleration of block A.
The initial velocity v0 of a hockey puck is 90 mi/h. Determine (a) The largest value (less than 45°) of the angle α for which the puck will enter the net, (b) The corresponding time required for
Many car companies are performing research on collision avoidance systems. A small prototype applies engine braking that decelerates the vehicle according to the relationship a = -k√t, where a and
Knowing that dC = 5 m, determine (a) The distances dB and dD, (b) The maximum tension in the cable. 2.5 m 2 m da B 10 KN 3 m- C 2 m 10 KN dp D 10 KN -3 m E
Knowing that dC = 9 ft, determine (a) The distances dB and dD, (b) The reaction at E. A 6 ft 6 ft 9 ft B 1 kip dB dc C 1 kip dp D 2 kips 9 ft 12 ft E
Knowing that the radius of each pulley is 120 mm and neglecting friction, determine the internal forces at (a) Point C, (b) Point J that is 100 mm to the left of C. A 300 mm 200 mm 200 mm B 600
Knowing that the radius of each pulley is 100 mm and neglecting friction, determine the internal forces at (a) Point C, (b) Point J that is 100 mm to the left of C. A 300 mm 200 mm 200 mm B 600
If dA = dC = 6 ft, determine (a) The components of the reaction at E, (b) The maximum tension in the cable. 10 ft- 10 ft-10 ft-10 ft- B 200 lb C de 400 lb D 200 lb
For the frame of Problem 7.17, determine the magnitude and location of the maximum bending moment in member BC.PROBLEM 7.17 A 5-in.-diameter pipe is supported every 9 ft by a small frame consisting
For the beam shown, draw the shear and bending-moment diagrams, and determine the magnitude and location of the maximum absolute value of the bending moment, knowing that (a) M = 0, (b) M = 24 kip
Two slender rods of negligible weight are pin-connected at C and attached to blocks A and B, each of weight W. Knowing that θ = 80° and that the coefficient of static friction between the blocks
Solve Prob. 8.34, assuming that the weight of the car is equally distributed over its front and rear wheels.PROBLEM 8.34 A driver starts the engine of an automobile that is stopped with its front
An 8° wedge is to be forced under a machine base at B. Knowing that the coefficient of static friction at all surfaces of contact is 0.15, (a) Determine the force P required to move the wedge, (b)
A 5-in.-diameter pipe is supported every 9 ft by a small frame consisting of two members as shown. Knowing that the combined weight of the pipe and its contents is 10 lb/ft and neglecting the effect
If dA = 8 ft and dC = 10 ft, determine the components of the reaction at E. -10 ft-10 ft- BO 200 lb C -10 ft-10 ft- de 400 lb D 200 lb
A driver starts the engine of an automobile that is stopped with its front wheels resting against a curb and tries to drive over the curb. Knowing that the radius of the wheels is 12 in., that the
Determine (a) Distance dC for which portion DE of the cable is horizontal, (b) The corresponding reactions at A and E. 6 ft 6 ft B 1 kip 9 ft ¡dB dc 1 kip dp D 2 kips 9 ft 12 ft E
The total mass of cable ACB is 20 kg. Assuming that the mass of the cable is distributed uniformly along the horizontal, determine (a) The sag h, (b) The slope of the cable at A. 4.5 m A D -8
A uniform 20-kg tube resting on a loading dock will be moved by means of a cable attached at end A. Knowing that the coefficient of static friction between the tube and the dock is 0.30, determine
The axle of the pulley is frozen and cannot rotate with respect to the block. Knowing that the coefficient of static friction between cable ABCD and the pulley is 0.30, determine (a) The maximum
A 200-lb sliding door is mounted on a horizontal rail as shown. The coefficients of static friction between the rail and the door at A and B are 0.15 and 0.25, respectively. Determine the horizontal
The cylinder shown is of weight W and radius r. Express in terms W and r the magnitude of the largest couple M that can be applied to the cylinder if it is not to rotate, assuming the coefficient of
Determine the minimum value of P that must be applied to the wedge in order to move the 900-kg block. The coefficient of static friction is 0.30 at all surfaces of contact. 6⁰ P Fig. P8.50 900 kg
The coefficients of friction between the block and the rail are μs = 0.25 and μk = 0.20. Find the magnitude and direction of the smallest force P required (a) To start the block moving up the
Solve Problem 8.62 assuming that the wedge is to be forced under the machine base at A instead of B.PROBLEM 8.62An 8° wedge is to be forced under a machine base at B. Knowing that the coefficient of
The coefficients of friction between the block and the rail are μs = 0.25 and μk = 0.20. Knowing that θ = 60°, determine the smallest value of P required (a) To start the block moving up the
A motor M is used to slowly reel in the cable shown. Knowing that the mass per unit length of the cable is 0.4 kg/m, determine the maximum tension in the cable when h = 5 m. A -10 m- h C B M
Determine whether the block shown is in equilibrium and find the magnitude and direction of the friction force when θ = 35° and P = 100 lb. M₂ = 0.30 Mk=0.20 P 250 lb 0 Fig. P8.3 and P8.4
A 120-lb cabinet is mounted on casters that can be locked to prevent their rotation. The coefficient of static friction between the floor and each caster is 0.30. If h = 32 in., determine the
