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engineering
engineering mechanics statics

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

The uniform crate resting on the dolly has a mass of 500 kg and mass center at G. If the front casters contact a high step, and the coefficient of static friction between the crate and the dolly is μs = 0.45, determine the greatest force P that can be applied without causing motion of the crate.
Two blocks A and B, each having a mass of 6 kg, are connected by the linkage shown. If the coefficients of static friction at the contacting surfaces are μB = 0.8 and μA = 0.2, determine the largest vertical force P that may be applied to pin C without causing the blocks to slip. Neglect the
The car has a mass of 1.6 Mg and center of mass at G. If the coefficient of static friction between the shoulder of the road and the tires is μs = 0.4 determine the greatest slope θ the shoulder can have without causing the car to slip or tip over if the car travels along the shoulder at constant
The cylinder is confined by the brake, where μs = 0.4. Determine the required compression in the spring in order to resist a torque of 800 N · m on the cylinder. The spring has a stiffness of k = 3 MN/m and an unstretched length of 60 mm. End C of member ABC slides freely along the smooth
The uniform 5-kg rod rests on the ground at B and against the wall at A. If the rod does not slip at B, determine the smallest coefficient of static friction at A which will prevent slipping at A. X B N 1 m A 4 m 3 m
Two blocks A and B, each having a mass of 6 kg, are connected by the linkage shown. If the coefficient of static friction at the contacting surfaces is μs = 0.5 determine the largest vertical force P that may be applied to pin C without causing the blocks to move. Neglect the weight of the links.
The load bar of negligible weight is screwed in place between the walls of the truck bed in order to keep loads from shifting. Determine the torsional moment M that must be applied to the center of the bar so that it produces a compression in the bar of 80 lb. The square-threaded screw at A has a
If it takes a vertical force of 60,000 lb to separate the two parts at A and C, determine the force P the hydraulic cylinder must exert on the wedge in order to push it forward. The coefficient of static friction between the wedge and members AB and CD is μs = 0.2. 60,000 lb 7.5° AL ACT P 60,000
If a horizontal force of F = 50 N is applied perpendicular to the handle of the lever at E, determine the clamping force developed at G. The mean diameter and lead of the single square-threaded screw at C and D are 25 mm and 5 mm, respectively.The coefficient of static friction is μs = 0.3. –
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. To tighten the screw, a force of F = 20 N is applied perpendicular to the handle. Determine the clamping force in the board
Determine the maximum force P that can be appliedwithout causing the two 50-kg crates to move. The coefficient ofstatic friction between each crate and the ground is μs = 0.25. A B 30°
Determine the moment of inertia for the area about the y axis. y y = h 6³ -b- h -X
Determine the moment of inertia of the quarter circular area about the x axis. y x² + y² = r² X
Determine the moment of inertia of the area about the x axis. 9 in. -y=9-x² -3 in.. X
Determine the moment of inertia of the area about the y axis. 9 in. y 3 in. -y=9-x²² X
Determine the moment of inertia of the area about the y axis. 1 m 2m y = 2x-x² X
Determine the moment of inertia for the area about the x axis. y²= = a a a² b -X
Determine the moment of inertia Ix of the area about the x axis. 150 mm 150 mm O -100 mm--100 mm-150 mm- 75 mm X
Determine the moment of inertia of the area about the y axis. y -3 in.-3 in.- 2 in. 6 in. 4 in. X
Determine the moments of inertia Iu and Iv and the product of inertia Iuv for the rectangular area. The u and v axes pass through the centroid C. Take u = 30°. 3 in. v C 8 in. 0 u X
