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engineering
engineering mechanics statics

Questions and Answers of Engineering Mechanics Statics

An athlete pulls handle A to the left with a constant velocity of 0.5 m/s. Determine (a) The velocity of the weight B, (b) The relative velocity of weight B with respect to the handle A. B
A commuter train traveling at 40 mi/h is 3 mi from a station. The train then decelerates so that its speed is 20 mi/h when it is 0.5 mi from the station. Knowing that the train arrives at the station
In a 400-m race, runner A reaches her maximum velocity vA in 4 s with constant acceleration and maintains that velocity until she reaches the half-way point with a split time of 25 s. Runner B
Car A is traveling at 40 mi/h when it enters a 30 mi/h speed zone. The driver of car A decelerates at a rate of 16 ft/s2 until reaching a speed of 30 mi/h, which she then maintains. When car B, which
An elevator starts from rest and moves upward, accelerating at a rate of 1.2 m/s2 until it reaches a speed of 7.8 m/s, which it then maintains. Two seconds after the elevator begins to move, a man
A temperature sensor is attached to slider AB which moves back and forth through 60 in. The maximum velocities of the slider are 12 in./s to the right and 30 in./s to the left. When the slider is
An airport shuttle train travels between two terminals that are 1.6 mi apart. To maintain passenger comfort, the acceleration of the train is limited to ±4 ft/s2, and the jerk, or rate of change of
A training airplane has a velocity of 126 ft/s when it lands on an aircraft carrier. As the arresting gear of the carrier brings the airplane to rest, the velocity and the acceleration of the
While delivering newspapers, a girl throws a newspaper with a horizontal velocity v0. Determine the range of values of v0 if the newspaper is to land between Points B and C. 4 ft 8 in. 8 in. 8 in. 7
During a manufacturing process, a conveyor belt starts from rest and travels a total of 1.2 ft before temporarily coming to rest. Knowing that the jerk, or rate of change of acceleration, is limited
An airplane used to drop water on brushfires is flying horizontally in a straight line at 130 knots (1 knot = 1.15 mph) at an altitude of 175 ft. Determine the distance d at which the pilot should
A ski jumper starts with a horizontal take-off velocity of 25 m/s and lands on a straight landing hill inclined at 30° Determine (a) The time between take-off and landing, (b) The length d of the
Human centrifuges are often used to simulate different acceleration levels for pilots and astronauts. Space shuttle pilots typically face inwards towards the center of the gondola in order to
During a rainstorm the paths of the raindrops appear to form an angle of 30° with the vertical and to be directed to the left when observed from a side window of a train moving at a speed of 15
A baseball player hits a 5.1-oz baseball with an initial velocity of 130 ft/s at an angle of 40° with the horizontal as shown. Determine (a) The kinetic energy of the ball immediately after it is
As part of a department store display, a model train D runs on a slight incline between the store’s up and down escalators. When the train and shoppers pass Point A, the train appears to a shopper
At a given instant in an airplane race, airplane A is flying horizontally in a straight line, and its speed is being increased at the rate of 8m/s2.Airplane B is flying at the same altitude as
Racecar A is traveling on a straight portion of the track while racecar B is traveling on a circular portion of the track. At the instant shown, the speed of A is increasing at the rate of 10 m/s2,
A motorist starts from rest at Point A on a circular entrance ramp when t = 0, increases the speed of her automobile at a constant rate and enters the highway at Point B. Knowing that her speed
The pitcher in a softball game throws a ball with an initial velocity v0 of 108 km/h at an angle  with the horizontal. If the height of the ball at Point B is 0.68 m, determine (a) The angle
The diameter of the eye of a stationary hurricane is 20 mi and the maximum wind speed is 100 mi/h at the eye wall, r = 10 mi. Assuming that the wind speed is constant for constant r and decreases
An athlete is holding 30 lb of weights at a height of 6 inches above the stack as shown. To lower the weights, she applies a constant force of 5 lb to the handle. Determine the velocity of the
When a small boat travels north at 15 km/h, a flag mounted on its stern forms an angle θ = 50° with the centerline of the boat as shown. A short time later, when the boat travels east at 25 km/h,
A worker uses high-pressure water to clean the inside of a long drainpipe. If the water is discharged with an initial velocity v0 of 11.5 m/s, determine (a) The distance d to the farthest Point B on
A model rocket is launched from Point A with an initial velocity v0 of 75 m/s. If the rocket’s descent parachute does not deploy and the rocket lands a distance d = 100 m from A, determine (a) The
The three blocks shown move with constant velocities. Find the velocity of each block, knowing that the relative velocity of A with respect to C is 300 mm/s upward and that the relative velocity of B
Knowing that at the instant shown block A has a velocity of 8 in./s and an acceleration of 6 in./s2 both directed down the incline, determine (a) The velocity of block B, (b) The acceleration of
Determine the normal component of acceleration of a car traveling at 72 km/h on an exit ramp of radius ρ = 150 m. 대 B A
Determine the maximum speed that the cars of the roller-coaster can reach along the circular portion AB of the track if ρ is 25 m and the normal component of their acceleration cannot exceed 3 g.
