Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 4.9, Problem 148P
To determine
The equivalent resultant force the wet concrete exerts on the farm AB and the location of the resultant force measured from point B.
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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
Engineering Mechanics: Statics & Dynamics (14th Edition)
Ch. 4.4 - In each case, determine the moment of the force...Ch. 4.4 - In each case, set up the determinant to find the...Ch. 4.4 - Determine the moment of the force about point O.Ch. 4.4 - Determine the moment of the force about point O.Ch. 4.4 - Determine the moment of the force about point O.Ch. 4.4 - Determine the moment of the force about point O....Ch. 4.4 - Determine the moment of the force about point O.Ch. 4.4 - Determine the moment of the force about point O.Ch. 4.4 - Determine the resultant moment produced by the...Ch. 4.4 - Determine the resultant moment produced by the...
Ch. 4.4 - Determine the resultant moment produced by the...Ch. 4.4 - Determine the moment of force F about point O....Ch. 4.4 - Prob. 11FPCh. 4.4 - Prob. 12FPCh. 4.4 - Prob. 1PCh. 4.4 - Prove the triple scalar product identity A (B C)...Ch. 4.4 - Prob. 3PCh. 4.4 - Prob. 4PCh. 4.4 - Determine the moment about point B of each of the...Ch. 4.4 - The crowbar is subjected to a vertical force of P...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 - Determine the moment of each force about the bolt...Ch. 4.4 - If FB = 30 lb and FC = 45 lb, determine the...Ch. 4.4 - Prob. 11PCh. 4.4 - The towline exerts a force of P = 6 kN at the end...Ch. 4.4 - Prob. 13PCh. 4.4 - The 20-N horizontal force acts on the handle of...Ch. 4.4 - Two men exert forces of F = 80 lb and P = 50 lb on...Ch. 4.4 - Prob. 16PCh. 4.4 - Prob. 17PCh. 4.4 - The tongs are used to grip the ends of the...Ch. 4.4 - Prob. 19PCh. 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 - Old clocks were constructed using a fusee B to...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 - Determine the moment of the force F about point P....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 - Prob. 41PCh. 4.4 - A 20-N horizontal force is applied perpendicular...Ch. 4.4 - Prob. 43PCh. 4.4 - The pipe assembly is subjected to the 80-N force....Ch. 4.4 - Prob. 45PCh. 4.4 - Prob. 46PCh. 4.4 - Prob. 47PCh. 4.4 - Prob. 48PCh. 4.4 - Prob. 49PCh. 4.4 - Prob. 50PCh. 4.4 - Using a ring collar, the 75-N force can act in the...Ch. 4.5 - In each case, determine the resultant moment of...Ch. 4.5 - Prob. 4PPCh. 4.5 - Prob. 13FPCh. 4.5 - Prob. 14FPCh. 4.5 - Determine the magnitude of the moment of the 200-N...Ch. 4.5 - Determine the magnitude of the moment of the force...Ch. 4.5 - Prob. 17FPCh. 4.5 - Determine the moment of force F about the x, the...Ch. 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 - Prob. 55PCh. 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 - Prob. 58PCh. 4.5 - Prob. 59PCh. 4.5 - Prob. 60PCh. 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 - Prob. 65PCh. 4.5 - Prob. 66PCh. 4.6 - Determine the resultant couple moment acting on...Ch. 4.6 - Determine the resultant couple moment acting on...Ch. 4.6 - Prob. 21FPCh. 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 - Prob. 67PCh. 4.6 - Prob. 68PCh. 