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engineering
engineering mechanics statics

Questions and Answers of Engineering Mechanics Statics

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°
Express the force as a Cartesian vector. F = 500 N 45° 60°
Express the force as a Cartesian vector. x Z F = 50 lb 45° 15
Determine the angle θ of for connecting member B to the plate so that the resultant force of FA and FB is directed horizontally to the right. Also, what is the magnitude of the resultant force?
Express the force as a Cartesian vector. F = 750 N 45% 60%
Determine the resultant force acting on the hook. x 30° 45° F₂ = 800 lb F₁ = 500 lb
Express the position vector rAB in Cartesian vector form, then determine its magnitude and coordinate direction angles. 3 m / A/ 2 m ГAB - 4 m - в 3 m 3 m - у
Determine the length of the rod and the position vector directed from A to B. What is the angle θ? X 4 ft 4 ft
Express the force as a Cartesian vector. 2 m 3 m A m F = 630 N 4m B 4 m
Express the force as a Cartesian vector. X A 4 m Z F = 900 N /2m -7 m- B /2m
Determine the magnitude of the resultant force at A. X FB = 840 N 3 m B 2 m 3 m A 6 m Fc = 420 N C - 2 m
Determine the resultant force at A. A 6 ft 2 ft Fc = 490 lb FB = 600 lb 4 ft 2 ft 3 ft B 4 ft 4 ft
Determine the angle θ between the force and theline AO. F=(-6i+9j+3 k) kN Je 2 m -2m- 16 E
Determine the angle θ between the force and the line AB. 4 m 4 m B F=600 N -3 m
Determine the components of the force acting parallel and perpendicular to the axis of the pole. F = 600 lb 4 ft 60% 30° 2 ft y
Determine the angle θ between the force and the line AO. F = 650 N 13 12 A X
Find the magnitude of the projected component of the force along the pipe AO. 5m 4 m B F = 400 N 4m 6m
Determine the magnitudes of the x, y, z components of the force F. X F₁ Z F. α = 60° F = 80 lb B = 45° Fy
Determine the magnitude of the resultant force acting on the ring at O, if FA = 750 N and θ = 45°. What is its direction, measured counterclockwise from the positive x axis? 30° B FA FB = 800 N ·X
Determine the angle θ between the two cables. 2 m 3 m F₂ = 40 N A L N F₁ = 70 N 3m C 4 m -3 m- 2 m B y
Express each force in Cartesian vector form. F₁ = 90 N X Z F3 = 200 N 60° 39 F₂ = 150 N 45° -y
Represent each cable force as a Cartesian vector. Fc = 400 N A 2 m FE= 350 N FB = 400 N 3 m E N 2m 2 m B 3 m y
Determine the magnitude of the projection of the force F1 along cable AC. 2 m 3 m F₂ = 40 N A Z SXFORCES F₁ = 70 N 3 m C 4 m -3 m- X 2 m B y
Determine the magnitude of the projection of F₁ along the line of action of F2. N 60° 30⁰- F₂= 25 lb 60° 30° F₁ = 30 lb y
Determine the magnitude of the projected component of the 100-lb force acting along the axis BC of the pipe. X 4 ft 2 ft y C B N 6 ft A 3 ft F = 100 lb 8 ft D
If F = {16i + 10j - 14k) N, determine the magnitude of the of F along the axis of the pole and perpendicular projection to it. X N 4 m 60° F 2 m
Determine the magnitudes of the projections of the force acting along the x and y axes. X 300 mm -30% A 30° F = 300 N 300 mm 300 mm
Determine the magnitude of the projection of the force acting along line OA. X Z 300 mm -30°- 30° 300 mm - y F = 300 N 300 mm
Determine the angle θ between the two cables. X C 10 ft 8 ft 8 ft Z 10 ft A B FAB 12 lb 6 ft 4 ft y
The uniform bar AD has a mass of 20 kg. If the attached spring is unstretched when θ = 90°, determine the angle θ for equilibrium. Note that the spring always remains in the vertical position due
