Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 5.4, Problem 33P
The dimensions of a jib crane, which is manufactured by the Basick Co., are given in the figure. If the crane has a mass of 800 kg and a center of mass at G, and the maximum rated force at its end is F = 15 kN, determine the reactions at its bearings. The bearing at A is a journal bearing and supports only a horizontal force, whereas the bearing at B is a thrust bearing that supports both horizontal and vertical components.
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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
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• 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:
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Using MATLAB Numerical Functions (ode45)
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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 5 Solutions
Engineering Mechanics: Statics & Dynamics (14th Edition)
Ch. 5.2 - Draw the free-body diagram for the following...Ch. 5.2 - Draw the free-body diagram for the following...Ch. 5.2 - Draw the free-body diagram for the following...Ch. 5.2 - Draw the free-body diagram for the following...Ch. 5.2 - Draw the free-body diagram for the following...Ch. 5.2 - Draw the free-body diagram for the following...Ch. 5.2 - Draw the free-body diagram for the following...Ch. 5.2 - Draw the free-body diagram for the following...Ch. 5.2 - Draw the free-body diagram for the following...Ch. 5.4 - Draw the free body diagram of each object. Prob....
Ch. 5.4 - Determine the horizontal and vertical components...Ch. 5.4 - Determine the horizontal and vertical components...Ch. 5.4 - The truss is supported by a pin at A and a roller...Ch. 5.4 - Prob. 4FPCh. 5.4 - The 25 kg bar has a center of mass at G. If it is...Ch. 5.4 - Prob. 6FPCh. 5.4 - Prob. 10PCh. 5.4 - Determine the reactions at the supports. Prob....Ch. 5.4 - Determine the horizontal and vertical components...Ch. 5.4 - Determine the reactions at the supports. Prob....Ch. 5.4 - Determine the reactions at the supports. Prob....Ch. 5.4 - Prob. 15PCh. 5.4 - Determine the tension in the cable and the...Ch. 5.4 - Prob. 17PCh. 5.4 - Determine the components of reaction at the...Ch. 5.4 - The man has a weight W and stands at the center of...Ch. 5.4 - A uniform glass rod having a length L is placed in...Ch. 5.4 - Prob. 21PCh. 5.4 - If the intensity of the distributed load acting on...Ch. 5.4 - Prob. 23PCh. 5.4 - Prob. 24PCh. 5.4 - Prob. 25PCh. 5.4 - The mobile crane is symmetrically supported by two...Ch. 5.4 - Prob. 27PCh. 5.4 - Prob. 28PCh. 5.4 - Determine the force P needed to pull the 50-kg...Ch. 5.4 - Prob. 30PCh. 5.4 - Prob. 31PCh. 5.4 - Determine the magnitude of force at the pin A and...Ch. 5.4 - The dimensions of a jib crane, which is...Ch. 5.4 - Prob. 34PCh. 5.4 - The smooth pipe rests against the opening at the...Ch. 5.4 - Prob. 36PCh. 5.4 - The cantilevered jib crane is used to support the...Ch. 5.4 - Prob. 38PCh. 5.4 - Prob. 39PCh. 5.4 - Determine the stiffness k of each spring so that...Ch. 5.4 - The bulk head AD Is subjected to both water and...Ch. 5.4 - The boom supports the two vertical loads. Neglect...Ch. 5.4 - Prob. 43PCh. 5.4 - The 10-kg uniform rod is pinned at end A. If It is...Ch. 5.4 - Prob. 45PCh. 5.4 - Prob. 46PCh. 5.4 - Prob. 47PCh. 5.4 - Prob. 48PCh. 5.4 - The rigid metal strip of negligible weight is used...Ch. 5.4 - Prob. 50PCh. 5.4 - Prob. 51PCh. 5.4 - Prob. 52PCh. 5.4 - Prob. 53PCh. 5.4 - Prob. 54PCh. 5.4 - The uniform rod has a length I and weight W. It is...Ch. 5.4 - Prob. 56PCh. 5.4 - Prob. 57PCh. 5.4 - Prob. 58PCh. 5.4 - The rod supports a weight of 200 lb and is pinned...Ch. 5.4 - Prob. 60PCh. 5.4 - Prob. 61PCh. 5.4 - The man attempts to pull the tour wheeler up the...Ch. 5.4 - Where is the best place to arrange most of the...Ch. 5.7 - Draw the free-body diagram of each object.Ch. 5.7 - In each case, write the moment equations about the...Ch. 5.7 - Prob. 7FPCh. 5.7 - Prob. 8FPCh. 5.7 - Prob. 9FPCh. 5.7 - Determine the support reactions at the smooth...Ch. 5.7 - Prob. 11FPCh. 5.7 - Determine the components of reaction that the...Ch. 5.7 - The uniform loads has a mass of 600 kg and is...Ch. 5.7 - Due to equal distribution of fuel in the wing...Ch. 5.7 - Prob. 5-63 5-64. Determine the components of...Ch. 5.7 - Prob. 65PCh. 5.7 - The smooth uniform rod AB is supported by a...Ch. 5.7 - The uniform concrete slab has a mass of 2400 kg....Ch. 5.7 - The 100-lb door has its center of gravity at G....Ch. 5.7 - Determine me tension in each cable and the...Ch. 5.7 - The stiff-leg derrick used on ships is supported...Ch. 5.7 - Determine the components of reaction at the...Ch. 5.7 - Determine the components of reaction at the...Ch. 5.7 - The bent rod is supported at A, B, and C by smooth...Ch. 5.7 - The bent rod is supported at A, B, and C by smooth...Ch. 5.7 - Prob. 75PCh. 5.7 - Prob. 76PCh. 5.7 - The member is supported by a square rod which fits...Ch. 5.7 - Prob. 78PCh. 5.7 - Prob. 79PCh. 5.7 - The bar AB is supported by two smooth collars. At...Ch. 5.7 - Prob. 81PCh. 5.7 - Prob. 82PCh. 5.7 - Prob. 83PCh. 5.7 - Both pulleys are fixed to the shaft and as the...Ch. 5.7 - Member AB is supported by a cable BC and at A by a...Ch. 5.7 - If the roller at 8 can sustain a maximum load of 3...Ch. 5.7 - Determine the reactions at the supports A and B...Ch. 5.7 - Prob. 3RPCh. 5.7 - Prob. 4RPCh. 5.7 - Determine the x, y, z components of reaction at...Ch. 5.7 - Prob. 6RPCh. 5.7 - Determine the x, y, z components of reaction at...Ch. 5.7 - Determine the x and z components of reaction at...
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