Determine the moment of inertia of the homogenous triangular prism with respect to the y axis. Express the result in terms of the mass m of the prism. For integration, use thin plate elements parallel to the x-y plane having a thickness of dz. Y Z -9- 七 z=(x-1)-
The hemisphere is formed by rotating the shaded area about the y axis. Determine the moment of inertia Iy and express the result in terms of the total mass m of the hemisphere. The material has a constant density ρ. - x² + y² = r² r -X
When no force is applied to the brake pedal of the lightweight truck, the retainer spring AB keeps the pedal in contact with the smooth brake light switch at C. If the force on the switch is 3 N, determine the unstretched length of the spring if the stiffness of the spring is k = 80 N/m. B -100
The assembly is used to support the 120-kg container having a center of mass at G. If the spring has an unstretched length of 250 mm and stiffness of k = 300 kN/m, determine its height h and the reaction at the rollers A and B. G 3 m. B h k A 2 m 2 m
The block has a mass of 80 kg and center of mass at G. Determine the smooth reactions on the supporting platform at A, B, and C. A 60° G. B 60⁰° 0.3 m -0.8 m-
If the truck and its contents have a mass of 50 kg with center of gravity at G, determine the normal reaction on both wheels and the magnitude and direction of the minimum force required at the grip B needed to lift the load. B 0.2 m 60° A 0.4 m 0.5 m 0.4 m 0.4 m 0.1 m
The 10-kg uniform rod is pinned at end A. If it is subjected to a couple moment of 50 N · m, determine the smallest angle θ for equilibrium. The spring is unstretched when θ = 0, and has a stiffness of k = 60 N/m. k = 60 N/m -0.5 m- B A 2 m 50 N - m
The boom is intended to support two vertical loads, F₁ and F2. If the cable CB can sustain a maximum load of 1500 N before it fails, determine the critical loads if F₁ = 2F₂. Also, what is the magnitude of the maximum reaction at pin A? C A 1.5 m ترا 30° 5 4 F₁ 1 m D B F₂
The boom supports the two vertical loads. Neglect the size of the collars at D and B and the thickness of the boom, and compute the horizontal and vertical components of force at the pin A and the force in cable CB. Set F1 = 800 N and F2 = 350 N. C A 1.5 m 3 30° 5 4 1 m D B F₂
The cantilevered jib crane is used to support the load of 780 lb. If x = 5 ft, determine the reactions at the supports. Note that the supports are collars that allow the crane to rotate freely about the vertical axis. The collar at B supports a force in the vertical direction, whereas the one at A
The bar of negligible weight is supported by two springs, each having a stiffness k = 100 N/m. If the springs are originally unstretched, determine the angle u the bar makes with the horizontal, when the 30-N force is applied to the bar. C -1m- 30 N B -2 m k wowowe
If the beam is horizontal and the springs are unstretched when the load is removed, determine the angle of tilt of the beam when the load is applied. k₁= 1 kN/m 00000 3 m 600 N/m 3 m B KB = 1.5 kN/m D
The crane lifts the 400-kg load L. The primary boom AB has a mass of 1.20 Mg and a center of mass at G1, whereas the secondary boom BC has a mass of 0.6 Mg and a center of mass at G2. Determine the tension in the cable BD and the horizontal and vertical components of reaction at the pin A.
The mechanism shown was thought by its inventor to be a perpetual-motion machine. It consists of the stand A, two smooth idler wheels B and C, and in between a uniform hollow cylindrical ring D suspended in the manner shown. The ring has a weight W and it was expected to revolve in the direction
Auniform glass rod having a length L is placed in the smooth hemispherical bowl having a radius r. Determine the angle of inclination θ for equilibrium. А B
The uniform plate has a weight of 500 lb. Determine the tension in each of the supporting cables. B -3 ft- C 200 lb 2 ft
Determine the reactions at the smooth contact points A, B, and C on the bar. 250 N 30 0.4 m 0.2 m C 30% B 0.15 m
Determine the components of reaction at the fixed support A. Neglect the thickness of the beam. 3m A 60° 200 N 200 N 200 N +-₁m-+-1m- 30° 400 N