The nozzle at A discharges cooling water with an initial velocity v0 at an angle of 6° with the horizontal onto a grinding wheel 350 mm in diameter. Determine the range of values of the initial
The velocities of skiers A and B are as shown. Determine the velocity of A with respect to B. B 45 ft/s 25° 30 ft/s A 10⁰
Instruments in airplane A indicate that with respect to the air the plane is headed 30° north of east with an airspeed of 300 mi/h. At the same time radar on ship B indicates that the relative
While holding one of its ends, a worker lobs a coil of rope over the lowest limb of a tree. If he throws the rope with an initial velocity v0 at an angle of 65° with the horizontal, determine the
At halftime of a football game souvenir balls are thrown to the spectators with a velocity v0. Determine the range of values of v0 if the balls are to land between Points B and C. 40° 2 m 1.5 m 8
A tennis player serves the ball at a height h = 2.5 m with an initial velocity of v0 at an angle of 5° with the horizontal. Determine the range for which of v0 for which the ball will land in the
A basketball player shoots when she is 16 ft from the backboard. Knowing that the ball has an initial velocity v0 at an angle of 30° with the horizontal, determine the value of v0 when d is equal
A golfer hits a golf ball with an initial velocity of 140 ft/s at an angle of 25° with the horizontal. Knowing that the fairway slopes downward at an average angle of 5°, determine the distance d
A volleyball player serves the ball with an initial velocity v0 of magnitude 13.40 m/s at an angle of 20° with the horizontal. Determine (a) If the ball will clear the top of the net, (b) How far
A long trough is supported by a continuous hinge along its lower edge and by a series of horizontal cables attached to its upper edge. Determine the tension in each of the cables, at a time when the
The gear-pulling assembly shown consists of a crosshead CF, two grip arms ABC and FGH, two links BD and EG, and a threaded center rod JK. Knowing that the center rod JK must exert a 4800-N force on
The upper blade and lower handle of the compound-lever shears are pin connected to the main element ABE at A and B, respectively, and to the short link CD at C and D, respectively. Determine the
The elevation of the platform is controlled by two identical mechanisms, only one of which is shown. A load of 1200 lb is applied to the mechanism shown. Knowing that the pin at C can transmit only a
The action of the backhoe bucket is controlled by the three hydraulic cylinders shown. Determine the force exerted by each cylinder in supporting the 3000-lb load shown. 1 ft 2 ft 7 ft 2 ft K 6
A cone and a cylinder of the same radius a and height h are attached as shown. Determine the location of the centroid of the composite body. -a- h h
Determine the location of the center of gravity of the parabolic reflector shown, which is formed by machining a rectangular block so that the curved surface is a paraboloid of revolution of base
The friction force between a 6 * 6-ft square sluice gate AB and its guides is equal to 10 percent of the resultant of the pressure forces exerted by the water on the face of the gate. Determine the
A 4 * 2-ft gate is hinged at A and is held in position by rod CD. End D rests against a spring whose constant is 828 lb/ft. The spring is undeformed when the gate is vertical. Assuming that the force
A foot valve for a pneumatic system is hinged at B. Knowing that a = 28°, determine the moment of the 16-N force about Point B by resolving the force into components along ABC and in a direction
For the shift lever shown, determine the magnitude and the direction of the smallest force P that has a 210-lb · in. clockwise moment about B. B P af |—8 in. — A 22 in.
