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physics
mechanics
Vector Mechanics for Engineers Statics and Dynamics 11th edition Ferdinand Beer, E. Russell Johnston Jr., David Mazurek, Phillip Cornwell, Brian Self - Solutions
An 8-kg mass can be supported in the three different ways shown. Knowing that the pulleys have a 100-mm radius, determine the reaction at A in each case.(a)(b)(c)
A uniform rod AB with a length of l and weight of W is suspended from two cords AC and BC of equal length. Determine the angle θ corresponding to the equilibrium position when a couple M is applied to the rod.
Rod AD is acted upon by a vertical force P at end A and by two equal and opposite horizontal forces of magnitude Q at points B and C. Neglecting the weight of the rod, express the angle θ corresponding to the equilibrium position in terms of P and Q.
A vertical load P is applied at end B of rod BC.(a) Neglecting the weight of the rod, express the angle θ corresponding to the equilibrium position in terms of P, l, and the counterweight W.(b) Determine the value of θ corresponding to equilibrium if P = 2W.
A vertical load P is applied at end B of rod BC.(a) Neglecting the weight of the rod, express the angle θ corresponding to the equilibrium position in terms of P, l, and the counterweight W.(b) Determine the value of θ corresponding to equilibrium if P = 2W.
A collar B of weight W can move freely along the vertical rod shown. The constant of the spring is k, and the spring is unstretched when θ = 0.(a) Derive an equation in θ, W, k, and l that must be satisfied when the collar is in equilibrium.(b) Knowing that W = 300 N, l = 500 mm, and k = 800
Eight identical 500 × 750-mm rectangular plates, each of mass m = 40 kg, are held in a vertical plane as shown. All connections consist of frictionless pins, rollers, or short links. In each case, determine whether(a) The plate is completely, partially, or improperly constrained,(b) The
A 500-lb cylindrical tank, 8 ft in diameter, is to be raised over a 2-ft obstruction. A cable is wrapped around the tank and pulled horizontally as shown. Knowing that the corner of the obstruction at A is rough, find the required tension in the cable and the reaction at A.
Determine the reactions at A and B when a = 180 mm.
A T-shaped bracket supports the four loads shown. Determine the reactions at A and B(a) If a = 10 in.,(b) If a = 7 in.
Rod AB is supported by a pin and bracket at A and rests against a frictionless peg at C. Determine the reactions at A and C when a 170-N vertical force is applied at B.
Solve Problem 4.75, assuming that the 170-N force applied at B is horizontal and directed to the left.PROBLEM 4.75Rod AB is supported by a pin and bracket at A and rests against a frictionless peg at C. Determine the reactions at A and C when a 170-N vertical force is applied at B.
Member ABC is supported by a pin and bracket at B and by an inextensible cord attached at A and C and passing over a frictionless pulley at D. The tension may be assumed to be the same in portions AD and CD of the cord. For the loading shown and neglecting the size of the pulley, determine the
Knowing that θ = 30°, determine the reaction (a) at B, (b) at C.
For the bracket and loading of Problem 4.7, determine the smallest distance a if the bracket is not to move.PROBLEM 4.7 A T-shaped bracket supports the four loads shown. Determine the reactions at A and B(a) If a = 10 in.,(b) If a = 7 in.
Knowing that θ = 60°, determine the reaction (a) at B, (b) at C.
Determine the reactions at A and B when β = 50°.
Determine the reactions at A and B when β = 80°.
Rod AB is bent into the shape of an arc of circle and is lodged between two pegs D and E. It supports a load P at end B. Neglecting friction and the weight of the rod, determine the distance c corresponding to equilibrium when a = 20 mm and R = 100 mm.
A slender rod of length L is attached to collars that can slide freely along the guides shown. Knowing that the rod is in equilibrium, derive an expression for the angle θ in terms of the angle β.
An 8-kg slender rod of length L is attached to collars that can slide freely along the guides shown. Knowing that the rod is in equilibrium and that β = 30°, determine (a) the angle θ that the rod forms with the vertical, (b) the reactions at A and B.
A slender rod BC of length L and weight W is held by two cables as shown. Knowing that cable AB is horizontal and that the rod forms an angle of 40° with the horizontal, determine (a) the angle θ that cable CD forms with the horizontal, (b) the tension in each cable.
A thin ring of mass 2 kg and radius r = 140 mm is held against a frictionless wall by a 125-mm string AB. Determine(a) The distance d,(b) The tension in the string,(c) The reaction at C.
A slender rod of length L and weight W is attached to a collar at A and is fitted with a small wheel at B. Knowing that the wheel rolls freely along a cylindrical surface of radius R, and neglecting friction, derive an equation in θ, L, and R that must be satisfied when the rod is in equilibrium.
Knowing that for the rod of Problem 4.89, L = 15 in., R = 20 in., and W = 10 lb, determine (a) the angle θ corresponding to equilibrium, (b) the reactions at A and B.
