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engineering
engineering mechanics statics

Engineering Mechanics Statics & Dynamics 15th Edition Russell C. Hibbeler - Solutions

At the instant shown, cars A and B are traveling at velocities of 40 m/s and 30 m/s, respectively. If A is increasing its speed at 4 m/s2, whereas the speed of B is decreasing at 3 m/s2, determine the velocity and acceleration of B with respect to A. The radius of curvature at B is ρB = 200 m. VB
A man can row a boat at 5m/s in still water. He wishes to cross a 50-m-wide river to point B, 50 m downstream. If the river flows with a velocity of 2m/s , determine the speed of the boat and the time needed to make the crossing. A -50 m 2 m/s 0 50 m B
A man can swim at 4 ft/s in still water. He wishes to cross the 40-ft-wide river to point B, 30 ft downstream. If the river flows with a velocity of 2 ft/s, determine the speed of the man and the time needed to make the crossing. While in the water he must not direct himself toward point B to reach
At the instant shown car A is traveling with a velocity of 30 m/s and has an acceleration of 2 m/s2 along the highway. At the same instant B is traveling on the trumpet interchange curve with a speed of 15 m/s, which is decreasing at 0.8 m/s2. Determine the relative velocity and relative
The football player at A throws the ball in the y–z plane at a speed vA = 50 ft/s and an angle θA = 60° with the horizontal. At the instant the ball is thrown, the player is at B and is running with constant speed along the line BC in order to catch it. Determine this speed, vB, so that he
Determine the required magnitude of force P to of the linkage at θ = 60°. Each linkmaintain equilibriumhas a mass of 20 kg. A 1.5 m B C 1.5 m
Determine the tension in cable AC. The lamp weighs 10 lb. B 45% DOGGA 30°
The toggle joint is subjected to the load P.Determine the compressive force F it creates on thecylinder at A as a function of θ. L P L A F
The homogeneous block has a mass of 10 kg and rests on the smooth corners of two ledges. Determine the angle θ for placement that will cause the block to be stable. 200 mm -150 mm- 200 mm
Determine the magnitude of force P required to hold the 50-kg smooth rod in equilibrium at θ = 60°. B 5 m 0 A P
The linkage is subjected to a force of P = 2 kN. Determine the angle θ for equilibrium. The spring is unstretched when θ = 0°. Neglect the mass of the links. k = 15 kN/m A B -0.6 m- -0.6 m- D P = 2 kN C 0.6 m
The linkage is subjected to a force of P = 6 kN. Determine the angle θ for equilibrium. The spring is unstretched at θ = 60°. Neglect the mass of the links. A 0.9 m 0 k = 20 kN/m wwwwwwww P= 6 kN 0.9 m C
Determine the angle θ where the 50-kg bar is in equilibrium. The spring is unstretched at θ = 60°. A 5 m 10 k = 600 N/m B
The block A has a mass of 40 kg. Determine the angle θ for equilibrium and investigate the stability of the mechanism in this position. The spring has a stiffness of k = 1.5 kN/m and is unstretched when θ = 90°. Neglect the mass of the links. Hi C B 600 mm A E 450 mm
The scissors linkage is subjected to a force of P = 150 N. Determine the angle θ for equilibrium. The spring is unstretched at θ = 0°. Neglect the mass of the links. A O k = 15 kN/m2 B 0.3 m 0.3 m P = 150 N
If vertical forces P1 = 40 lb and P2 = 20 lb act at C and E as shown, determine the angle θ for equilibrium. The spring is unstretched when θ = 45°. Neglect the weight of the members. E A P₁ 2 ft 2 ft www. k = 200 lb/ft B 2 ft 2 ft P₂ C D
Determine the force P that must be applied perpendicular to the handle in order to hold the mechanism in equilibrium for any angle θ of rod CD. There is a couple moment M applied to the link BA. A smooth collar attached at A slips along rod CD. L A P L/2 -1/2- M B D
The members of the mechanism are pin connected. If a vertical force of 800 N acts at A, determine the angle θ for equilibrium. The spring is unstretched when θ = 0°. Neglect the mass of the links. B 1m 1 m 800 N D k = 6 kN/m 1m
Determine the horizontal force F required to maintain equilibrium of the slider mechanism when θ = 60°. Set M = 6 N · m D 0.5 m A F 0.5 m B M S 0.5 m
