EP MODIFIED MASTERING ENGINEERING WITH
14th Edition
ISBN: 9780133941357
Author: HIBBELER
Publisher: PEARSON CO
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Chapter 2.6, Problem 16FP
To determine
The expression of force 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 2 Solutions
EP MODIFIED MASTERING ENGINEERING WITH
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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