Two transmission belts pass over a double-sheaved pulley that is attached to an axle supported by bearings at A and D. The radius of the inner sheave is 125 mm and the radius of the outer sheave is 250 mm. Knowing that when the system is at rest, the tension is 90 N in both portions of belt B and
Solve Problem 4.91, assuming that the pulley rotates at a constant rate and that TB = 104 N, T′B = 84 N, TC = 175 N.PROBLEM 4.91Two transmission belts pass over a double-sheaved pulley that is attached to an axle supported by bearings at A and D. The radius of the inner sheave is 125 mm and
A small winch is used to raise a 120-lb load. Find (a) the magnitude of the vertical force P that should be applied at C to maintain equilibrium in the position shown, (b) the reactions at A and B, assuming that the bearing at B does not exert any axial thrust.
A 4×8-ft sheet of plywood weighing 34 lb has been temporarily placed among three pipe supports. The lower edge of the sheet rests on small collars at A and B and its upper edge leans against pipe C. Neglecting friction at all surfaces, determine the reactions at A, B, and C.
A 250 × 400-mm plate of mass 12 kg and a 300-mm-diameter pulley are welded to axle AC that is supported by bearings at A and B. For β = 30°, determine (a) the tension in the cable, (b) the reactions at A and B. Assume that the bearing at B does not exert any axial thrust.
Solve Prob. 4.95 for β = 60°.PROBLEM 4.95A 250 × 400-mm plate of mass 12 kg and a 300-mm-diameter pulley are welded to axle AC that is supported by bearings at A and B. For β = 30°, determine(a) The tension in the cable,(b) The reactions at A and B. Assume that the bearing at B does
The 20 × 20-in. square plate shown weighs 56 lb and is supported by three vertical wires. Determine the tension in each wire.
The 20 × 20-in. square plate shown weighs 56 lb and is supported by three vertical wires. Determine the weight and location of the lightest block that should be placed on the plate if the tensions in the three wires are to be equal.
An opening in a floor is covered by a 1×1.2-m sheet of plywood of mass 18 kg. The sheet is hinged at A and B and is maintained in a position slightly above the floor by a small block C. Determine the vertical component of the reaction (a) at A, (b) at B, (c) at C.
Two crates, each of mass 350 kg, are placed as shown in the bed of a 1400-kg pick-up truck. Draw the free-body diagram needed to determine the reactions at each of the two rear wheels A and front wheels B.
A light rod AD is supported by frictionless pegs at B and C and rests against a frictionless wall at A. A vertical 120-lb force is applied at D. Draw the free-body diagram needed to determine the reactions at A, B, and C.
A tension of 20 N is maintained in a tape as it passes through the support system shown. Knowing that the radius of each pulley is 10 mm, draw the free-body diagram needed to determine the reaction at C.
Two tape spools are attached to an axle supported by bearings at A and D. The radius of spool B is 1.5 in. and the radius of spool C is 2 in. Knowing that TB = 20 lb and that the system rotates at a constant rate, draw the free body diagram needed to determine the reactions at A and D. Assume that
A 12-m pole supports a horizontal cable CD and is held by a ball and socket at A and two cables BE and BF. Knowing that the tension in cable CD is 14 kN and assuming that CD is parallel to the x axis (∅ = 0), draw the free-body diagram needed to determine the tension in cables BE and BF and
A 20-kg cover for a roof opening is hinged at corners A and B. The roof forms an angle of 30° with the horizontal, and the cover is maintained in a horizontal position by the brace CE. Draw the free-body diagram needed to determine the magnitude of the force exerted by the brace and the
Locate the centroid of the plane area shown.
For the machine element shown, locate the x coordinate of the center of gravity.
For the machine element shown, locate the z coordinate of the center of gravity.
For the machine element shown, locate the y coordinate of the center of gravity.
For the machine element shown, locate the z coordinate of the center of gravity.
For the machine element shown, locate the y coordinate of the center of gravity.
For the machine element shown, locate the x coordinate of the center of gravity.
Locate the center of gravity of the sheet-metal form shown.
A corner reflector for tracking by radar has two sides in the shape of a quarter circle with a radius of 15 in. and one side in the shape of a triangle. Locate the center of gravity of the reflector, knowing that it is made of sheet metal of uniform thickness.
A wastebasket, designed to fit in the corner of a room, is 16 in. high and has a base in the shape of a quarter circle of radius 10 in. Locate the center of gravity of the wastebasket, knowing that it is made of sheet metal of uniform thickness.
Locate the centroid of the plane area shown.
An elbow for the duct of a ventilating system is made of sheet metal of uniform thickness. Locate the center of gravity of the elbow.
A mounting bracket for electronic components is formed from sheet metal of uniform thickness. Locate the center of gravity of the bracket.
A thin sheet of plastic of uniform thickness is bent to form a desk organizer. Locate the center of gravity of the organizer.
A thin steel wire of uniform cross section is bent into the shape shown. Locate its center of gravity.
The frame of a greenhouse is constructed from uniform aluminum channels. Locate the center of gravity of the portion of the frame shown.
Locate the center of gravity of the figure shown, knowing that it is made of thin brass rods of uniform diameter.
Locate the center of gravity of the figure shown, knowing that it is made of thin brass rods of uniform diameter.
