Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 2.9, Problem 118P
Determine the angle θ between cables AB and AC.
Probs. 2-117/118
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The elastic bar from Problem 1 spins with angular velocity ω about an axis, as shown in the figure below. The radial acceleration at a generic point x along the bar is a(x) = ω 2 x. Under this radial acceleration, the bar stretches along x with displacement function u(x). The displacement u(x) is governed by the following equations: ( d dx (σ(x)) + ρa(x) = 0 PDE σ(x) = E du dx Hooke’s law (2) where σ(x) is the axial stress in the rod, ρ is the mass density, and E is the (constant) Young’s modulus. The bar is pinned on the rotation axis at x = 0 and it is also pinned at x = L.
Determine:1. Appropriate BCs for this physical problem.2. The displacement function u(x).3. The stress function σ(x).
The heated rod from Problem 3 is subject to a volumetric heatingh(x) = h0xLin units of [Wm−3], as shown in the figure below. Under theheat supply the temperature of the rod changes along x with thetemperature function T(x). The temperature T(x) is governed by thefollowing equations:(−ddx (q(x)) + h(x) = 0 PDEq(x) = −kdTdx Fourier’s law of heat conduction(4)where q(x) is the heat flux through the rod and k is the (constant)thermal conductivity. Both ends of the bar are in contact with a heatreservoir at zero temperature.
Determine:1. Appropriate BCs for this physical problem.2. The temperature function T(x).3. The heat flux function q(x).
A heated rod of length L is subject to a volumetric heating h(x) = h0xLinunits of [Wm−3], as shown in the figure below. Under the heat supply thetemperature of the rod changes along x with the temperature functionT(x). The temperature T(x) is governed by the following equations:(−ddx (q(x)) + h(x) = 0 PDEq(x) = −kdTdx Fourier’s law of heat conduction(3)where q(x) is the heat flux through the rod and k is the (constant)thermal conductivity. The left end of the bar is in contact with a heatreservoir at zero temperature, while the right end of the bar is thermallyinsulated.
Determine:1. Appropriate BCs for this physical problem.2. The temperature function T(x).3. The heat flux function q(x).
Chapter 2 Solutions
Engineering Mechanics: Statics & Dynamics (14th Edition)
Ch. 2.3 - In each case, construct the parallelogram law to...Ch. 2.3 - In each case, show how to resolve the force F into...Ch. 2.3 - Determine the magnitude of the resultant force...Ch. 2.3 - Two forces act on the hook. Determine the...Ch. 2.3 - Determine the magnitude of the resultant force and...Ch. 2.3 - Resolve the 30-lb force into components along the...Ch. 2.3 - The force F = 450 lb acts on the frame. Resolve...Ch. 2.3 - If force F is to have a component along the u axis...Ch. 2.3 - If = 60 and F = 450 N, determine the magnitude of...Ch. 2.3 - If the magnitude of the resultant force is to be...