Determine the x and z components of reaction at the journal bearing A, and the tension in cords BC and BD. X 2 m C 6 m 3 m B 3 m D F₁ = {-800k) N 4 m F₂ = (350j} N
Determine the horizontal and vertical components of reaction at the pin A and the reaction at the roller B on the lever. 14 in. -30° F = 50 lb -20 in.- A -18 in- B
Replace the loading by an equivalent single resultant force and specify the x and y coordinates of its line of action. 100 N 3 m 3 m 200 NEW YE | 200 N | 2 mlm3m - - ,100 N
Replace the loading by an equivalent single resultant force and specify the x and y coordinates of its line of action. 3 m 100 N 500 N 400 N -4 m- 4 m
Determine the horizontal and vertical components of reaction at the pin A and the reaction on the beam at C. 1.5 m D -1.5 m- C -1.5 m- 4 kN B
Determine the horizontal and vertical components of reaction at the supports. Neglect the thickness of the beam. 500 lb. -5 ft- -5 ft- B -5 ft- 600 lb-ft
Replace the loading by an equivalent resultant force and specify where the resultant's line of action intersects the beam measured from O. O 500 lb 250 lb 500 lb +38+36-36-36- -3 ft--3 ft- -3 ft-3 ft- X
Determine the couple moment acting on the pipe assembly and express the result as a Cartesian vector. x B FA = 450 N 0.4 m 4 0.3 m 0 FB = 450 N C
Replace the loading by an equivalent resultant force and specify where the resultant's line of action intersects the member AB measured from A. 0.5 m 0.5 m 8 kN 3 m B y 0.5 m A -1.5 m- 6 kN X 5 kN
Replace the loading by an equivalent resultant force and specify where the resultant's line of action intersects the horizontal segment of the member measured from A. 20 kN -2m- -2 m- B -2 m- 3 2m 15 kN
Determine the magnitude of F so that the resultant couple moment acting on the beam is 1.5 kN m clockwise. FA 0.9 m 2 kN B -F 0.3 m 2 kN
Replace the loading by an equivalent resultant force and specify where the resultant's line of action intersects the member measured from A. -3 ft- 200 lb -3 ft- -3 ft-30° 100 lb 50 lb
Draw the free-body diagram for the following problems.a) The beam in Prob. 5–10.b) The beam in Prob. 5–11.c) The beam in Prob. 5–12.d) The beam in Prob. 5–14.
Determine the resultant couple moment acting on the triangular plate. 200 lb 200 lb 4 ft 300 lb -4 ft- 150 lb 4 ft 300 lb 150 lb
Determine the resultant couple moment acting on the pipe assembly. (Mc)3 = 300 lb-ft 1.5 ft 2 ft. (Mc)₁ 450 lb-ft -2 ft 2 ft (Mc)₂ = 250 lb-ft 3,5 ft
Determine the moment of force F about the x, the y, and the z axis. Solve the problem using both a scalar and a vector analysis. X N 2 m 5 3m 2m S + F = 500 N
Determine the couple moment acting on the beam. A 10 kN 1m -4 m- 10 kN 5 1 m B
Determine the magnitude of the moment of the force F = {300i 200j + 150k} N about the OA axis. 0.3 m 0.4 m F 0.2 m B
Determine the magnitude of the moment of the force F = {300i 200j + 150k} N about the x axis. X 0.3 m 0.4 m F 0.2 m B
Determine the magnitude of the moment of the 200-N force about the x axis. Solve the problem using both a scalar and a vector analysis. X 0.3 m. 120° 45° F = 200 N 60° 0.25 m y
Determine the moment of force F about point O. Express the result as a Cartesian vector. 4 ft 1 ft 4 ft. Z F = 120 lb Lo A 2 ft
Determine the moment of the force F = {50i - 40j + 20k} lb about the AB axis. Express the result as a Cartesian vector. x 2 ft 3 ft 4 ft B
Determine the moment of force F about point O. Express the result as a Cartesian vector. F = 500 N X B 3 m 4 m
Determine the resultant moment produced by the forces about point O. F₂ = 200 lb 30° -6 ft F₁ = 300 lb 6 ft 30°
Determine the magnitude of the moment of the force about the y axis. F = (30i - 20j + 50k} N A -4 m- 2 m 3 m
If F₁ = {100i-120j +75k} lb and F₂ = {-200i + 250j + 100k} lb, determine the resultant moment produced by these forces about point O. Express the result as a Cartesian vector. t 3 ft 4 ft 5 ft F₂
Determine the resultant moment produced by the forces about point O. 0.25 m 0.125 m, 0 0.3 m- 60° F₁ = 500 N F₂ = 600 N
Determine the resultant moment produced by the forces about point O. O -1m- 600 N -2 m 500 N 45° 2.5 m 300 N