If the potential function for a conservative one-degree-of-freedom system is V = (10 cos2θ + 25 sinθ)J, where 0° < θ < 180° determine the positions for equilibrium and investigate the
If the potential function for a conservative one-degree-of-freedom system is V = (12sin2θ + 15 cosθ)J, where 0° < θ < 180° determine the positions for equilibrium and investigate the
The potential energy of a one-degree-of-freedom system is defined by V = (20x3 - 10x2 - 25x - 10)ft•lb, where x is in ft. Determine the equilibrium positions and investigate the stability for
The dumpster has a weight W and a center of gravity at G. Determine the force in the hydraulic cylinder needed to hold it in the general position θ. 十6-。
Use the method of virtual work to determine the tensions in cable AC. The lamp weighs 10 lb. B 45° 30
The pendulum consists of a 8-kg circular disk A, a 2-kg circular disk B, and a 4-kg slender rod. Determine the radius of gyration of the pendulum about an axis perpendicular to the page and passing
Solve Prob. 10–76 using Mohr’s circle. Data From Problem 10-76Determine the orientation of the principal axes having an origin at point O, and the principal moments of inertia for the
Determine the orientation of the principal axes having an origin at point O, and the principal moments of inertia for the rectangular area about these axes. y 6 in. 3 in.
Determine the product of inertia for the shaded area with respect to the x and y axes. y -2 in.--2 in.- 2 in. 1 in. 4 in.
Determine the product of inertia for the beam’s crosssectional area with respect to the x and y axes. 1 in. 1 in. 8 in. 3 in. 1 in. 12 in.
Determine the product of inertia of the shaded area with respect to the x and y axes. x²+ y? = 4 2 in. 2 in.
Locate the centroid y̅ of the cross section and determine the moment of inertia of the section about the x' axis. 0.4 m y 0.05 m 0.3 m- 0.2 m 0.2 m 0.2 m'0.2 m
Determine the moment of inertia about the y axis. y 150 mm --150 mm- 20 mim 200 mm C 20 mm 200 mm 20 mim
Determine the moment of inertia about the x axis. y 150 mm --150 mm 20 mm 200 mm C 20 mm 200 mm 20 mm
Determine the moment of inertia Ix of the shaded area about the x axis. |-100 mm--100 mm150 mm 150 mm 150 mm 75 mm
Determine the moment of inertia Ix of the shaded area about the x axis. y -100 mm-100 mm- - 150 mm - 150 mm 75 mm 150 mm
Determine the location y̅ of the centroid of the channel’s cross-sectional area and then calculate the moment of inertia of the area about this axis. 50 mm 50 mm 250 mm 50 mm 350 mm
Determine the moment of inertia of the composite area about the y axis. -3 in. 6 in. 3 in. 3 in.
Determine the moment of inertia of the composite area about the x axis. y 3 in. - 6 in. 3 in. 3 in.
Determine the moment of inertia for the shaded area about the x axis. y? = a
Determine the moment of inertia for the shaded area about the x axis. y? = 2x 2 m y = x 2 m- E-
Determine the moment of inertia for the shaded area about the y axis. y -y? = 1 - x 1m 1 m -1m -
Determine the moment of inertia for the shaded area about the x axis. -y? = 1 - x 1 m 1 m 1 m -
Determine the moment of inertia for the shaded area about the y axis. y h メー。 h
Determine the moment of inertia for the shaded area about the x axis. y h h y = -b-
Determine the moment of inertia for the shaded area about the y axis. 4 in. y² = x 16 in.