Form the vector product P1 × P2 and use the result obtained to prove the identitysin (θ1 – θ2) = sin θ1 cos θ2 – cos θ1 sin θ2. 0₁ P₁ 8₂ P₂
Two forces P and Q are applied as shown at Point A of a hook support. Knowing that P = 75 N and Q = 125 N, determine graphically the magnitude and direction of their resultant using (a) The
The two couples shown are to be replaced with a single equivalent couple. Determine (a) The couple vector representing the equivalent couple, (b) The two forces acting at B and C that can be used
Two forces P and Q are applied as shown at Point A of a hook support. Knowing that P = 60 lb and Q = 25 lb, determine graphically the magnitude and direction of their resultant using (a) The
The barge B is pulled by two tugboats A and C. At a given instant the tension in cable AB is 4500 lb and the tension in cable BC is 2000 lb. Determine by trigonometry the magnitude and direction of
Knowing that the tension in cable BC is 725 N, determine the resultant of the three forces exerted at Point B of beam AB. 800 mm A -840 mm- L = 1160 mm 500 N B 3 13 12 780 N
Two forces P and Q are applied as shown to an aircraft connection. Knowing that the connection is in equilibrium and that P = 600 lb and Q = 800 lb, determine the tension in rods A and B.
A foot valve for a pneumatic system is hinged at B. Knowing that a = 28°, determine the moment of the 16-N force about Point B by resolving the force into horizontal and vertical components.
Knowing that α = 75°, determine the resultant of the three forces shown. a 120 lb 20° 80 lb 60 lb a'
An 8-lb force P is applied to a shift lever. Determine the moment of P about B when a is equal to 25°. BO P 8 in. A 22 in.
Form the scalar product B · C and use the result obtained to prove the identity cos (α - β) = cos α cos β + sin α sin β. У a B B C X
An 11-lb force P is applied to a shift lever. The moment of P about B is clockwise and has a magnitude of 250 lb · in. Determine the value of a. B P 8 in A 22 in.
A dirigible is tethered by a cable attached to its cabin at B. If the tension in the cable is 1040 N, replace the force exerted by the cable at B with an equivalent system formed by two parallel
Before the trunk of a large tree is felled, cables AB and BC are attached as shown. Knowing that the tensions in cables AB and BC are 555 N and 660 N, respectively, determine the moment about O of
Three cables are attached to the top of the tower at A. Determine the angle formed by cables AD and AB. 48 m D 0 14m-16 m B -16 m 12 m C 24 m
Determine the volume of the parallelepiped of Fig. 3.20b when (a) P = 2i – 4j + 3k, Q = –5i – j + 2k, and S = i – 7j – k, (b) P = 6i – 5 j – 2k, Q = i + 2j + 3k, and S = –4i
A force P of magnitude 520 lb acts on the frame shown at point E. Determine the moment of P about a line joining points O and D. 7.5 in. 7.5 in. F 10 in. E ΓΙΑ 0 P 30 in. H D G B 10 in. x 10 in.
A force P acts on the frame shown at point E. Knowing that the absolute value of the moment of P about a line joining points F and B is 300 lb∙ft, determine the magnitude of the force P. 7.5
Three cables are attached to the top of the tower at A. Determine the angle formed by cables AB and AC. 48 m D 14 m. 0 16 m B -16 m 12 m 24 m
A line passes through the points (–4 m, –3 m) and (2 m, 7 m). Determine the perpendicular distance d from the line to the origin O of the system of coordinates.
A 4-m-long beam is subjected to a variety of loadings. (a) Replace each loading with an equivalent force-couple system at end A of the beam. (b) Which of the loadings are equivalent? 400 N 200
To keep a door closed, a wooden stick is wedged between the floor and the doorknob. The stick exerts at B a 175-N force directed along line AB. Replace that force with an equivalent force-couple
Determine the moment about the origin O of the force F = 2i – 3j + 5k that acts at a point A. Assume that the position vector of A is (a) r = i + j + k, (b) r = 4i + 6j –
In Prob. 3.23, Determine the perpendicular distance from point A to the line of action of the 200-N force.PROBLEM 3.23 A 200-N force is applied as shown to the bracket ABC. Determine the moment of
The roof of a building frame is subjected to the wind loading shown. Determine (a) The equivalent force-couple system at D, (b) The resultant of the loading and its line of action. 400 lb 200
Two cables exert forces of 90 kN each on a truss of weight W = 200 kN. Find the resultant of these three forces acting on the truss and the point of intersection of its line of action with line AB.
