INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
14th Edition
ISBN: 9780133918922
Author: Russell C. Hibbeler
Publisher: PEARSON
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Textbook Question
Chapter 4.6, Problem 24FP
Determine the couple moment acting on the pipe assembly and express the result as a Cartesian
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100
As a spring is heated, its spring constant decreases. Suppose the spring is heated and then cooled so that the
spring constant at time t is k(t) = t sin + N/m. If the mass-spring system has mass m = 2 kg and a
damping constant b = 1 N-sec/m with initial conditions x(0) = 6 m and x'(0) = -5 m/sec and it is
subjected to the harmonic external force f (t) = 100 cos 3t N. Find at least the first four nonzero terms in
a power series expansion about t = 0, i.e. Maclaurin series expansion, for the displacement:
• Analytically (hand calculations)
Creating Simulink Model
Plot solutions for first two, three and four non-zero terms as well as the Simulink solution on the same graph
for the first 15 sec. The graph must be fully formatted by code.
Two springs and two masses are attached in a straight vertical line as shown in Figure Q3. The system is set
in motion by holding the mass m₂ at its equilibrium position and pushing the mass m₁ downwards of its
equilibrium position a distance 2 m and then releasing both masses. if m₁ = m² = 1 kg, k₁ = 3 N/m and
k₂ = 2 N/m.
(y₁ = 0)
www
k₁ = 3
Jm₁ = 1
k2=2
www
(Net change in
spring length
=32-31)
(y₂ = 0)
m₂ = 1
32
32
System in
static
equilibrium
System in
motion
Figure Q3 - Coupled mass-spring system
Determine the equations of motion y₁ (t) and y₂(t) for the two masses m₁ and m₂ respectively:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Produce an animation of the system for all solutions for the first minute.
Two large tanks, each holding 100 L of liquid, are interconnected by pipes, with the liquid flowing from tank
A into tank B at a rate of 3 L/min and from B into A at a rate of 1 L/min (see Figure Q1). The liquid inside each
tank is kept well stirred. A brine solution with a concentration of 0.2 kg/L of salt flows into tank A at a rate of
6 L/min. The diluted solution flows out of the system from tank A at 4 L/min and from tank B at 2 L/min. If,
initially, tank A contains pure water and tank B contains 20 kg of salt.
A
6 L/min
0.2 kg/L
x(t)
100 L
4 L/min
x(0) = 0 kg
3 L/min
1 L/min
B
y(t)
100 L
y(0) = 20 kg
2 L/min
Figure Q1 - Mixing problem for interconnected tanks
Determine the mass of salt in each tank at time t≥ 0:
Analytically (hand calculations)
Using MATLAB Numerical Functions (ode45)
Creating Simulink Model
Plot all solutions on the same graph for the first 15 min. The graph must be fully formatted by code.
Chapter 4 Solutions
INTERNATIONAL EDITION---Engineering Mechanics: Statics, 14th edition (SI unit)
Ch. 4.4 - P41. In each case, determine the moment of the...Ch. 4.4 - P42. In each case, set up the determinant to find...Ch. 4.4 - F41. Determine the moment of the force about point...Ch. 4.4 - F42. Determine the moment of the force about point...Ch. 4.4 - F43. Determine the moment of the force about point...Ch. 4.4 - Neglect the thickness of the member.Ch. 4.4 - F45. Determine the moment of the force about point...Ch. 4.4 - F46. Determine the moment of the force about point...Ch. 4.4 - F47. Determine the resultant moment produced by...Ch. 4.4 - F48. Determine the resultant moment produced by...
