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engineering
engineering mechanics statics 15th

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

Resolve each force acting on the gusset paired into its x and y components, and express each force as a Cartesian vector. F₁ = 650 N 45° F₂=750 N -x F₁ - 900 N
Determine the magnitude of the resultant force acting on the gusset plate and its direction. measured counterclockwise from the positive x-axis. F3 = 650 N 00 45° F₂ = 750 N -X F₁ = 900 N
The three forces are applied to the bracket. Determine the range of values for the magnitude of force P so that the resultant of the three forces does not exceed 2400 N. 3000 N 90%- Prob. 2-38 800 N 60° -X
Express F1, F2 and F3 as cartesian vectors. F3 = 750 N 45° 30° F₂= 625 N Im 5 X F₁-850 N
The three concurrent forces acting on the post produce a zero resultant force FR = 0. If F2 = 1/2 F1. and F1 is to be 900 from F2 as shown, determine the required magnitude of F3 expressed in terms of F1 and the angle θ. F₁ F3
Three forces act on the ring. Determine the range of values for the magnitude of P so that the magnitude of the resultant force does not exceed 2500 N. Force P is always directed to the right. 1500 N aip que 60° 45° 600 N ►P-X
If FB = 600 N and θ = 20°, determine the magnitude of the resultant force and its direction measured counterclockwise from the positive y-axis. FB B y 30° A FA= 700 N x
Three forces act on the bracket. Determine the magnitude and direction θ of F1 so that the resultant force is directed along the positive x’ axis and has a magnitude of 800 N. F3 = 180 N 13 12 y AF₂= 200 N 60° 0 F₁
If F1 = 300 N and θ = 10°, determine the magnitude of the resultant force and its direction measured counterclockwise from the positive x’ axis. F3 = 180 N 13 12 y AF₂= 200 N 60° 0 F₁
Express F1, F2 and F3 as Cartesian vectors. F₁ = 60 lb 30% 。。 Probs. 2-50/51 20° F₂ = 50 lb
Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix:(a) (212 mN2)(b) (52800 ms2)(c) [548 (106)]1/2 ms
If F2 = 150 lb and θ = 55°, determine the magnitude of the resultant force and its direction measured clockwise from the positive x-axis. F3 = 52 lb 13/12 HID 100 F₁ = 80 lb 25° F₂ X "1
Three forces act on the bracket. Determine the magnitude and direction 11 of F so that the resultant force is directed along the positive x’ axis and has a magnitude of 8kN. 4 kN 15° F 30° 6 kN -X
Specify the magnitude F3 and directions α3. β3 and γ3 so that the resultant force of the three forces is FR = {9j} kN. X F3 αz Y3 135 -B312 Prob. 2-77 F₂ = 10 KN 30° F₁ = 12 kN
Three forces act on the ring. Determine the magnitude and coordinate direction angles of the resultant force. F₂ = 500 N 30° X 60° F3 = 100 N 60° 120° F₁ = 400 N 45° y
If the coordinate direction angles for F3 are α3 = 120°, β = 60°. and γ = 60°. determine the magnitude and coordinate direction angles of the resultant force acting on the eyebolt. 30 F₁ = 700 lb F3 = 800 lb F₂= 600 lb
If the direction of the resultant force acting on the eyebolts is defined by the unit vector uFR = cos 30° j + sin 30°k. determine the coordinate direction angles of F3 and the magnitude of FR. 30 F₁ = 700 lb F3 = 800 lb F₂= 600 lb
Determine the length of the connecting rod AB by first formulating a position vector from A to B and then determining its magnitude. 30° B 300 mm 150 mm Prob. 2-86 X
Represent each of the following combinations of units in the correct SI form using an appropriate prefix: (a) Mg/mm (b) mN/μs(c) μm · Mg
Water has a density of 1.94 slug/ft3. What is the density expressed in SI units? Express the answer to three significant figures.
The density (mass/volume) of aluminum is 5.26 slug/ft3. Determine its density in SI units. Use an appropriate prefix.