A 3-lb weight is attached to the end of rod ABC. If the rod is supported by a smooth slider block at C and rod BD, determine the angle for equilibrium. Neglect the weight of the rods and the slider. C 6 in. B 4 in. 10 in. A
A spring with a torsional stiffness k is attached to the hinge at B. It is unstretched when the rod assembly is in the vertical position. Determine the weight W of the block that results in neutral equilibrium. Establish the potential energy function for a small angle θ, i.e., approximate sin θ
A cone is attached to the hemisphere. If both pieces have the same density, determine the height h of the cone if the configuration is to be in neutral equilibrium. 3 ft h
The block weighs W and is supported by links AB and BC. Determine the necessary spring stiffness k required to hold the system in neutral equilibrium. The springs are subjected to an initial compression F0 when the links are vertical as shown. XXXXXX k В mu- k C
Determine the moment of inertia of the area about the x axis. 1m - 2 m y = 2x-x²
The automobile jack is subjected to a vertical load of F = 8 kN. If a square-threaded screw, having a lead of 5 mm and a mean diameter of 10 mm, is used in the jack, determine the force that must be applied perpendicular to the handle to (a) Raise the load, and (b) Lower the load; μs =
The friction pawl is pinned at A and rests against the wheel at B. It allows freedom of movement when the wheel is rotating counterclockwise about C. Clockwise rotation is prevented due to friction of the pawl which tends to bind the wheel. If (μs)B = 0.6, determine the design angle θ which will
Determine the moment of inertia of the area about the x axis. Solve the problem in two ways, using rectangular differential elements: (a) Having a thickness dx and(b) Having a thickness of dy. 2.5 ft -y=2.5-0.1.x² -5 ft- -X
Draw the free-body diagram for the following problems.a) The crane in Prob. 5–59.b) The smooth pipe in Prob. 5–61.c) The bar in Prob. 5–62. 5 m A -P O
Draw the free-body diagram for the following problems.a) The jib crane in Prob. 5–37.b) The bar in Prob. 5–39.c) The davit in Prob. 5–41.d) The boom in Prob. 5–42. B 4 ft A -X- 8 ft T 780 lb 40⁰
Draw the free-body diagram for the following problems.a) The beam in Prob. 5–53.b) The brake pedal Prob. 5–54.c) The exercise machine Prob. 5–55.d) The hatch door in Prob. 5–58. Ө B
Draw the free-body diagram for the following problems.a) The rod in Prob. 5–44.b) The hand truck and load when it is lifted in Prob. 5–45.c) The beam in Prob. 5–47.d) The boom frame in Prob. 5–52. k = 60 N/m -0.5 m- P A B 2m 50 N·m
Draw the free-body diagram for the following problems.a) The lamp in Prob. 5–19.b) The rod in Prob. 5–20.c) The assembly in Prob. 5–21.d) The beam in Prob. 5–22. 0.3 m 0.4 m 0.15 m C B -0.5 m- G
Draw the free-body diagram for the following problems.a) The clamp in Prob. 5–32.b) The jib crane in Prob. 5–33.c) The crane in Prob. 5–35.d) The beam in Prob. 5–36. -150 mm- B 250 mm
Draw the free-body diagram for the following problems.a) The rod in Prob. 5–25.b) The bar in Prob. 5–27.c) The disk in Prob. 5–28. 3 -3 ft- 4 100 lb + -3 ft- B 200 lb-ft 2 ft 13 12
Draw the free-body diagram for the following problems.a) The beam in Prob. 5–15.b) The linkage in Prob. 5–16.c) The frame in Prob. 5–17.d) The beam in Prob. 5–18. -8 m- 75 N/m 800 N·m
Determine the force P that must be applied to the handle of the lever so that the wheel is on the verge of turning if M = 300 N · m. The coefficient of static friction between the belt and the wheel is μs = 0.3. M 300 mm B 60 mm -25 mm D 700 mm P
Determine the centroid y̅ of the area. IN 2 m -1 m- -y = 2x² -1 m- X
Locate the centroid y̅ of the beam's cross-sectionalarea. 25 mm 50 mm 100 mm +-75 mm---75 mm- 25 mm C- 50 mm - 25 mm y
Determine the minimum tension in the rope at points A and B that is necessary to maintain equilibrium. Take μs = 0.3 between the rope and the fixed post D. 300 lb T D B 60° A
The hand clamp is constructed using a square-threaded screw having a mean diameter of 36 mm, a lead of 4 mm, and a coefficient of static friction at the screw of μs = 0.3. If the clamping force in the board AB is 300 N, determine the reversed force -F that must be applied perpendicular to the
