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engineering
engineering mechanics statics

Questions and Answers of Engineering Mechanics Statics

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
A group of hikers uses a GPS while doing a 40 mile trek in Colorado. A curve fit to the data shows that their altitude can be approximated by the function, y(t) = 0.12t5 - 6.75t4 + 135t3 - 1120t2 +
Two cars are approaching an intersection at constant speeds as shown. What velocity will car B appear to have to an observer in car A? (a) (b) (c) (d) (e)
Two model rockets are fired simultaneously from a ledge and follow the trajectories shown. Neglecting air resistance, which of the rockets will hit the ground first?(a) A(b) B(c) They hit at the same
Blocks A and B are released from rest in the positions shown. Neglecting friction between all surfaces, which figure below best indicates the direction α of the acceleration of block B? a. b. ag a =
A child walks across merry-go-round A with a constant speed u relative to A. The merry-go-round undergoes fixed axis rotation about its center with a constant angular velocity ω
A Scotch yoke is a mechanism that transforms the circular motion of a crank into the reciprocating motion of a shaft (or vice versa). It has been used in a number of different internal combustion
A bus travels the 100 miles between A and B at 50 mi/h and then another 100 miles between B and C at 70 mi/h. The average speed of the bus for the entire 200-mile trip is:(a) more than 60 mi/h(b)
Ball A is thrown straight up. Which of the following statements about the ball are true at the highest point in its path?(a) The velocity and acceleration are both zero.(b) The velocity is zero, but
A projectile enters a resisting medium at x = 0 with an initial velocity v0 = 1000 ft/s and travels 3 in. before coming to rest. Assuming that the velocity of the projectile is defined by the
Two cars A and B race each other down a straight road. The position of each car as a function of time is shown. Which of the following statements are true (more than one answer can be correct)?(a) At
The brakes of a car are applied, causing it to slow down at a rate of 10 ft/s2. Knowing that the car stops in 300 ft, determine (a) How fast the car was traveling immediately before the brakes were
The Ferris wheel is rotating with a constant angular velocity ω. What is the direction of the acceleration of Point A?(a) →(b) ↑(c) ↓(d) ←(e) The acceleration is zero. A
The elevator shown in the figure moves downward with a constant velocity of 4 m/s. Determine (a) the velocity of the cable C, (b) the velocity of the counterweight W, (c) the relative velocity of
A sprinter in a 100-m race accelerates uniformly for the first 35 m and then runs with constant velocity. If the sprinter’s time for the first 35 m is 5.4 s, determine(a) His acceleration, (b) His
Block B moves downward with a constant velocity of 20 mm/s. At t = 0, block A is moving upward with a constant acceleration, and its velocity is 30 mm/s. Knowing that at t = 3 s slider block C has
The motion of a particle is defined by the relation x = t3- 61 + 9t + 5, , where x is expressed in feet and t in seconds. Determine(a) When the velocity is zero,(b) The position, acceleration, and
Block B starts from rest, block A moves with a constant acceleration, and slider block C moves to the right with a constant acceleration of 75 mm/s2. Knowing that at 2s the velocities of B and C are
An airplane begins its take-off run at A with zero velocity and a constant acceleration a. Knowing that it becomes airborne 30 s later at B with a take-off velocity of 270 km/h, determine (a) The
As relay runner A enters the 65-ft-long exchange zone with a speed of 30 ft/s, he begins to slow down. He hands the baton to runner B 2.5 s later as they leave the exchange zone with the same
A farmer wants to get his hay bales into the top loft of his barn by walking his horse forward with a constant velocity of 1 ft/s. Determine the velocity and acceleration of the hay bale when the
A group of students launches a model rocket in the vertical direction. Based on tracking data, they determine that the altitude of the rocket was 89.6 ft at the end of the powered portion of the
Two rockets are launched at a fireworks display. Rocket A is launched with an initial velocity v0 = 100 m/s and rocket B is launched t1 seconds later with the same initial velocity. The two rockets
An athlete pulls handle A to the left with a constant acceleration. Knowing that after the weight B has been lifted 4 in. its velocity is 2 ft/s, determine (a) The accelerations of handle A and
Collars A and B start from rest, and collar A moves upward with an acceleration of 3t2mm/st2. Knowing that collar B moves downward with a constant acceleration and that its velocity is 150 mm/s after
A racecar travels around the track shown at a constant speed. At which point will the racecar have the largest acceleration?(a) A(b) B(c) C(d) The acceleration will be zero at all the points. A D B D
The elevator shown starts from rest and moves upward with a constant acceleration. If the counterweight W moves through 30 ft in 5 s, determine (a) The acceleration of the elevator and the cable
The system shown starts from rest, and each component moves with a constant acceleration. If the relative acceleration of block C with respect to collar B is 60mm/s2 upward and the relative
Ball A is thrown straight up with an initial speed v0 and reaches a maximum elevation h before falling back down. When A reaches its maximum elevation, a second ball is thrown straight upward with
A parachutist is in free fall at a rate of 200 km/h when he opens his parachute at an altitude of 600 m. Following a rapid and constant deceleration, he then descends at a constant rate of 50 km/h
Based on experimental observations, the acceleration of a particle is defined by the relation a = -(0.1 + sin x/b), where a and x are expressed in m/s2 and meters, respectively. Knowing that b = 0.8m

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