Ch. 4.4 - F49. Determine the resultant moment produced by...Ch. 4.4 - Express the result as a Cartesian vector.Ch. 4.4 - Express the result as a Cartesian vector.Ch. 4.4 - Express the result as a Cartesian vector.Ch. 4.4 - If A, B, and D are given vectors, prove the...Ch. 4.4 - Prove the triple scalar product identity A (B C)...Ch. 4.4 - Given the three nonzero vectors A, B and C, show...Ch. 4.4 - Determine the moment about point A of each of the...Ch. 4.4 - Determine the moment about point B of each of the...Ch. 4.4 - Find the moment of each force about point A and...Ch. 4.4 - Determine the moment of each of the three forces...Ch. 4.4 - Determine the moment of each of the three forces...Ch. 4.4 - Take FB = 40 lb, FC = 50 lb. Probs. 49/10Ch. 4.4 - If FB = 30 lb and FC = 45 lb, determine the...Ch. 4.4 - What is this moment?Ch. 4.4 - If x = 10 m, determine the position of the boom...Ch. 4.4 - What is the moment of this force about point B....Ch. 4.4 - Determine the moment of this force about point O....Ch. 4.4 - Determine the moment of each force about A. Which...Ch. 4.4 - If the man at B exerts a force of P = 30 lb on his...Ch. 4.4 - The mechanic reads the torque on the scale at B....Ch. 4.4 - Determine the torque (moment) MP that the applied...Ch. 4.4 - The tongs are used to grip the ends of the...Ch. 4.4 - The handle of the hammer is subjected to the force...Ch. 4.4 - In order to pull out the nail at B, the force F...Ch. 4.4 - The purpose of the fusee is to increase the...Ch. 4.4 - The tower crane is used to hoist the 2-Mg load...Ch. 4.4 - The tower crane is used to hoist a 2-Mg load...Ch. 4.4 - If the 1500-lb boom AB, the 200-lb cage BCD, and...Ch. 4.4 - If the 1500-lb boom AB, the 200-lb cage BCD, and...Ch. 4.4 - Determine the moment of the force F about point O....Ch. 4.4 - Express the result as a Cartesian vector.Ch. 4.4 - The force F = {400i 100j 700k} lb acts at the...Ch. 4.4 - The force F = {400i 100j 700k} lb acts at the end...Ch. 4.4 - Determine the moment of the force F about point P....Ch. 4.4 - The pipe assembly is subjected to the force of F =...Ch. 4.4 - The pipe assembly is subjected to the force of F =...Ch. 4.4 - Determine the moment of the force of F = 600 N...Ch. 4.4 - Determine the smallest force F that must be...Ch. 4.4 - Determine the coordinate direction angles , , of...Ch. 4.4 - Determine the moment of force F about point O. The...Ch. 4.4 - Determine the moment of the force F about the door...Ch. 4.4 - Determine the moment of the force F about the door...Ch. 4.4 - Determine the smallest force F that must be...Ch. 4.4 - Determine the smallest force F that must be...Ch. 4.4 - A 20-N horizontal force is applied perpendicular...Ch. 4.4 - The pipe assembly is subjected to the 80-N force....Ch. 4.4 - The pipe assembly is subjected to the 80-N force....Ch. 4.4 - A force F = {6i 2j + 1k}kN produces a moment of...Ch. 4.4 - The force F = {6i + 8j + 10k}N creates a moment...Ch. 4.4 - A force F having a magnitude of F = 100N acts...Ch. 4.4 - Force F acts perpendicular to the inclined plane....Ch. 4.4 - Force F acts perpendicular to the inclined plane....Ch. 4.4 - Strut AB of the 1-m-diameter hatch door exerts a...Ch. 4.4 - Using a ring collar, the 75-N force can act in the...Ch. 4.5 - P43. In each case, determine the resultant moment...Ch. 4.5 - P44. In each case, set up the determinant needed...Ch. 4.5 - F413. Determine the magnitude of the moment of the...Ch. 4.5 - F414. Determine the magnitude of the moment of the...Ch. 4.5 - Prob. 15FPCh. 4.5 - F416. Determine the magnitude of the moment of the...Ch. 4.5 - Express the result as a Cartesian vector.Ch. 4.5 - Prob. 18FPCh. 4.5 - The lug nut on the wheel of the automobile is to...Ch. 4.5 - Solve Prob. 4-52 if the cheater pipe AB is slipped...Ch. 4.5 - The A-frame is being hoisted into an upright...Ch. 4.5 - The A-frame is being hoisted into an upright...Ch. 4.5 - Determine the magnitude of the moments of the...Ch. 4.5 - Determine the moment of