A uniform 20-kg tube rests on a loading dock with its end B located at a distance a = 0.25 m from the edge C of the dock. A cable attached at end A forming an angle θ = 60° with the tube will be
The elevation of the end of the steel beam supported by a concrete floor is adjusted by means of the steel wedges E and F. The base plate CD has been welded to the lower flange of the beam, and the
Solve Prob. 8.52 assuming that the end of the beam is to be lowered.PROBLEM 8.52The elevation of the end of the steel beam supported by a concrete floor is adjusted by means of the steel wedges E and
A slender steel rod of length 225 mm is placed inside a pipe as shown. Knowing that the coefficient of static friction between the rod and the pipe is 0.20, determine the largest value of θ for
A 200-lb block rests as shown on a wedge of negligible weight. Knowing that the coefficient of static friction is 0.25 at all surfaces of contact, determine the angle θ for which sliding is
Two uniform rods each of weight W and length L are maintained in the position shown by a couple M0 applied to rod CD. Knowing that the coefficient of static friction between the rods is 0.40,
The 10-lb uniform rod AB is held in the position shown by the force P. Knowing that the coefficient of static friction is 0.20 at A and B, determine the smallest value of P for which equilibrium is
The coefficient of static friction between block B and the horizontal surface and between the rope and support C is 0.40. Knowing that mA = 12 kg, determine the smallest mass of block B for which
Determine the mass moment of inertia of the steel fixture shown with respect to (a) The x axis, (b) The y axis, (c) The z axis. N 16 mm 40 mm 24 mm 70 mm y 50 mm 38 mm 80 mm 50 mm X
Determine the minimum value of P that must be applied to the wedge in order to move the 900-kg block. The coefficient of static friction is 0.30 at all surfaces of contact. 6⁰ 6⁰ Fig. P8.51 900 kg
The link arrangement shown is frequently used in highway bridge construction to allow for expansion due to changes in temperature. At each of the 60-mm-diameter pins A and B the coefficient of static
The position of the automobile jack shown is controlled by a screw ABC that is single-threaded at each end (right-handed thread at A, left-handed thread at C). Each thread has a pitch of 2.5 mm and a
In the vise shown, the screw is single-threaded in the upper member; it passes through the lower member and is held by a frictionless washer. The pitch of the screw is 3 mm, its mean radius is 12 mm,
High-strength bolts are used in the construction of many steel structures. For a 1-in.-nominal-diameter bolt, the required minimum bolt tension is 51 kips. Assuming the coefficient of friction to be
The block and tackle shown are used to raise a 150-lb load. Each of the 3-in.-diameter pulleys rotates on a 0.5-in.-diameter axle. Knowing that the coefficient of static friction is 0.20, determine
Determine the moments of inertia of the shaded area shown with respect to the x and y axes when a = 20 mm. 1.5a 1.5a | Fig. P9.35 -3a-
The vertical motion of mass A is defined by the relation x = cos(10t) - 0.1sin(10t), where x and t are expressed in mm and seconds, respectively. Determine (a) The position, velocity and
A slender rod of length L is lodged between peg C and the vertical wall and supports a load P at end A. Knowing that the coefficient of static friction between the peg and the rod is 0.15 and
A 6-in.-radius pulley of weight 5 lb is attached to a 1.5-in.-radius shaft that fits loosely in a fixed bearing. It is observed that the pulley will just start rotating if a 0.5-lb weight is added to
The setup shown is used to measure the output of a small turbine. The coefficient of kinetic friction is 0.20 and the reading of each spring scale is 16 lb when the flywheel is at rest.
Determine the moment of inertia and the radius of gyration of the shaded area shown with respect to the y axis. || + X
Knowing that a couple of magnitude M = 150 N∙m is required to start the vertical shaft rotating, determine the coefficient of static friction between the annular surfaces of contact. 25 mm 75 mm 10
The slender rod AB is attached to a collar B and rests on a small wheel at C. Neglecting the radius of the wheel and the effect of friction, derive an expression for the magnitude of the force Q
Two 20-mm steel plates are welded to a rolled S section as shown. Determine the moments of inertia and the radii of gyration of the combined section with respect to the centroidal x and y axes. 80
Determine the moment of inertia and the radius of gyration of the shaded area shown with respect to the x axis. У 2b у-2b-cx² у=k b x
A hawser is wrapped two full turns around a capstan head. By exerting a 160-lb force on the free end of the hawser, a sailor can resist a force of 10,000 lb on the other end of the hawser.
Determine the weight W that balances the 10-lb load placed on the linkage shown. 10 lb —4 in.- Fig. P10.8 A D 2 in. 4 in.- BC EF -3 in- W
A girl operates a radio-controlled model car in a vacant parking lot. The girl’s position is at the origin of the xy coordinate axes, and the surface of the parking lot lies in the x-y plane. She

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