Determine the moment of the force about point O. 0 3 m 45° wwwwww 500 N
Determine the moment of the force about point O. -100 mm- 200 mm 50 N +Kans -100 mm-
Determine the moment of the force about point O. 30° 600 lb 20% 5 ft 0.5 ft
In each case, determine the moment about point O.(a)(b)(c) 100 N -5m- 2 m
In each case, determine the moment about point O.(a)(b) -3m- 500 N 5 |--1m- T 1 m
Replace the force F having a magnitude of F = 50 lb and acting at point A by an equivalent force and couple moment at point C. 10 ft 20 ft N 15 ft VF 30 ft B 10 ft
In each case, determine the moment of the force about point O.(a)(b) -2m- 500 N
Determine the magnitude of F1 and the distance y if x = 1.5 m and F2 = 1000 N. y 2 m C X D G B F₁ -F₂
Determine the tension in the cables in order to support the 100-kg crate. x C B 2 m Z 2.5 m 2 m D 2 m 1 m
Determine the magnitude of the force P and the orientation of the 200-lb force required to keep the particle in equilibrium. (-1 ft, -7 ft, 4 ft) F3= 200 lb X N F₁=360 lb F₂= 120 lb 20° ✓ F₁ = 300 lb P y
If cable AB is subjected to a tension of 700 N, determine the tension in cables AC and AD and the magnitude of the vertical force F. 3 m 6 m- 6 m -3 m 0 B 2 m. 2 m 1.5 m -y
Determine the force in each cable needed to support the 500-lb load. B 2 ft. 6 ft C .6 ft D 8 ft
Determine the force in each cord for equilibrium of the 60-kg bucket. D 3 m- E C -3 m- -3 m F B 4 m 4 m
Determine the tension in cables AB, BC, and CD, necessary to support the 10-kg and 15-kg traffic lights at B and C, respectively. Also, find the angle θ. A 15° B for с 10
Determine the maximum weight of the flowerpot that can be supported without exceeding a cable tension of 50 lb in either cable AB or AC. B 3 5 30° A
Determine the maximum weight of the engine that can be supported without exceeding a tension of 450 lb in chain AB and 480 lb in chain AC. B A 30°
If the bolt exerts a force of 50 lb on the pipe in the direction shown, determine the forces FA and FB that the smooth contacts at A and B exert on the pipe. FB B C FA 30° 50 lb
Determine the projected component of the force along the line OA. F = 650 N 13 12 A X
Determine the magnitude of the resultant force FR and its direction, measured clockwise from the positive u axis. 70° 45° F₂ = 500 N V 30° U F₁ = 300 N
Two forces act on the hook. Determine the magnitudeof the resultant force. 40° 500 N 30° 200 N
Round off the following numbers to three significant figures: (a) 3.45555 m, (b) 45.556 s, (c) 5555 N, (d) 4525 kg.
Determine the magnitude of the resultant force F′R = F1 + F2 and its orientation θ, measured counterclockwise from the positive x axis. F₁ = 260 lb 45° F₂=310 lb 12 5 13 y X
Evaluate (204 mm)(0.00457 kg) (34.6 N) to three significant figures and express the answer in SI units using an appropriate prefix.
Solve Prob. 2-4 with F = 350 lb. A 30° B 45°
Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive x axis. y 800 N 30° ·X 600 N
Express F1 and F2 as Cartesian vectors. F₁ = 600 N X 30⁰ N 45° F₂ = 450 N
Resolve the 30-lb force into components along the u and v axes, and determine the magnitude of each of these components. 15° 30 lb 130° U
Determine the magnitude and direction of the resultant force. 250 N 30° 400 N 300 N -X
Determine the magnitude of the resultant force acting on the corbel and its direction θ, measured counterclockwise from the x axis. F3 = 600 lb b F₂ = 400 lb F₁ = 700 lb 30⁰ -X
Determine the projection of the force F along the pole. -2m z F = {2i + 4j+ 10k) kN 1m 2m
If θ = 60°, determine the magnitude of the resultant force andits direction measured clockwise from the horizontal. 40° B A FA = 8 KN FB = 6 KN
Determine the magnitude of the resultant force FR = F1 + F3 and its orientation u, measured counterclockwise from the positive x axis. F3 = 250 N F₂ = 360 N y 30% 45° 30° ·x F₁ = 400 N
Determine the coordinate direction angles of the force. 2 45° -30° F = 75 lb У
Express the force as a Cartesian vector. x 60° F = 500 N 60°

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