this force F about an axis...Ch. 4.5 - The board is used to hold the end of a four-way...Ch. 4.5 - The board is used to hold the end of a four-way...Ch. 4.5 - The A-frame is being hoisted into an upright...Ch. 4.5 - Determine the magnitude of the moment of the force...Ch. 4.5 - Determine the magnitude of the moment of the force...Ch. 4.5 - Determine the magnitude of the moment of the force...Ch. 4.5 - A horizontal force of F = {50i} N is applied...Ch. 4.5 - Determine the magnitude of the horizontal force F...Ch. 4.5 - The force of F = 30 N acts on the bracket as...Ch. 4.6 - F419. Determine the resultant couple moment acting...Ch. 4.6 - F420. Determine the resultant couple moment acting...Ch. 4.6 - Determine the magnitude of F so that the resultant...Ch. 4.6 - Determine the couple moment acting on the beam.Ch. 4.6 - Determine the resultant couple moment acting on...Ch. 4.6 - Determine the couple moment acting on the pipe...Ch. 4.6 - A clockwise couple M = 5 N m is resisted by the...Ch. 4.6 - A twist of 4 N m is applied to the handle of the...Ch. 4.6 - If the resultant couple of the three couples...Ch. 4.6 - Two couples act on the beam. If F = 125 lb,...Ch. 4.6 - Two couples act on the beam. Determine the...Ch. 4.6 - Determine the magnitude of the couple forces F so...Ch. 4.6 - The ends of the triangular plate are subjected to...Ch. 4.6 - The man tries to open the valve by applying the...Ch. 4.6 - If the valve can be opened with a couple moment of...Ch. 4.6 - Determine the magnitude of F so that the resultant...Ch. 4.6 - Two couples act on the beam as shown. If F = 150...Ch. 4.6 - Two couples act on the beam as shown. Determine...Ch. 4.6 - Two couples act on the frame. If the resultant...Ch. 4.6 - Two couples act on the frame. If d = 4 ft...Ch. 4.6 - Two couples act on the frame. If d = 4 ft,...Ch. 4.6 - Express the moment of the couple acting on the...Ch. 4.6 - If M1 = 180 lb ft, M2 = 90 lb ft, and M3 = 120...Ch. 4.6 - Determine the magnitudes of couple moments M1, M2,...Ch. 4.6 - The gears are subjected to the couple moments...Ch. 4.6 - Prob. 86PCh. 4.6 - Determine the resultant couple moment of the two...Ch. 4.6 - Express the moment of the couple acting on the...Ch. 4.6 - In order to turn over the frame, a couple moment...Ch. 4.6 - Express the moment of the couple acting on the...Ch. 4.6 - If the couple moment acting on the pipe has a...Ch. 4.6 - If F = 80 N, determine the magnitude and...Ch. 4.6 - If the magnitude of the couple moment acting on...Ch. 4.6 - Express the moment of the couple acting on the rod...Ch. 4.6 - If F1 = 100 N, F2 = 120 N, and F3 = 80 N,...Ch. 4.6 - Prob. 96PCh. 4.7 - P45. In each case, determine the x and y...Ch. 4.7 - Replace the leading system by an equivalent...Ch. 4.7 - Prob. 26FPCh. 4.7 - Replace the loading system by an equivalent...Ch. 4.7 - Replace the loading system by an equivalent...Ch. 4.7 - Replace the loading system by an equivalent...Ch. 4.7 - Replace the loading system by an equivalent...Ch. 4.7 - Replace the force system by an equivalent...Ch. 4.7 - Replace the force system by an equivalent...Ch. 4.7 - Replace the force system acting on the beam by an...Ch. 4.7 - Replace the force system acting on the beam by an...Ch. 4.7 - Replace the loading system acting on the beam by...Ch. 4.7 - Replace the loading system acting on the post by...Ch. 4.7 - Replace the loading system acting on the post by...Ch. 4.7 - Replace the force system acting on the post by a...Ch. 4.7 - Replace the force system acting on the frame by an...Ch. 4.7 - The forces F1 = {4i + 2j 3k) kN and F2 = {3i 4j...Ch. 4.7 - A biomechanical model of the lumbar region of the...Ch. 4.7 - Replace the force system by an equivalent...Ch. 4.7 - Replace the loading by an equivalent resultant...Ch. 4.7 - Replace the force of F = 80 N acting on the pipe...Ch. 4.7 - The belt passing over the pulley is subjected to...Ch. 4.7 - The belt passing over the pulley is subjected to...Ch. 4.8 - P46. In each case, determine the x