Determine the magnitude of the resultant force FR = F1 + F2 and its direction, measured clockwise from the positive u axis. A F 30° 45° C
Determine the magnitude of the resultant force FR = F1 + F2 and its orientation θ, measured clockwise from the positive x axis. F3 = 250 N F₂ = 360 N 30% 45% 30° F₁ = 400 N X
If the resultant force acting on the bracket is to be 750 N directed along the positive x-axis, determine the magnitude of F and its direction θ. 00 325 N 13 12 45° 600 N F X
If the magnitude of the resultant force acting on the bracket is to be 80 Ib directed along the u axis. determine the magnitude of F and its direction θ. 90 lb 45° F 50 lb U -X
Determine the magnitude and coordinate direction angles of the resultant of the two forces acting at point A. X Fc= 400 N, 2m FE=350 N FB = 400 N 3 m E 2 m E 2 m B 3m
If cable AD is tightened by a turnbuckle and develops a tension of 1300 lb, determine the tension developed in cables AB and AC, and the force developed along the z-axis of the Antema tower AE. 30 ft NO ft B x- 15 ft 12.5 ft Z A E 10 ft. 15 ft
Determine the force in each cable needed to support the 500-lb cylinder. 3 ft 6 ft B -6 ft- D N 3 ft 5 ft C 6 ft 2 ft y
If a vertical force of 2.5 kN is applied to the hook at A, determine the tension in each of the three cables for equilibrium. Set d = 1 m. X B 3 m 1.5 m A (P Pasazanmar F = 2.5 KN 3 m 1 m D 0.75 m y
A “scale” is constructed with a 4-ft-long cord and the 10-lb block D. The cord is fixed to a pin at A and passes over two small pulleys at B and C. Determine the weight of the suspended block at B if the system is in equilibrium when s = 1.5 ft. - 1 ft - B DS C s = 1.5 ft
Determine the magnitudes of the components of the force acting along the axis AB of the wrench handle and perpendicular to it. 300 mm B 500 mm Prob. 2-116 F = 80 N A 30° 45°
Determine the angle θ between the cables AB and AC. 2 m B -1 m 1 m D 6 m 3 m
Determine the resultant force acting on the hook, and its direction measured clockwise from the positive x axis. S F₂ = 800 N درا Prob. 2-55 60⁰° X F₁ = 500 N
The force F acts on the bracket within the octant shown. If the magnitudes of the x and z components of F are Fx = 300 N and Fz = 600 N, respectively, and FZ = 600, determine the magnitude of F and its y component. Also. find the coordinate direction angles α and y. x N
The two forces F1 and F2 have a resultant force of FR = {— 100 k} lb. Determine the magnitude and coordinate direction angles of F2. F₂ BO 50° -30° F₁ = 60 lb
The bracket is subjected to the two forces shown. Express each force in Cartesian vector form and then determine the resultant force FR. Find the magnitude and coordinate direction angles of the resultant force. F₂ BO 50° -30° F₁ = 60 lb
The bracket is subjected to the two forces shown. Express each force in Cartesian vector form and then determine the resultant force FR. Find the magnitude and coordinate direction angles of the resultant force. Z 120% 60° Prob. 2-69 F₂ = 400 N 45° 25° 35° F₁ = 250 N
Express each force in Cartesian vector form and then determine the resultant force. Find the magnitude and coordinate direction angles of the resultant force. or form and then determine the resultant force. Find the magnitude and coordinate direction angles of the resultant force. X 60° F₁ = 300
Two forces F1 and F2 act on the screw eye. If the resultant force FR has a magnitude of 150 lb and the coordinate direction angles are shown. determine the angle y, the magnitude of F2, and its coordinate direction angles. X Z 130°. F₂ 120° FR = 150 lb F₁ = 80 lb
The spur gear is subjected to the two forces. Express each force as a Cartesian vector. F₂= 180 lb 60° 60° 24. 7 135° 25 F₁ = 50 lb
Determine the coordinate angle γ for F2 and express each force acting on the bracket as a Cartesian vector. X N 45° 60° F₁ = 450 N 45°. 30° F₂ = 600 N -y
Determine the resultant of the two forces and express the result as a Cartesian vector. x F₂= 180 lb 60° 60⁰ 24. 135° 25 F₁ = 50 lb
Determine the magnitude and coordinate direction angles of the resultant force acting on the bracket. X N 45° 60° F₁ = 450 N 45°. 30° F₂ = 600 N -y
The pipe is subjected to the force F, which has components acting along the x, y. z axes. If the magnitude of F is 12 kN, and α = 120° and γ = 450, determine the magnitudes of its three components. X F
