Question: Use traces to sketch and identify the

> A horizontal beam AB with cross-sectional dimensions (b = 0 .75 in.) × (h = 8.0in.) is supported by an inclined strut CD and carries a load P = 2700 lb at joint B (see figure part a). The strut, which consists of two bars each of thickness 5

> A torque To is transmitted between two flanged shafts by means of ten 20-mm bolts (see figure and photo). The diameter of the bolt circle is d = 250 mm. If the allowable shear stress in the bolts is 85 MPa, what is the maximum permissible torque? (Disreg

> Two bars AC and BC of the same material support a vertical load P (see figure). The length L of the horizontal bar is fixed, but the angle u can be varied by moving support A vertically and changing the length of bar AC to correspond with the new positio

> Continuous cable ADB runs over a small frictionless pulley at D to support beam OABC, which is part of an entrance canopy for a building (see figure). A downward distributed load with peak intensity qo = 5 kN/m at O acts on the beam (see figure). Assume

> Continuous cable ADB runs over a small frictionless pulley at D to support beam OABC, which is part of an entrance canopy for a building (see figure). The canopy segment has a weight W = 1700 lb that acts as a concentrated load in the middle of segment A

> A flat bar of a width 60 mm b 5 and thickness 10 mm t 5 is loaded in tension by a force P (see figure). The bar is attached to a support by a pin of a diameter d that passes through a hole of the same size in the bar. The allowable tensile stress on the

> An elevated jogging track is supported at intervals by a wood beam AB (L = 7 .5 ft) that is pinned at A and supported by steel rod BC and a steel washer at B. Both the rod (dBC = 3 /16 in.) and the washer (dB = 1 .0 in.) were designed using a rod tension

> An aluminum tube is required to transmit an axial tensile force P = 33 k (see figure part a). The thickness of the wall of the tube is 0.25 in. (a) What is the minimum required outer diameter dmin if the allowable tensile stress is 12,000 psi? (b) Repeat

> A bar of solid circular cross section is loaded in tension by forces P (see figure). The bar has a length L = 16.0in. and diameter d = 0.50 in. The material is a magnesium alloy having a modulus of elasticity E = 6.4 × 106psi. The allowable

> An angle bracket having a thickness t = 0.75 in. is attached to the flange of a column by two 5/8-inch diameter bolts (see figure). A uniformly distributed load from a floor joist acts on the top face of the bracket with a pressure p = 275 ps

> A bar made of structural steel having the stress strain diagram shown in the figure has a length of 60 in. The yield stress of the steel is 50 ksi, and the slope of the initial linear part of the stress-strain curve is 29,000 ksi. (a) The bar is loaded a

> Imagine that a long steel wire hangs vertically from a high-altitude balloon. (a) What is the greatest length (feet) it can have without yielding if the steel yields at 40 ksi? (b) If the same wire hangs from a ship at sea, what is the greatest length?

> A hollow circular post ABC (see figure) supports a load P1 = 1700 lb acting at the top. A second load 2 P is uniformly distributed around the cap plate at B. The diameters and thicknesses of the upper and lower parts of the post are dab = 1.25 in, tab =

> A steel column of hollow circular cross section is supported on a circular, steel base plate and a concrete pedestal (see figure). The column has an outside diameter d = 250 mm and supports a load P = 750 kN. (a) If the allowable stress in the column is

> A mountain bike is moving along a flat path at constant velocity. At some instant, the rider (weight = 670 N) applies pedal and hand forces, as shown in the figure part a. (a) Find reaction forces at the front and rear hubs. (Assume that the bike is pin

> An elliptical exerciser machine (see figure part a) is composed of front and back rails. A simplified plane-frame model of the back rail is shown in figure part b. Analyze the plane-frame model to find reaction forces at supports A, B, and C for the posi

> A soccer goal is subjected to gravity loads (in the 2z direction, w = 73 N/m for DG, BG, and BC; w = 29 N/m for all other members; see figure) and a force F = 200 N applied eccentrically at the mid-height of member DG. Find reactions at supports C, D, an

> Space frame ABC is clamped at A, except it is free to rotate at A about the x and y axes. Cables DC and EC support the frame at C. Force Py = 250lb is applied at the mid-span of AB, and a concentrated moment Mx = 220 in.-lb acts at joint B. (a) Find reac

> Space frame ABCD is clamped at A, except it is free to translate in the x direction. There is also a roller support at D, which is normal to line CDE. A triangularly distributed force with peak intensity qo = 75 N/m acts along AB in the positive z direct