and y...Ch. 4.8 - P47. In each case, determine the resultant force...Ch. 4.8 - Replace the loading system by an equivalent...Ch. 4.8 - Replace the loading system by an equivalent...Ch. 4.8 - Replace the loading system by an equivalent...Ch. 4.8 - Replace the loading system by an equivalent...Ch. 4.8 - Replace the loading shown by an equivalent single...Ch. 4.8 - Replace the loading shown by an equivalent single...Ch. 4.8 - The weights of the various components of the truck...Ch. 4.8 - The weights of the various components of the truck...Ch. 4.8 - Prob. 115PCh. 4.8 - Prob. 116PCh. 4.8 - Replace the loading acting on the beam by a single...Ch. 4.8 - Replace the loading acting on the beam by a single...Ch. 4.8 - Replace the loading on the frame by a single...Ch. 4.8 - Replace the loading on the frame by a single...Ch. 4.8 - Replace the loading on the frame by a single...Ch. 4.8 - Replace the force system acting on the post by a...Ch. 4.8 - Replace the force system acting on the post by a...Ch. 4.8 - Replace the parallel force system acting on the...Ch. 4.8 - Replace the force and couple system acting on the...Ch. 4.8 - Replace the force and couple system acting on the...Ch. 4.8 - Prob. 127PCh. 4.8 - Determine the magnitudes of FA and FB so that the...Ch. 4.8 - The tube supports the four parallel forces....Ch. 4.8 - The building slab is subjected to four parallel...Ch. 4.8 - The building slab is subjected to four parallel...Ch. 4.8 - If FA= 40 kN and FB = 35 kN, determine the...Ch. 4.8 - Prob. 133PCh. 4.8 - Replace the two wrenches and the force, acting on...Ch. 4.8 - Replace the force system by a wrench and specify...Ch. 4.8 - Replace the five forces acting on the plate by a...Ch. 4.8 - Replace the three forces acting on the plate by a...Ch. 4.9 - Determine the resultant force and specify where it...Ch. 4.9 - Determine the resultant force and specify where it...Ch. 4.9 - Determine the resultant force and specify where it...Ch. 4.9 - Determine the resultant force and specify where it...Ch. 4.9 - Determine the resultant force and specify where it...Ch. 4.9 - Determine the resultant force and specify where it...Ch. 4.9 - Replace the loading by an equivalent resultant...Ch. 4.9 - Replace the distributed loading with an equivalent...Ch. 4.9 - Replace the loading by an equivalent resultant...Ch. 4.9 - Currently eighty-five percent of all neck injuries...Ch. 4.9 - Replace the distributed loading by an equivalent...Ch. 4.9 - Replace this loading by an equivalent resultant...Ch. 4.9 - The distribution of soil loading on the bottom of...Ch. 4.9 - Replace the loading by an equivalent resultant...Ch. 4.9 - Replace the distributed loading by an equivalent...Ch. 4.9 - Determine the length b of the triangular load and...Ch. 4.9 - The form is used to cast a concrete wall having a...Ch. 4.9 - Prob. 149PCh. 4.9 - Replace the loading by an equivalent force and...Ch. 4.9 - Prob. 151PCh. 4.9 - Replace the loading by an equivalent resultant...Ch. 4.9 - Replace the leading by a single resultant force,...Ch. 4.9 - Replace the distributed loading by an equivalent...Ch. 4.9 - Prob. 155PCh. 4.9 - Determine the length b of the triangular load and...Ch. 4.9 - Determine the equivalent resultant force and...Ch. 4.9 - Determine the magnitude of the equivalent...Ch. 4.9 - The distributed load acts on the shaft as shown....Ch. 4.9 - Replace the distributed loading with an equivalent...Ch. 4.9 - Prob. 161PCh. 4.9 - Wet concrete exerts a pressure distribution along...Ch. 4.9 - and mass center at G. If the maximum moment that...Ch. 4.9 - R42. Replace the force F having a magnitude of F =...Ch. 4.9 - Determine the moment of this force about the...Ch. 4.9 - Determine the magnitude of the couple forces so...Ch. 4.9 - Prob. 5RPCh. 4.9 - R46. Replace the force system acting on the frame...Ch. 4.9 - Determine the equivalent resultant force and...Ch. 4.9 - R48. Replace the distributed loading by an...
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