If the force T1 is applied to the rope at A, determine the force T2 at B needed to pull the rope over the two fixed drums having the angles of contact and the coefficients of static friction shown. T₁ μ1 B₁ B₂ B T₂ H₂
If couple forces of F = 10 lb are applied perpendicular to the lever of the clamp at A and B, determine the clamping force on the boards. The single square-threaded screw of the clamp has a mean diameter of 1 in. and a lead of 0.25 in.The coefficient of static friction is μs = 0.3. 6 in.- in.----6
Determine the minimum tension in the rope at points A and B which is necessary to maintain equilibrium. The coefficient of static friction between the rope and the fixed post D is μs = 0.3. The rope is wrapped only once around the post. 5 kN D A D *xx.xx.xx B T
The 50-lb cylinder is attached to a cord which passes over the fixed drum. If the coefficient of static friction at the drum is μs = 0.3, determine the maximum force P that can be applied to the roller when θ = 30° without causing the cylinder to move. -1 ft 5 ft P
The 50-lb cylinder is attached to a cord which passes over the fixed drum. If the coefficient of static friction between the cord and the drum is μs = 0.3, determine the angle θ of of the cord if the maximum vertical load that can be applied to the roller without causing the cylinder to move is P
The choker sling is used to lift the smooth pipe that has a mass of 600 kg. If the coefficient of static friction between the loop at the end A of the sling and the rope is μs = 0.3, determine the angle u at the connection. A 0-
The load can be supported by two boys when the cord is suspended over the pipe (a half-turn). If each boy can pull with a force of 125 lb, determine the maximum weight of the load. Can one boy support the same load when the cord is wrapped one-and-a-half times around the pipe? The coefficient of
A girl weighing 100 lb attempts to pull herself up a tree using a rope which is draped over the limb at B. If μs = 0.4, determine the smallest force at which she must pull on the rope to lift herself. Do you think this is possible? B
Two boys have a tug-of-war using a rope. In the process the rope rubs against a post such that it is deflected 3° on each side of the post. If boy A weighs 60 lb and boy B weighs 50 lb, determine if it possible for one of them to pull the rope toward him. The coefficient of static friction between
Two boys have a tug-of-war using a rope. In the process the rope rubs against a post such that it is deflected 3º on each side of the post. If boy A weighs 60 lb and boy B weighs 50 lb, determine if it is possible for one of them to pull the rope toward him. The coefficient of static friction
A conveyer belt is used to transfer granular material and the frictional resistance on the top of the belt is F = 500 N. Determine the smallest stretch of the spring attached to the moveable axle of the idle pulley B so that the belt does not slip at the drive pulley A when the torque M is applied.
A tube has a total weight of 200 lb, length ∫ = 8 ft, and radius = 0.75 ft. If it rests in sand for which the coefcient of static friction is μs = 0.23, determine the torque M needed to turn it. Assume that the pressure distribution along the length of the tube is dened by p = p0 sin θ. For
If the coefficient of static friction at the cone clutch is μs, determine the smallest force P that should be applied to the handle in order to transmit the torque M. B M P4 C b
The corkscrew is used to remove the 15-mm-diameter cork from the bottle. Determine the smallest vertical force P that must be applied to the handle if the gauge pressure in the bottle is p = 175 kPa and the cork pushes against the sides of the bottle’s neck with a uniform pressure of 90 kPa. The
The 4-lb pulley has a diameter of 1 ft and the axle has a diameter of 1 in. If the coefficient of kinetic friction between the axle and the pulley is μk = 0.20, determine the vertical force P on the rope required to lift the 20-lb block at constant velocity. P 6 in.