The pipe is subjected to the force F, which has components acting Fx = 1.5kN and Fz = 1.25kN. If β = 75°, determine the magnitude of F and Fy. X F
Express each force as a Cartesian vector, and then determine the magnitude and coordinate direction angles of the resultant force. 6 ft 마 B 2 ft 13/12 15 2.5 ft - 4 ft- F1 = 80 lb A F2 = 501b
The positions of point A on the flag pole and point B on the light have been measured relative to the electronic distance meter at O. Determine the distance between A and B. B x 50⁰ 138 ft 20° 232 ft 30° 45%
The 8-m-long cable is anchored to the ground at A. If x = 4 m and y = 2 m, determining the coordinate z to the highest point of attachment along the column. A B
The 80-ft-long cable is attached to the boom at A. If x = 60 ft. determine the coordinates y and z to the end of cable B. Take z = 3y. A Z B Probs. 2-93/94 -y
At a given instant, the position of a plane at A and a train at B are measured relative to a radar antenna at O. Determine the distance d between A and B at this instant. To solve the problem. formulate a position vector, directed from A to B, and then determine its magnitude. X 5
The cable is attached to the boom at A and to point B. which has coordinates of x = 80 ft. y = 40 ft. z = 40 ft. Determine the length of the cable and the angle between the positive z-axis and the cable. X A Z B -y
Determine the position (x, y, 0) for fixing cable BA so that the resultant force exerted on the pole is directed along its axis, from B toward O. Also, what is the magnitude of the resultant force? 2 m X -3m_ m. E₂=250 N F=300 N A B 4m F₁ = 350 N m
The force F has a magnitude of 80 lb and acts at the midpoint C of the rod. Express this force as a Cartesian vector. A 2 ft. X B Z F = 80 lb 0 3 ft L 6 ft
Determine the magnitude and coordinate direction angles α, β. ϒ of the resultant force acting on the pole. Set x = 4m, y = 2m. -3 m F₂=250 N = 300 N 4 m F₁ = 350 N m
Determine the magnitude of the projected component of force F along the pole. 6 m 4 m D B F = 600 N 4 m 3 m 4 m
Determine the angles between the wire segments. X -0.6 m- N -0.4 m- Prob. 2-104 0.2 m B 0.8 m 0.5 m
Determine the magnitude of the projected component of force F along the pole. F = (-20i + 50j - 10k} lb A 6 ft 1-281- X 3 ft Prob. 2-105
Determine the angle θ between the two cables. 2 m 3 m F₂ = 40 N |A Z F₁ = 70 N 3 m 4m -3 m- 2m B
Determine the components of F that act along rod AC and perpendicular to it. Point B is located at the midpoint of the rod. 6 m 4 m D B F = 600 N 4 m 3 m 4 m
Determine the magnitude of the projection of the force F1 along cable AC. 2m 3 m F₂ = 40 N A N F₁ = 70 N 3m 4 m -3m- X 2m B y
A force of F = {- 40k} lb acts at the end of the pipe. Determine the magnitudes of the components F1 and F2 which are directed along the pipe’s axis and perpendicular to it. Z -5 ft- F₂ 3 ft 3 ft F₁ F = {-40 k} lb
Determine the magnitudes of the components of F = 600 N acting along and perpendicular to segment DE of the pipe assembly. 2 m 2 m 2 m 2 m 3 m E B F = 600 N
Determine the angle θ between the pipe segments BA and BC. X 4 ft 3 ft Z F = (30i - 45j + 50k} lb C 4 ft 4 ft. 2 ft
Determine the magnitudes of the components of F acting along and perpendicular to segment BC of the pipe assembly. 4 ft 3 ft F = (30i - 45j + 50k} lb B 4 ft 2 ft
Determine the magnitudes of the components of the force acting parallel and perpendicular to the diagonal AB of the crate. 1 ft A 3 ft B 1.5 ft F = 90 lb 60° -45⁰ -y
Determine the magnitudes of the projection of the force acting along the x and y axes. 300 mm -30° 300 mm Prob. 2-127 30° F = 300 N 300 mm
Determine the projection of the force acting in the direction of cable AC. Express the result as a Cartesian vector. X C 10 ft 8 ft -8 ft- 10 ft- Prob. 2-130 A B FAB=12 lb 6 ft 4 ft
Given the three vectors A, B. and D, show that A(B + D) = (A · B) + (A · D). X -0.6 m A N -0.4 m. C o 0.2 m B 0.8 m 0.5 m D -y
Represent each of the following quantities in the correct SI form using an appropriate prefix: (a) 0.000 431 kg.(b) 35.3(103) N, (c) 0.005 32 km.
Represent each of the following combinations of units in the correct SI form: (a) Mg/ms. (b) N/mm,(c) mN/(kg.ps).
Evaluate each of the following to three significant figures and express each answer in SI units using an appropriate prefix: (a) (200 kN)2. (b) (0.005 mm)2. (c) (400 rn)3.
The specific weight (wt./vol.) of brass is 520 lb/ft3. Determine its density (mass/vol.) in SI units. Use an appropriate prefix.