The vectors P and Q are two adjacent sides of a parallelogram. Determine the area of the parallelogram when (a) P = –2i + 2j – 6k and Q = 8i + 2j + 4k, (b) P = 3i – 9j – 7k and Q =
A plane contains the vectors A and B. Determine the unit vector normal to the plane when A and B are equal to, respectively, (a) 7i + 8j – 2k and 9i – 4j – 5k, (b) 6i – 3j + 9k and
Given the vectors P = 3i + 2j + k, Q = 5i + j – 2k, and S = i + 3j + Sz k, determine the value of Sz for which the three vectors are coplanar. N 15 m CL.B в -2.5 m Х
The jib crane shown is oriented so that its boom AD is parallel to the x axis and is used to move a heavy crate. Knowing that the tension in cable AB is 2.6 kips, replace the force exerted by the
A hand truck is used to move a compressed-air cylinder. Knowing that the combined weight of the truck and cylinder is 180 lb, determine (a) The vertical force P that should be applied to the handle
A 30-lb vertical force P is applied at A to the bracket shown, which is held by screws at B and C. (a) Replace P with an equivalent force-couple system at B. (b) Find the two horizontal forces at B
The 12-ft boom AB has a fixed end A, and the tension in cable BC is 570 lb. Replace the force that the cable exerts at B with an equivalent force-couple system at A. y| A 8 ft 12 ft 4.8 ft В x
A crane column supports a 16-kip load as shown. Replace the load with an equivalent system consisting of an axial force along AB and a couple. A, 5 in. 7 in. B dibo ilbo dip dib bo 16 kips
Two links AB and DE are connected by a bell crank as shown. Knowing that the tension in link AB is 150 lb, determine (a) The tension in link DE,(b) The reaction at C. 3 in. A B -4 in.. 90⁰ C -6
Two external shafts of a gearbox are subject to the torques (or moments) shown. Determine the vertical components of the forces that must be exerted by the bolts at A and B to maintain the gearbox in
Determine the maximum tension that can be developed in cable AB if the maximum allowable value of the reaction at C is 2.6 kN. A B 125 mm 75 mm с 300 mm- P D
The 10-m beam AB rests upon, but is not attached to, supports at C and D. Neglecting the weight of the beam, determine the range of values of P for which the beam will remain in equilibrium.
Four horizontal forces act on a vertical quarter-circular plate of radius 250 mm. Determine the magnitude and point of application of the resultant of the four forces if P = 40 N. 80 N 30 200 N 120
The required tension in cable AB is 1200 N. Determine (a) The vertical force P that must be applied to the pedal, (b) The corresponding reaction at C. B 125 mm 75 mm, C -300 mm- P D
Determine the magnitude of the force P for which the resultant of the four forces acts on the rim of the plate. 80 N 200 N 120 N 250 mm
Consider the volleyball net shown. Determine the angle formed by guy wires AB and AC.A small boat hangs from two davits, one of which is shown in the figure. The tension in line ABAD is 82 lb.
Shafts A and B connect the gear box to the wheel assemblies of a tractor, and shaft C connects it to the engine. Shafts A and B lie in the vertical yz plane, while shaft C is directed along the x
Using the method of Section 4.7, solve Problem 4.22.PROBLEM 4.22 A lever AB is hinged at C and attached to a control cable at A. If the lever is subjected to a 500-N horizontal force at B,
A traffic-signal pole may be supported in the three ways shown; in part c, the tension in cable BC is known to be 1950 N. Determine the reactions for each type of support shown. 7.2 m B 3 m- 2.1
A lever AB is hinged at C and attached to a control cable at A. If the lever is subjected to a 500-N horizontal force at B, determine (a) The tension in the cable, (b) The reaction at C. A 250
The spanner shown is used to rotate a shaft. A pin fits in a hole at A, while a flat, frictionless surface rests against the shaft at B. If a 300-N force P is exerted on the spanner at D, find (a)
The ladder AB, of length L and weight W, can be raised by cable BC. Determine the tension T required to raise end B just off the floor (a) In terms of W and θ, (b) If h = 8 ft, L = 10 ft, and W =
Two links AB and DE are connected by a bell crank as shown. Determine the maximum force that can be safely exerted by link AB on the bell crank if the maximum allowable value for the reaction at C is
For the boom and loading shown, determine (a) The tension in cord BD, (b) The reaction at C. A 12 in. + 3 kips 16 in. B -32 in. D C 32 in.
A rod AB, hinged at A and attached at B to cable BD, supports the loads shown. Knowing that d = 150 mm, determine (a) The tension in cable BD, (b) The reaction at A. Ao -d- 90 N Do 90 N -100 mm 100

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