PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Chapter 17, Problem 8FP
To determine
The angular velocity of the disk in
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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 17 Solutions
PEARSON ETEXT ENGINEERING MECH & STATS
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Ch. 17 - Determine the location y of the center of mass G...Ch. 17 - Prob. 18PCh. 17 - Prob. 19PCh. 17 - Determine the moment of inertia of the wheel about...Ch. 17 - The pendulum consists of the 3-kg slender rod and...Ch. 17 - Prob. 22PCh. 17 - Determine the moment of inertia of the overhung...Ch. 17 - Prob. 1FPCh. 17 - Prob. 2FPCh. 17 - Prob. 3FPCh. 17 - Prob. 4FPCh. 17 - At the instant shown both rods of negligible mass...Ch. 17 - Prob. 6FPCh. 17 - The door has a weight of 200 lb and a center of...Ch. 17 - The door has a weight or 200 lb and a center of...Ch. 17 - The jet aircraft has a total mass of 22 Mg and a...Ch. 17 - The sports car has a weight of 4500 lb and center...Ch. 17 - The bar has a weight per length w and is supported...Ch. 17 - The smooth 180-lb pipe has a length of 20 ft and a...Ch. 17 - The smooth 180-lb pipe has a length of 20 ft and a...Ch. 17 - Prob. 44PCh. 17 - If the carts mass is 30 kg and it is subjected to...Ch. 17 - Prob. 50PCh. 17 - Prob. 53PCh. 17 - Prob. 54PCh. 17 - The 100-kg wheel has a radius of gyration about...Ch. 17 - Prob. 8FPCh. 17 - Prob. 9FPCh. 17 - Prob. 10FPCh. 17 - Prob. 11FPCh. 17 - Prob. 12FPCh. 17 - The 10-kg wheel has a radius of gyration kA = 200...Ch. 17 - The uniform 24-kg plate is released from rest at...Ch. 17 - The uniform slender rod has a mass m. If it is...Ch. 17 - The tent rod has a mass of 2 kg/m. If it is...Ch. 17 - Disk A has a weight of 5 lb and disk B has a...Ch. 17 - Prob. 66PCh. 17 - The reel of cable has a mass of 400 kg and a...Ch. 17 - Prob. 72PCh. 17 - Cable is unwound from a spool supported on small...Ch. 17 - The 5-kg cylinder is initially at rest when it is...Ch. 17 - Prob. 76PCh. 17 - Disk D turns with a constant clockwise angular...Ch. 17 - Prob. 78PCh. 17 - Prob. 81PCh. 17 - Prob. 85PCh. 17 - The Catherine wheel is a firework that consists of...Ch. 17 - The uniform 60-kg slender bar is initially at rest...Ch. 17 - Prob. 14FPCh. 17 - Prob. 15FPCh. 17 - The 20- kg sphere rolls down the inclined plane...Ch. 17 - The 200-kg spool has a radius of gyration about...Ch. 17 - The 12-kg slender rod is pinned to a small roller...Ch. 17 - If the disk in Fig. 17-19 rolls without slipping,...Ch. 17 - The uniform 150-lb beam is initially at rest when...Ch. 17 - The spool has a mass of 100 kg and a radius of...Ch. 17 - Solve Prob.17-96 if the cord and force P = 50 N...Ch. 17 - The spool has a mass of 100 kg and a radius of...Ch. 17 - A force of F= 10 N is applied to the 10-kg ring as...Ch. 17 - If the coefficient of static friction at C is s =...Ch. 17 - If P = 30 lb, determine the angular acceleration...Ch. 17 - If the coefficient of static friction between the...Ch. 17 - The semicircular disk having a mass of 10 leg is...Ch. 17 - The circular concrete culvert rols with an angular...Ch. 17 - The uniform disk of mass m is rotating with an...Ch. 17 - The uniform disk of mass m is rotating with an...Ch. 17 - The uniform beam has a weight W. If it is...Ch. 17 - The 500-lb beam is supported at A and B when it is...Ch. 17 - Prob. 1RPCh. 17 - Prob. 2RPCh. 17 - Prob. 3RPCh. 17 - Prob. 4RPCh. 17 - Prob. 5RPCh. 17 - Prob. 6RPCh. 17 - Prob. 7RPCh. 17 - Prob. 8RP
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