Ch. 2.3 - Determine the magnitude of the resultant force FR...Ch. 2.3 - The vertical force F acts downward at A on the...Ch. 2.3 - Solve with F = 350 lb. Prob. 2-4/5Ch. 2.3 - Determine the magnitude of the resultant force FR...Ch. 2.3 - Resolve the force F1 into components acting along...Ch. 2.3 - Resolve the force F2 into components acting along...Ch. 2.3 - If the resultant force acting on the support is to...Ch. 2.3 - Determine the magnitude of the resultant force and...Ch. 2.3 - The plate is subjected to the two forces at A and...Ch. 2.3 - Determine the angle for connecting member A to...Ch. 2.3 - The force acting on the gear tooth is F = 20lb....Ch. 2.3 - The component of force F acting along line aa is...Ch. 2.3 - Force F acts on the frame such that its component...Ch. 2.3 - Force F acts on the frame such that its component...Ch. 2.3 - Determine the magnitude and direction of the...Ch. 2.3 - Determine the magnitude and direction of the...Ch. 2.3 - Determine the design angle (0 90) for strut AB...Ch. 2.3 - Determine the design angle (0 90) between...Ch. 2.3 - Determine the magnitude and direction of the...Ch. 2.3 - Prob. 22PCh. 2.3 - Prob. 23PCh. 2.3 - Prob. 24PCh. 2.3 - If F1 = 30 lb and F2 = 40 lb, determine the angles...Ch. 2.3 - Determine the magnitude and direction of FA SO...Ch. 2.3 - Determine the magnitude and direction, measured...Ch. 2.3 - Determine the magnitude of force F so that the...Ch. 2.3 - If the resultant force of the two tugboats is 3...Ch. 2.3 - If FB = 3 kN and = 45, determine the magnitude of...Ch. 2.3 - If the resultant force of the two tugboats is...Ch. 2.4 - Resolve each force acting on the post into its x...Ch. 2.4 - Determine the magnitude and direction of the...Ch. 2.4 - Prob. 9FPCh. 2.4 - If the resultant force acting on the bracket is to...Ch. 2.4 - If the magnitude of the resultant force acting on...Ch. 2.4 - Determine the magnitude of the resultant force and...Ch. 2.4 - Determine the magnitude of the resultant force and...Ch. 2.4 - Prob. 33PCh. 2.4 - Prob. 34PCh. 2.4 - Determine the magnitude of the resultant force and...Ch. 2.4 - Resolve each force acting on the gusset plate into...Ch. 2.4 - Determine the magnitude of the resultant force...Ch. 2.4 - Prob. 38PCh. 2.4 - Prob. 39PCh. 2.4 - Determine the magnitude of the resultant force and...Ch. 2.4 - Determine the magnitude of the resultant force and...Ch. 2.4 - Express F1, F2, and F3 as Cartesian vectors.Ch. 2.4 - Prob. 43PCh. 2.4 - Prob. 44PCh. 2.4 - Prob. 45PCh. 2.4 - Determine the magnitude and orientation of FB so...Ch. 2.4 - Determine the magnitude and orientation. measured...Ch. 2.4 - Prob. 48PCh. 2.4 - Prob. 49PCh. 2.4 - Express F1, F2, and F3 as Cartesian vectors.Ch. 2.4 - Prob. 51PCh. 2.4 - Prob. 52PCh. 2.4 - Prob. 53PCh. 2.4 - Prob. 54PCh. 2.4 - Prob. 55PCh. 2.4 - Prob. 56PCh. 2.4 - If the resultant force acting on the bracket is...Ch. 2.4 - Prob. 58PCh. 2.4 - If F = 5 kN and = 30, determine the magnitude of...Ch. 2.6 - Sketch the following forces on the x, y, z...Ch. 2.6 - In each case, establish F as a Cartesian vector,...Ch. 2.6 - Show how to resolve each force into its x, y, z...Ch. 2.6 - Determine the coordinate direction angles of the...Ch. 2.6 - Prob. 14FPCh. 2.6 - Prob. 15FPCh. 2.6 - Prob. 16FPCh. 2.6 - Prob. 17FPCh. 2.6 - Prob. 18FPCh. 2.6 - The force F has a magnitude of 80 lb and acts...Ch. 2.6 - Prob. 61PCh. 2.6 - Prob. 62PCh. 2.6 - Prob. 63PCh. 2.6 - Prob. 64PCh. 2.6 - The screw eye is subjected to the two forces...Ch. 2.6 - Prob. 66PCh. 2.6 - Determine the magnitude and coordinate direction...Ch. 2.6 - Determine the magnitude and coordinate direction...Ch. 2.6 - Determine the magnitude and coordinate direction...Ch. 2.6 - Determine the magnitude and coordinate direction...Ch. 2.6 - Specify the magnitude and coordinate direction...Ch. 2.6 - Prob. 72PCh. 2.6 - Prob. 73PCh. 2.6 - Prob. 74PCh. 2.6 - Prob. 75PCh. 2.6 - Prob. 76PCh. 2.6 - Prob. 77PCh. 2.6 - Prob. 78PCh. 2.6 - Determine the coordinate direction angles of the...Ch. 2.6 - The bracket is subjected to the two forces shown....Ch. 2.6 - Prob. 81PCh. 2.6 - Prob. 82PCh. 2.6 - If the direction of the resultant force acting on...Ch. 2.6 - Prob. 84PCh. 2.6 - The pole is subjected to the force F which has...Ch. 2.8 - In each case, establish a position vector from...Ch. 2.8 - In each case, express F as a Cartesian vector....Ch. 2.8 - Express the position vector rAB in Cartesian...Ch. 2.8 - Prob. 20FPCh. 2.8 - Express the force as a Cartesian vector. Prob....Ch. 2.8 - Prob. 22FPCh. 2.8 - Prob. 23FPCh. 2.8 - Prob. 24FPCh. 2.8 - Determine the length of the connecting rod AB by...Ch. 2.8 - Express force F as a Cartesian vector; then...Ch. 2.8 - Prob. 88PCh. 2.8 - Prob. 89PCh. 2.8 - Prob. 90PCh. 2.8 - Prob. 91PCh. 2.8 - Prob. 92PCh. 2.8 - If FB = 560 N and FC = 700 N, determine the...Ch. 2.8 - If FB = 700 N, and FC = 560 N, determine the...Ch. 2.8 - The plate is suspended using the three cables...Ch. 2.8 - The three supporting cables exert the forces shown...Ch. 2.8 - Determine the magnitude and coordinate direction...Ch. 2.8 - Prob. 98PCh. 2.8 - Prob. 99PCh. 2.8 - Prob. 100PCh. 2.8 - The two mooring cables exert forces on the stern...Ch. 2.8 - Prob. 102PCh. 2.8 - Determine the magnitude and coordinate direction...Ch. 2.8 - If the force in each cable tied to the bin is 70...Ch. 2.8 - If the resultant of the four forces is FR = {360k}...Ch. 2.9 - P2.8. in each case set up the dot product to find...Ch. 2.9 - Prob. 9PPCh. 2.9 - Prob. 25FPCh. 2.9 - Determine the angle between the force and the...Ch. 2.9 - Prob. 27FPCh. 2.9 - Prob. 28FPCh. 2.9 - Find the magnitude of the projected component of...Ch. 2.9 - Prob. 30FPCh. 2.9 - Determine the magnitudes of the components of the...Ch. 2.9 - Prob. 106PCh. 2.9 - Prob. 107PCh. 2.9 - Prob. 108PCh. 2.9 - Prob. 109PCh. 2.9 - Prob. 110PCh. 2.9 - Prob. 111PCh. 2.9 - Prob. 112PCh. 2.9 - Determine the magnitudes of the components of F =...Ch. 2.9 - Prob. 114PCh. 2.9 - Prob. 115PCh. 2.9 - Prob. 116PCh. 2.9 - Determine the magnitudes of the projected...Ch. 2.9 - Determine the angle between cables AB and AC....Ch. 2.9 - Prob. 119PCh. 2.9 - Prob. 120PCh. 2.9 - Determine the angle between the two cables...Ch. 2.9 - Determine the angle between the cables AB and AC....Ch. 2.9 - Determine the magnitude of the projected component...Ch. 2.9 - Determine the magnitude of the projected component...Ch. 2.9 - Determine the magnitude of the projection of force...Ch. 2.9 - Prob. 126PCh. 2.9 - Prob. 127PCh. 2.9 - Prob. 128PCh. 2.9 - Determine the magnitude of the projected component...Ch. 2.9 - Prob. 130PCh. 2.9 - Prob. 131PCh. 2.9 - Determine the magnitude of the projected component...Ch. 2.9 - Prob. 133PCh. 2.9 - Prob. 134PCh. 2.9 - Prob. 135PCh. 2.9 - Prob. 136PCh. 2.9 - Prob. 137PCh. 2.9 - Prob. 138PCh. 2.9 - Prob. 139PCh. 2.9 - Determine the magnitude of the resultant force FR...Ch. 2.9 - Resolve F into components along the u and v axes...Ch. 2.9 - Prob. 3RPCh. 2.9 - The cable at the end of the crane boom exerts a...Ch. 2.9 - Prob. 5RPCh. 2.9 - Prob. 6RPCh. 2.9 - Prob. 7RPCh. 2.9 - Prob. 8RP
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