Determine the magnitude of the resultant force FR and its direction. measured clockwise from the positive u-axis. 70° 45° F₂ = 500 N 30° U F₁ = 300 N
The force F = 450 lb acts on the frame. Resolve this force into components acting along members AB and AC. and determine the magnitude of each component. C B 450 lb 30°
If force F is to have a component along the u axis of F,, =6 kN. determine the magnitude of F and the magnitude of its component F1 along the y-axis. u 45° 105⁰ F
Express F1 and F2 as Cartesian vectors. F₁ = 600 N X Im 30% Prob. R2-6 45° |F₂ = 450 N
Determine the magnitude and direction of the resultant force. 250 N T 30° 400 N 300 N X
Resolve the force F2 into components along the μ and μ axes and determine the magnitudes of the components. 75° 30° 30° F₂ = 6 kN V F₁ = 4 kN
Resolve each force acting on the post into its x and y components. F₂ = 450 N 45° y F₁ = 300 N F3 = 600 N -X
Resolve the force F1 into components along the u and u axes and determine the magnitude of the components. 75° 30° 30° F₂ = 6 kN v F₁ = 4 kN
The pclvis P is connected to the femur F at A using three different muscles, which exert the forces shown on the femur. Determine the resultant force and specify its orientation O, measured counterclockwise from the positive x axis. y 60 N A 120 N 13 12 30° F P 80 N X
Determine the magnitude of the resultant force and its direction measured counterclockwise from the positive X axis. 30° F₁ = 40 lb 20⁰ X F = 50 lb
Express F1 and F2 as a cartisen forces. 30° F₁ = 40 lb 20⁰ X F = 50 lb
Four concurrent forces act on the plate. Determine the magnitude of the resultant force and its direction counterclockwise from the positive x-axis. 30⁰° F-38 lb F₂ = 100 lb F₁ = 60 lb 4 F₁ = 50 lb X
The three cable forces act on the eyebolt. Determine two possible magnitudes for P so that the resultant force has a magnitude of 800 N. 1000 lb 400 lb 30° P X
Determine the resultant force acting on the hook. 30° Z -45° F₂ = 800 lb F₁ = 500 lb
Express the force as a Cartesian vector. F = 750 N X 45% 60%
Determine the magnitude and direction of the resultant FR = F1 ± F2 + F3 of the three forces by first finding the resultant F’ = F1 + F2 and then finding FR = F’ + F3. F₁ = 30 N 3 S 4 F₂= 20 N -20° F3 = 50 N ·x
Express the force as a Cartesian vector. x F = 50 lb 45° 15 Prob. F2-16 3
Determine the angle θ for connecting member B to the plate so that the resultant of FA and FB is directed along the positive x axis. What is the magnitude of the resultant force? y FA = 400 lb 30% B X FB = 500 lb
Determine the magnitude and direction of the resultant FR = F1 ± F2 + F3 of the three forces by first finding the resultant F’ = F2 + F3 and then finding FR = F’ + F1. F₁ = 30 N 3 S 4 F₂= 20 N -20° F3 = 50 N ·x
Determine the angle θ = 600° for connecting member A to the plate so that the resultant of FA and FB is directed along the positive x axis. Also, what is the magnitude of the resultant force? -40° FA = 8 KN X BFB=6 kN
Express the force as a Cartesian vector. X 4 m -7 m F = 900 N 2 m B 2m y
Determine the design angle θ (0° < O < 90°) for member AB so that the 400-lb horizontal force has a component of 500 lb directed from A toward C. What is the component of force acting along member AB? Take θ =40°. B 400 lb
Express the force as a Cartesian vector. 2 m 3 m A F = 630 N m B Z 4 m 4 m
Determine the design angle θ (0° < O < 90°) for members AB and AC so that the 400-lb horizontal force has a component of 600 lb which acts up to the right, in the direction from B toward A. Also calculate the magnitude of the force component along AC. Take θ = 30°. B 400 lb
Determine the magnitude of the two towing forces FB and Fc if the resultant force has a magnitude FR = 10 kN and is directed along the positive x axis. Set θ = 15°. A Fc FB 20⁰ -I В -Х
If the resultant FR of the two forces acting on the jet aircraft is to be directed along the positive x axis and have a magnitude of 10 kN. determine the angle O of the cable attached to the truck at B so that FR is a minimum. What is the magnitude of force in each cable when this occurs?
If the resultant force of the two tugboats is required to be directed toward the positive x-axis, and FB is to be a minimum. determine the magnitude of FR and FB and the angle O. FA-2 KN 30° Fs A 50x B x
If the resultant force of the two tugboats is 3 kN. directed along the positive x axis, determine the required magnitude of force FB and its direction O. F₁ = 2 kN 30° FB O B -X

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