> A special vehicle brake is clamped at O when the brake force 1 P is applied (see figure). Force P1 = 50lb and lies in a plane that is parallel to the x-z plane and is applied at C normal to line BC. Force P2 = 40 lb and is applied at B in the 2y directio

> A plane frame has a pin support at A and roller supports at C and E (see figure). Frame segments ABD and CDEF are joined just left of joint D by a pin connection. (a) Find reactions at supports A, C, and E. (b) Find the resultant force in the pin just le

> A 150-lb rigid bar AB, with frictionless rollers at each end, is held in the position shown in the figure by a continuous cable CAD. The cable is pinned at C and D and runs over a pulley at A. (a) Find reactions at supports A and B. (b) Find the force in

> A plane frame with a pin support at A and roller supports at C and E has a cable attached at E, which runs over frictionless pulleys at D and B (see figure). The cable force is known to be 400 N. There is a pin connection just to the left of joint C. (a)

> A plane frame with pin supports at A and E has a cable attached at C, which runs over a frictionless pulley at F (see figure). The cable force is known to be 500 lb. (a) Find reactions at supports A and E. (b) Find internal stress resultants N, V, and M

> A large precast concrete panel for a warehouse is raised using two sets of cables at two lift lines, as shown in the figure part a. Cable 1 has a length L1 = 22 ft, cable 2 has a length L2 = 10 ft, and the distance along the panel between lift points B a

> A plane frame is constructed by using a pin connection between segments ABC and CDE. The frame has pin supports at A and E and joint loads at B and D (see figure). (a) Find reactions at supports A and E. (b) Find the resultant force in the pin at C.

> A 200-lb trap door (AB) is supported by a strut (BC) which is pin connected to the door at B (see figure). (a) Find reactions at supports A and C. (b) Find internal stress resultants N, V, and M on the trap door at 20 in. from A. B Pin or hinge conn

> Find support reactions at A and D and then calculate the axial force N, shear force V, and bending moment M at mid-span of column BD. Let L = 4 m, qo = 160 N/m, P 5 200 N, and Mo = 380 Nm? Mo 4 4 L/2 3 B 3 L L/2 y D

> Find support reactions at A and D and then calculate the axial force N, shear force V, and bending moment M at mid-span of AB. Let L = 14 ft, qo = 12 lb/ft, P = 50 lb, and Mo = 300 lb-ft. Mo 4 B A L 40 L/2 L

> A plane frame is restrained at joints A and D, as shown in the figure. Members AB and BCD are pin connected at B. A triangularly distributed lateral load with peak intensity of 80 N/m acts on CD. An inclined concentrated force of 200 N acts at the mid-sp

> A plane frame is restrained at joints A and C, as shown in the figure. Members AB and BC are pin connected at B. A triangularly distributed lateral load with a peak intensity of 90 lb/ft acts on AB. A concentrated moment is applied at joint C. (a) Find r

> A stepped shaft ABC consisting of two solid, circular segments is subjected to uniformly distributed torque t1 acting over segment 1 and concentrated torque T2 applied at C, as shown in the figure. Segment 1 of the shaft has a diameter of d1 = 57 mm and

> A stepped shaft ABC consisting of two solid, circular segments is subjected to torques T1 and T2 acting in opposite directions, as shown in the figure. The larger segment of the shaft has a diameter of d1 = 2.25 in. and a length L1 = 30 in.; the smaller

> A space truss is restrained at joints A, B, and C, as shown in the figure. Load P acts in the 1z direction at joint B and in the 2z directions at joint C. Coordinates of all joints are given in terms of dimension variable L (see figure). Let P = 5 kN and

> A space truss is restrained at joints A, B, and C, as shown in the figure. Load 2P is applied at in the 2x direction at joint A, load 3P acts in the 1z direction at joint B, and load P is applied in the 1z direction at joint C. Coordinates of all joints

> A tubular post of outer diameter d2 is guyed by two cables fitted with turnbuckles (see figure). The cables are tightened by rotating the turnbuckles, producing tension in the cables and compression in the post. Both cables are tightened to a tensile for

> A space truss is restrained at joints O, A, B, and C, as shown in the figure. Load P is applied at joint A and load 2P acts downward at joint C. (a) Find reaction force components Ax, By, and Bz in terms of load variable P. (b) Find the axial force in tr

> A space truss has three-dimensional pin supports at joints O, B, and C. Load P is applied at joint A and acts toward point Q. Coordinates of all joints are given in feet (see figure). (a) Find reaction force components Bx, Bz, and Oz. (b) Find the axial