Locate the centroid x̅ of the area. a - xy = c2² b- x
The 5-kg skateboard rolls down the 5° slope at constant speed. If the coefficient of kinetic friction between the 12.5-mm-diameter axles and the wheels is μk = 0.3, determine the radius of the wheels. Neglect rolling resistance of the wheels on the surface. The center of mass for the skateboard
A large stone having a mass of 500 kg is moved along the incline using a series of 150-mm-diameter rollers for which the coefficient of rolling resistance is 3 mm at the ground and 4 mm at the bottom surface of the stone. Determine the force T that will cause the stone to descend the plane at a
Determine the centroid (x̅,y̅) of the area. 1m -y=x²³ -1m- -X
Locate the centroid y̅ of the area. a - xy = c2² b- x
Locate the center of mass x̅ of the straight rod if its mass per unit length is given by m = 0.5 (1+x²) kg. -1 m X
Determine the centroid (x̅,y̅) of the area. 1m ₁y = r²³ 1 m X
Locate the center of mass x̅ of the straight rod if its mass per unit length is given by m = 0.5 (1+x²) kg. -1 m X
Locate the centroid z̅ of the hemisphere. X Z a - y² + z² =a²
Locate the centroid y̅ of the homogeneous solidformed by revolving the shaded area about the y axis. -1 m- -2²=¹ y 0.5 m -y
Locate the centroid x̅ of the shaded area. y a q xn h X
Locate the centroid (x̅, y̅, z̅) of the wire bent in theshape shown. 300 mm 600 mm z 400 mm
Locate the centroid y̅ of the area. 1 1 m y = 1-1/√x² (Y=1 -2 m- X
Locate the centroid y̅ of the beam's cross-sectionalarea. 50 mm 150 mm 150 mm 300 mm 25 mm 25 mm -X
Locate the centroid x̅ of the area. 4m (y=4x -4m
Locate the centroid y̅ of the area. 4 m 4 m -X
Locate the centroid y̅ of the beam's cross-sectionalarea. H 50 mm 400 mm- C 50 mm 50 mm 200 mm ·x
Locate the centroid x̅ of the area. y y = h -b- R2 h X
Locate the centroid y̅ of the area. y y = -b- h -X
Locate the centroid y̅ of the area. y 4 m 1 x = 4 = 1/6 x ² -8 m-
Locate the centroid x̅ of the area. y 4 m ↓ y = 4 - 1x² -8 m- X
Locate the centroid of the area. a y -L- -y = a sin x L X
Determine the magnitude of the hydrostatic force acting on gate AB, which has a width of 4 ft. The specific weight of water is γ = 62.4 lb/ft³. — -3 ft- В 4 ft
Determine the magnitude of the hydrostatic force acting per meter width of the wall. Water has a density of ρ = 1 Mg/m³. 6 m
Determine the magnitude of the hydrostatic force acting on gate AB, which has a width of 1.5 m. Water has a density of ρ = 1 Mg/m³. B -1.5 m- 2 m
Locate the centroid (x̅, y̅) of the exparabolic segment of area. b 4 ค y X
Determine the magnitude of the hydrostatic forceacting on gate AB, which has a width of 2 m. Water has adensity of ρ = 1 Mg/m³. 3 m 2 m A B
Locate the centroid y̅ of the area. 16 ft -y = (4-x²)² 4 ft- T 4 ft +
Locate the centroid x̅ of the area. 16 ft -y=(4-x²)² -4 ft- T 4 ft ↓ X
Determine the magnitude of the hydrostatic forceacting on gate AB, which has a width of 2 ft. The specificweight of water is γ = 62.4 lb/ft³. 6 ft 4 ft A B -3 ft-N
Locate the centroid x̅ of the area. y y = a h a²-x² +h h X
Locate the centroid x̅ of the area. 4 ft y 4 ft X
Locate the centroid y̅ of the area. 4 ft y 4 ft X
Locate the centroid y̅ of the area. y h y=-x²+h a- h X
Locate the centroid x̅ of the area. h y y=hx -b- a /y = (h)(x-b) X
Locate the centroid x̅ of the area. 100 mm -100 mm- y = x = 100* 10+² ·x
Locate the centroid y̅ of the area. y 100 mm -100 mm- y = x = 100 X
Locate the centroid x̅ of the area. h -y=h- y=h-hx h a" X
Locate the centroid y̅ of the area. h -y=h- - y = h = ax a h n X
Determine the distance y̅ to the centroid of the cone. N z = 2y -h- a y
Locate the centroid y̅ of the paraboloid. Z 2²=4y -4m- 4 m y
Determine the distance y̅ to the center of mass of the cone. The density of the material varies linearly from zero at the origin to ρ0 at x = h. N Z = y -h- a y
Locate the centroid x̅ of the solid. y y = x3/2 -X) C 4 in.- 8 in. X
The king’s chamber of the Great Pyramid of Giza is located at its centroid. Assuming the pyramid to be a solid, prove that this point is at z̅ (1/4)h, Use a rectangular differential plate element having a thickness dz and area (2x)(2y). 2 a
Locate the centroid of the solid. x N y² = a (a-²)

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