A scratch awl has a plastic handle and a steel blade and shank. Knowing that the density of plastic is 1030 kg/m3 and of steel is 7860 kg/m3, locate the center of gravity of the awl.
A bronze bushing is mounted inside a steel sleeve. Knowing that the specific weight of bronze is 0.318 lb/in3 and of steel is 0.284 lb/in3, determine the location of the center of gravity of the assembly.
Locate the centroid of the plane area shown.
A brass collar, of length 2.5 in., is mounted on an aluminum rod of length 4 in. Locate the center of gravity of the composite body. (Specific weights: brass = 0.306 lb/in3, aluminum = 0.101 lb/in3)
The three legs of a small glass-topped table are equally spaced and are made of steel tubing, which has an outside diameter of 24 mm and a cross-sectional area of 150 mm2. The diameter and the thickness of the table top are 600 mm and 10 mm, respectively. Knowing that the density of steel is 7860
Locate the centroid of the plane area shown.
The sides and the base of a punch bowl are of uniform thickness t. If t (a) The bowl,(b) The punch
Locate the centroid of the section shown, which was cut from a thin circular pipe by two oblique planes.
Locate the centroid of the plane area shown.
Locate the centroid of the plane area shown.
A uniform circular rod of weight 8 lb and radius 10 in. is attached to a pin at C and to the cable AB. Determine(a) The tension in the cable,(b) The reaction at C.
Locate the centroid of the plane area shown.
Determine by direct integration the centroid of the area shown.
Determine the reactions at the beam supports for the given loading?
A beam is subjected to a linearly distributed downward load and rests on two wide supports BC and DE, which exert uniformly distributed upward loads as shown. Determine the values of wBC and wDE corresponding to equilibrium when wA = 600 N/m.
A tank is divided into two sections by a 1 × 1-m square gate that is hinged at A. A couple of magnitude 490 N · m is required for the gate to rotate. If one side of the tank is filled with water at the rate of 0.1 m3 / min and the other side is filled simultaneously with methyl alcohol
Three brass plates are brazed to a steel pipe to form the flagpole base shown. Knowing that the pipe has a wall thickness of 8 mm and that each plate is 6 mm thick, determine the location of the center of gravity of the base. (Densities: brass = 8470 kg/m3; steel = 7860 kg/m3.)
Locate the centroid of the plane area shown.
Determine the y coordinate of the centroid of the shaded area in terms of r1, r2, and α .
Determine the x coordinate of the centroid of the trapezoid shown in terms of h1, h2, and a.
For the semiannular area of Prob. 5.12, determine the ratio r1 to r2 so that the centroid of the area is located at x = - ½ r2 and y = 0.
Locate the centroid of the plane area shown.
The horizontal x-axis is drawn through the centroid C of the area shown, and it divides the area into two component areas A1 and A2. Determine the first moment of each component area with respect to the x-axis, and explain the results obtained.
The horizontal x-axis is drawn through the centroid C of the area shown, and it divides the area into two component areas A1 and A2. Determine the first moment of each component area with respect to the x-axis, and explain the results obtained.
The first moment of the shaded area with respect to the x-axis is denoted by Qx.(a) Express Qx in terms of b, c, and the distance y from the base of the shaded area to the x-axis.(b) For what value of y is Qx maximum, and what is that maximum value?
A thin, homogeneous wire is bent to form the perimeter of the figure indicated.Locate the center of gravity of the wire figure thus formed.
A thin, homogeneous wire is bent to form the perimeter of the figure indicated. Locate the center of gravity of the wire figure thus formed.
A thin, homogeneous wire is bent to form the perimeter of the figure indicated.Locate the center of gravity of the wire figure thus formed.
A thin, homogeneous wire is bent to form the perimeter of the figure indicated. Locate the center of gravity of the wire figure thus formed.
The homogeneous wire ABC is bent into a semicircular arc and a straight section as shown and is attached to a hinge at A. Determine the value of ( for which the wire is in equilibrium for the indicated position.
The frame for a sign is fabricated from thin, flat steel bar stock of mass per unit length 4.73 kg/m. The frame is supported by a pin at C and by a cable AB. Determine(a) The tension in the cable,(b) The reaction at C.
Locate the centroid of the plane area shown.
The homogeneous wire ABCD is bent as shown and is attached to a hinge at C. Determine the length L for which portion BCD of the wire is horizontal.
The homogeneous wire ABCD is bent as shown and is attached to a hinge at C. Determine the length L for which portion AB of the wire is horizontal.
Determine the distance h for which the centroid of the shaded area is as far above line BB′ as possible when(a) k = 0.10,(b) k = 0.80.
Knowing that the distance h has been selected to maximize the distance y̅ from line BB′ to the centroid of the shaded area, show that y̅ = 2h/3.
Determine by direct integration the centroid of the area shown. Express your answer in terms of a and h.
Determine by direct integration the centroid of the area shown. Express your answer in terms of a and h.
Determine by direct integration the centroid of the area shown.
Locate the centroid of the plane area shown.
Determine by direct integration the centroid of the area shown. Express your answer in terms of a and b.
A homogeneous wire is bent into the shape shown. Determine by direct integration the x coordinate of its centroid. Express your answer in terms of a.
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