> Repeat 1.3-10 but use the method of sections to find member forces in AB and DC. Data from Problem 10: Find support reactions at A and B and then use the method of joints to find all member forces. Let b = 3 m and P = 80 kN. y 2P b/2 2

> Repeat 1.3-9 but use the method of sections to find member forces in AC and BD. Data from Problem 9: Find support reactions at A and B and then use the method of joints to find all member forces. Let c = 8 ft and P = 20 kips. -2P -Oc = 80° a O3 =

> Find support reactions at A and B and then use the method of joints to find all member forces. Let b = 3 m and P = 80 kN. y 2P b/2 2P D ec = 80° b/2 Og = 40° = 60° B

> Find support reactions at A and B and then use the method of joints to find all member forces. Let c = 8 ft and P = 20 kips. -2P -Oc = 80° a O3 = 40° = 60° D A B 2P c/2- c/2-

> A plane truss has a pin support at F and a roller support at D (see figure). (a) Find reactions at both supports. (b) Find the axial force in truss member FE. 16 kN 19 kN 3 m 13 kN A 3 m B 3 m D 3 m E 4.5 m f1 m

> A plane truss has a pin support at A and a roller support at E (see figure). (a) Find reactions at all supports. (b) Find the axial force in truss member FE. |3 kips 2 kips 10 ft D 1 kips A 10 ft B 10 ft C 10 ft 15 ft 3 ft G

> Consider the plane truss with a pin support at joint 3 and a vertical roller support at joint 5 (see figure). (a) Find reactions at support joints 3 and 5. (b) Find axial forces in truss members 11 and 13. 20 N 45 N 4 5 6 6. 7 12 11 7 10) 2 m 13 9 6

> Segments AB and BCD of beam ABCD are pin connected at x 5 10 ft. The beam is supported by a pin support at A and roller supports at C and D; the roller at D is rotated by 308 from the x axis (see figure). A trapezoidal distributed load on BC varies in in

> A pressurized circular cylinder has a sealed cover plate fastened with steel bolts (see figure). The pressure p of the gas in the cylinder is 290 psi, the inside diameter D of the cylinder is 10.0 in., and the diameter dB of the b

> A copper alloy pipe with a yield stress sY = 290 MPa is to carry an axial tensile load P = 1500 kN (see figure part a). Use a factor of safety of 1.8 against yielding. (a) If the thickness t of the pipe is one-eighth of its outer diameter, what is the mi

> Use traces to sketch and identify the surface. x = y2 - z2  

> Use traces to sketch and identify the surface. 3x2 - y2 + 3z2 = 0

> Use traces to sketch and identify the surface. 3x2 + y + 3z2 = 0

> Use traces to sketch and identify the surface. 9y2 + 4z2 = x2 1 36

> Differentiate the function. f (x) = ln(sin2x)

> Use traces to sketch and identify the surface. z2 - 4x2 - y2 = 4

> Use traces to sketch and identify the surface. x2 = 4y2 + z2

> Draw a diagram to show that there are two tangent lines to the parabola that y = x2 pass through the point (0, -4). Find the coordinates of the points where these tangent lines intersect the parabola.

> Use traces to sketch and identify the surface. 4x2 + 9y2 + 9z2 = 36

> Use traces to sketch and identify the surface. x = y2 + 4z2

> (a). Find and identify the traces of the quadric surface 2x2 - y2 + z2 = 1 and explain why the graph looks like the graph of the hyperboloid of two sheets in Table 1. (b). If the equation in part (a) is changed to x2 - y2 - z2 = 1, what happens to the gr

> (a). Find and identify the traces of the quadric surface x2 + y2 - z2 = 1 and explain why the graph looks like the graph of the hyperboloid of one sheet in Table 1. (b). If we change the equation in part (a) to x2 - y2 + z2 = 1, how is the graph affected

> Find a vector equation and parametric equations for the line. The line through the point (1, 0, 6) and perpendicular to the plane x + 3y + z = 5

> Find a vector equation and parametric equations for the line. The line through the point (0, 1 4, -10) and parallel to the line x = -1 + 2t, y = 6 - 3t, z = 3 + 9t

> Determine whether each statement is true or false in R3. (a). Two lines parallel to a third line are parallel. (b). Two lines perpendicular to a third line are parallel. (c). Two planes parallel to a third plane are parallel. (d). Two planes perpendicula

> Find the distance between the skew lines with parametric equations x = 1 + t, y = 1 + 6t, z = 2t, and x = 1 + 2s, y = 5 + 15s, z = -2 + 6s.