Determine the moment of inertia about the x axis. 2+ 4y = 4 1 m 2 m
Determine the moment of inertia for the shaded area about the y axis. 8 m 4 m
Determine the moment of inertia for the shaded area about the x axis. 8 m - 4 m
Determine the moment of inertia for the shaded area about the y axis. y? = 1- 0.5x 1 m 2 m
Determine the moment of inertia for the shaded area about the x axis. -y? 1- 0.5x 1 m 2 m
Determine the moment of inertia for the shaded area about the y axis. y y =x/2. 1 m 1 m
Determine the moment of inertia for the shaded area about the x axis. y y =x/2 1m 1 m
Determine the moment of inertia about the y axis. y y = b a
The water tank has a paraboloid-shaped roof. If one liter of paint can cover 3m2 of the tank, determine the number of liters required to coat the roof. y%3= 6 (144 – x) 2.5 m 12 m
A ring is generated by rotating the quartercircular area about the x axis. Determine its surface area. a 2а
A ring is generated by rotating the quartercircular area about the x axis. Determine its volume. a 2а
Locate the center of mass of the homogeneous block assembly. 250 mm 200 mm 100 mm 150 mm 150 mm 150 mm
Locate the centroid y̅ of the cross-sectional area of the beam constructed from a channel and a plate. Assume all corners are square and neglect the size of the weld at A. -20 mm y 350 mm C 10 mm 70
Locate the centroid (x̅,y̅) of the shaded area. y 1 in. 3 in. 3 in- -3 in.-
Locate the centroid (x̅,y̅) of the shaded area. 6 in. 3 in. 6 in. 6 in.
Determine the location y̅ of the centroid C of the beam having the cross-sectional area shown. 150 mm 15 mm IT B C 150 mm -15 mm 15 mm 100 mm
Locate the centroid y̅ for the beam’s cross-sectional area. 120 mm 240 mm 240 mm 240 mm 120 mm
Locate the centroid (x̅,y̅) of the metal cross section.Neglect the thickness of the material and slight bends at the corners. 50 mm 150 mm 50 mm 100 mm 100 mm 50 mm
Determine the location (x, y, z) of the centroid of the homogeneous rod. 200 mm 30° 600 mm 100 mm
Locate the center of gravity y̅ of the volume. The material is homogeneous. 100 4 in. 1 in.] y -10 in.-10 in.-
Locate the center of gravity z̅ of the solid. - 4,3 16 in. -8 in.-
Locate the centroid z̅ of the volume. 1 m = 0.5z 2 m y
Determine the centroid y̅ of the solid. -1) - 1) 1 ft -y 3 ft
Locate the centroid z̅ of the frustum of the right-circular cone. h R- y
Locate the centroid y̅ of the paraboloid. = 4y 4 m 4 m
Locate the center of gravity of the volume. The material is homogeneous. 2 m 2 m y? = 2z y
Locate the centroid x̅ of the circular sector. y C
Locate the centroid y̅ of the shaded area. h -y = h - a h y = h - ax
Locate the centroid x̅ of the shaded area. y -y =h- h y = h - a x
Locate the centroid y̅ of the shaded area. y = a sin a
Locate the centroid x̅ of the shaded area. y = a sin a - am
Locate the centroid y̅ of the shaded area. y h h a-b
Locate the centroid x̅ of the shaded area.
Locate the centroid y̅ of the shaded area. y =x 100 mm 00 100 mm
Locate the centroid x̅ of the shaded area. y y = x 100 mm 100 100 mm
Locate the centroid y̅ of the shaded area. 4 ft 4 ft
Locate the centroid x̅ of the shaded area. y 4 ft 4 ft
The plate has a thickness of 0.25 ft and a specific weight of γ = 180 lb/ft3. Determine the location of its center of gravity. Also, find the tension in each of the cords used to support it.
Locate the centroid y̅ of the shaded area. y ソ= +ん sr +h h
Locate the centroid x̅ of the shaded area. y 『テー+h h
Locate the centroid y̅ of the shaded area. -y = (4 – 16 ft IT 4 ft - 4 ft–
Locate the centroid x̅ of the shaded area. -y = (4 - r 16 ft IT 4 ft F4 ft-
Locate the centroid y̅ of the area. 2. x- 4 in. -8 in.-

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