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 - Prob. 73PCh. 4.6 - Prob. 74PCh. 4.6 - Prob. 75PCh. 4.6 - Determine the magnitude of F so that the resultant...Ch. 4.6 - Prob. 77PCh. 4.6 - Prob. 78PCh. 4.6 - Two couples act on the frame. If the resultant...Ch. 4.6 - Prob. 80PCh. 4.6 - Two couples act on the frame. If d = 4 ft,...Ch. 4.6 - Prob. 82PCh. 4.6 - If M1 = 180 lb ft, M2 = 90 lb ft, and M3 = 120...Ch. 4.6 - Prob. 84PCh. 4.6 - The gears are subjected to the couple moments...Ch. 4.6 - Determine the required magnitude of the couple...Ch. 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 - In each case, determine the x and y components of...Ch. 4.7 - F-25. Replace the leading system by an equivalent...Ch. 4.7 - F-26. Replace the loading system by an equivalent...Ch. 4.7 - Prob. 27FPCh. 4.7 - Prob. 28FPCh. 4.7 - Prob. 29FPCh. 4.7 - F-30. Replace the loading system by an equivalent...Ch. 4.7 - Replace the force system by an equivalent...Ch. 4.7 - Prob. 98PCh. 4.7 - Prob. 99PCh. 4.7 - Prob. 100PCh. 4.7 - Replace the loading system acting on the beam by...Ch. 4.7 - Prob. 102PCh. 4.7 - Prob. 103PCh. 4.7 - Prob. 104PCh. 4.7 - Replace the force system acting on the frame by an...Ch. 4.7 - Prob. 106PCh. 4.7 - Prob. 107PCh. 4.7 - Replace the force system by an equivalent...Ch. 4.7 - Prob. 109PCh. 4.7 - Prob. 110PCh. 4.7 - Prob. 111PCh. 4.7 - Prob. 112PCh. 4.8 - In each case, determine the x and y components of...Ch. 4.8 - Prob. 7PPCh. 4.8 - Replace the loading system by an equivalent...Ch. 4.8 - Prob. 32FPCh. 4.8 - Prob. 33FPCh. 4.8 - Prob. 34FPCh. 4.8 - Prob. 35FPCh. 4.8 - Prob. 36FPCh. 4.8 - Prob. 113PCh. 4.8 - Prob. 114PCh. 4.8 - Prob. 115PCh. 4.8 - Prob. 116PCh. 4.8 - Replace the loading acting on the beam by a single...Ch. 4.8 - Prob. 118PCh. 4.8 - Prob. 119PCh. 4.8 - Prob. 120PCh. 4.8 - Prob. 121PCh. 4.8 - Prob. 122PCh. 4.8 - Prob. 123PCh. 4.8 - Prob. 124PCh. 4.8 - Prob. 125PCh. 4.8 - Replace the force and couple system acting on the...Ch. 4.8 - If FA = 7 kN and FB = 5 kN, represent the force...Ch. 4.8 - Determine the magnitudes of FA and FB so that the...Ch. 4.8 - Prob. 129PCh. 4.8 - Prob. 130PCh. 4.8 - Prob. 131PCh. 4.8 - If FA= 40 kN and FB = 35 kN, determine the...Ch. 4.8 - If the resultant force is required to act at the...Ch. 4.8 - Prob. 134PCh. 4.8 - Replace the force system by a wrench and specify...Ch. 4.8 - Prob. 136PCh. 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 - Prob. 38FPCh. 4.9 - Prob. 39FPCh. 4.9 - Determine the resultant force and specify where it...Ch. 4.9 - Prob. 41FPCh. 4.9 - Prob. 42FPCh. 4.9 - Replace the loading by an equivalent resultant...Ch. 4.9 - Replace the distributed loading with an equivalent...Ch. 4.9 - Prob. 140PCh. 4.9 - Prob. 141PCh. 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 - Prob. 147PCh. 4.9 - Prob. 148PCh. 4.9 - If the soil exerts a trapezoidal distribution of...Ch. 4.9 - Prob. 150PCh. 4.9 - Prob. 151PCh. 4.9 - Prob. 152PCh. 4.9 - Replace the leading by a single resultant force,...Ch. 4.9 - Prob. 154PCh. 4.9 - Replace the distributed loading by an equivalent...Ch. 4.9 - Prob. 156PCh. 4.9 - Prob. 157PCh. 4.9 - Prob. 158PCh. 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 - Prob. 162PCh. 4.9 - Prob. 1RPCh. 4.9 - Replace the force F having a magnitude of F = 50...Ch. 4.9 - Prob. 3RPCh. 4.9 - Prob. 4RPCh. 4.9 - Prob. 5RPCh. 4.9 - Prob. 6RPCh. 4.9 - Prob. 7RPCh. 4.9 - Prob. 8RP
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