> Differentiate the function. f (x) = sin(ln x)

> Show that the lines with symmetric equations x = y = z and x + 1 = y/2 = z/3 are skew, and find the distance between these lines.

> Where does the normal line to the parabola y = x2 - 1 at the point (-1,0) intersect the parabola a second time? Illustrate with a sketch.

> Find equations of the planes that are parallel to the plane x + 2y - 2z = 1 and two units away from it.

> Show that the distance between the parallel planes ax + by + cz + d1 = 0 and ax + by + cz + d2 = 0 is //

> Find the distance between the given parallel planes. 6z = 4y - 2x, 9z = 1 - 3x + 6y

> Which of the following four lines are parallel? Are any of them identical? Li: x= 1 + 6t, y=1 – 3t, z= 12t + 5 L2: x= 1 + 2t, y= t, z =1 + 4t L3: 2x – 2 = 4 – 4y = z + 1 L4: r = (3, 1, 5) + t(4, 2, 8)

> Which of the following four planes are parallel? Are any of them identical? Pi: 3x + 6у — 32 — 6 Р:: 4х — 12у + 82 3D 5 Р:: 9у — 1 + 3х + 62 Р:: z — х + 2у — 2

> Find parametric equations for the line through the point (0, 1, 2) that is perpendicular to the line x = 1 + t, y = 1 - t, z = 2t and intersects this line.

> Find parametric equations for the line through the point (0, 1, 2) that is perpendicular to the line x = 1 + t, y = 1 - t, z = 2t and intersects this line.

> (a) Find the point at which the given lines intersect: (b). Find an equation of the plane that contains these lines. r = (1, 1, 0) + 1(1, –1, 2) r= (2,0, 2) + s(-1, 1,0)

> Find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c.

> Differentiate the function. f (x) = x ln x - x

> At what point on the y = 1 + 2ex – 3x curve is the tangent line parallel to the line ?Illustrate by 3x – y = 5 graphing the curve and both lines.

> Find dy/dx by implicit differentiation. x4 + x2y2 + y3 = 5

> Find an equation for the plane consisting of all points that are equidistant from the points (2, 5, 5) and (-6, 3, 1).

> Find an equation for the plane consisting of all points that are equidistant from the points (1, 0, -2) and (3, 4, 0).

> Find symmetric equations for the line of intersection of the planes. z = 2x - y - 5, z = 4x + 3y - 5

> Find symmetric equations for the line of intersection of the planes. 5x - 2y - 2z = 1, 4x + y + z = 6

> (a). Find parametric equations for the line of intersection of the planes and (b). find the angle between the planes. 3x - 2y + z = 1, 2x + y - 3z = 3

> (a). Find parametric equations for the line of intersection of the planes and (b). find the angle between the planes. x + y + z = 1, x + 2y + 2z = 1

> Determine whether the planes are parallel, perpendicular, or neither. If neither, find the angle between them. (Round to one decimal place.) x + 2y - z = 2, 2x - 2y + z = 1

> Determine whether the planes are parallel, perpendicular, or neither. If neither, find the angle between them. (Round to one decimal place.) x + 4y - 3z = 1, 23x + 6y + 7z = 0

> Find direction numbers for the line of intersection of the planes x + y + z = 1 and x + z = 0.

> Find equations of both lines that are tangent to the curve y = x3 – 3x2 + 3x -3 and are parallel to the line 3x – y = 15.

> Where does the line through (-3, 1, 0) and (-1, 5, 6) intersect the plane 2x + y - z = -2?

> Differentiate. y = secθ  tanθ 

> Find the point at which the line intersects the given plane. x = t - 1, y = 1 + 2t, z = 3 - t; 3x - y + 2z = 5

> Find the point at which the line intersects the given plane. x = 2 - 2t, y = 3t, z = 1 + t; x + 2y – z = 7

> Use intercepts to help sketch the plane. 6x + 5y - 3z = 15

> Use intercepts to help sketch the plane. 6x - 3y + 4z = 6

> Use intercepts to help sketch the plane. 3x + y + 2z = 6

> Use intercepts to help sketch the plane. 2x + 5y + z = 10

> Find an equation of the plane. The plane that passes through the line of intersection of the planes x - z = 1 and y + 2z = 3 and is perpendicular to the plane x + y - 2z = 1

> Find an equation of the plane. The plane that passes through the point (1, 5, 1) and is perpendicular to the planes 2x + y - 2z = 2 and x + 3z = 4

> Find an equation of the tangent line to the curve y = x4 + 1 that is parallel to the line 32x – y = 15.