International Edition---engineering Mechanics: Statics, 4th Edition
4th Edition
ISBN: 9781305501607
Author: Andrew Pytel And Jaan Kiusalaas
Publisher: CENGAGE L
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Chapter 7, Problem 7.56P
The square-threaded screw 0f the C-clamp has a mean diameter of 8 mm and a pitch of 1.6 mm. The coefficient of static friction between the threads is 0.2. If the torque
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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 7 Solutions
International Edition---engineering Mechanics: Statics, 4th Edition
Ch. 7 - Can the two blocks be in equilibrium in the...Ch. 7 - Determine the range of P for which the system of...Ch. 7 - Two identical chairs, each weighing 14 lb, are...Ch. 7 - The two homogeneous bars AB and BC are connected...Ch. 7 - The contact surface between the 36-lb block and...Ch. 7 - The uniform bar AB of weight W is leaning against...Ch. 7 - The center of gravity of the 50-kg spool is at G....Ch. 7 - The brake pads at C and D are pressed against the...Ch. 7 - The 200-lb homogenous cylinder of radius R is...Ch. 7 - The rear-wheel-drive pickup truck, with its center...
Ch. 7 - Solve Prob. 7.10 assuming that the pick-up truck...Ch. 7 - The 2-lb bar is pinned at A and rests on the 4-lb...Ch. 7 - The horizontal force P acts on the rim of the...Ch. 7 - The uniform bar and the homogeneous cylinder each...Ch. 7 - A stepladder consisting of two legs pinned...Ch. 7 - The mass of the unbalanced disk is m, and its...Ch. 7 - The two uniform sheets of plywood, each of length...Ch. 7 - Find the largest value of b/h at which the folding...Ch. 7 - The 3600-lb car with rear Wheel drive is...Ch. 7 - The 3600-lb car with rear wheel drive is...Ch. 7 - The man is trying to push the homogeneous 20-kg...Ch. 7 - A 1.1-kg disk A is placed on the inclined surface....Ch. 7 - The 40-lb spool is suspended from the hanger GA...Ch. 7 - A uniform plank is supported by a fixed support at...Ch. 7 - The uniform bar of weight W is supported by a...Ch. 7 - The uniform plank is initially at rest on the...Ch. 7 - The two homogeneous bars with the weights shown...Ch. 7 - The man pushes the 120-lb homogeneous crate with...Ch. 7 - The 80-kg crate has its center of gravity at G....Ch. 7 - Solve Prob. 7.29 if =0.Ch. 7 - The 120-lb door with its center of gravity at G is...Ch. 7 - Determine the largest force P for which the 16-kg...Ch. 7 - Determine the largest angle for which the...Ch. 7 - The cylinder and the block are connected by a...Ch. 7 - The weight of the cylindrical tank is negligible...Ch. 7 - The coeffient of static friction between the...Ch. 7 - The two homogenous boxes are stacked vertically....Ch. 7 - Two concrete blocks weighing 320 lb each form part...Ch. 7 - Derive the expression for the largest angle ? for...Ch. 7 - The 60-lb plank rests on a frictionless roller at...Ch. 7 - The 2000-lb weight of the trailer is distributed...Ch. 7 - Determine the smallest force P, applied to the...Ch. 7 - The homogenous cylinder of weight W is at rest...Ch. 7 - The uniform bar of length L and weight W is kept...Ch. 7 - The movable bracket of negligible weight is...Ch. 7 - The 200-lb man walks up the inclined plank of...Ch. 7 - Determine the smallest coefficient of static...Ch. 7 - Find the smallest distance d for which the hook...Ch. 7 - Prob. 7.49PCh. 7 - The block of weight W is pulled by the force P...Ch. 7 - The two 200-lb blocks are pushed apart by the 15...Ch. 7 - Determine the smallest horizontal force P that...Ch. 7 - The device shown is used to measure the kinetic...Ch. 7 - The single-threaded screw of the floor jack has a...Ch. 7 - A wedge is used to prop up the 6000-lb block of...Ch. 7 - The square-threaded screw 0f the C-clamp has a...Ch. 7 - The square-threaded screw with a pitch of 10 mm...Ch. 7 - The screw of the carjack has a pitch of 0.1 in....Ch. 7 - How many turns of rope around the capstan are...Ch. 7 - The force P applied to the brake handle enables...Ch. 7 - Prob. 7.61PCh. 7 - The 120-kg block A is suspended from a rope that...Ch. 7 - The leather rein used to fasten the horse to the...Ch. 7 - The 30-lb weight is attached to a rope that runs...Ch. 7 - The rail AB of negligible weight is suspended from...Ch. 7 - The blocks A and B of weights WA and WB are joined...Ch. 7 - The 150-lb weight is attached to a rope that...Ch. 7 - The 50-lb homogeneous bar AB is suspended from a...Ch. 7 - The collar bearing carries the axial load P = 400...Ch. 7 - Solve Sample Problem 7.16 if the contact pressure...Ch. 7 - The 600-lb cable spool is placed on a frictionless...Ch. 7 - Prob. 7.72PCh. 7 - The normal pressure acting on the disk of the...Ch. 7 - Prob. 7.74PCh. 7 - The single-plate clutch transmits the torque C...Ch. 7 - The clutch described in Prob. 7.75 is to transmit...Ch. 7 - The cone clutch transmits the torque C through a...Ch. 7 - The figure shows a steel bar being processed by a...Ch. 7 - The coefficient of rolling resistance between the...Ch. 7 - Prob. 7.80PCh. 7 - Calculate the horizontal force P required to push...Ch. 7 - The uniform pole BC of length L and weight W is...Ch. 7 - The homogeneous bar AB of weight W and length L is...Ch. 7 - Find the smallest angle for which the uniform...Ch. 7 - Prob. 7.85RPCh. 7 - Determine the largest angle for which the uniform...Ch. 7 - Can the uniform bar of weight W remain at rest in...Ch. 7 - The panel of weight W with its center of gravity...Ch. 7 - The woman is trying to move the crate of weight W...Ch. 7 - The screw of the clamp has a square thread of...Ch. 7 - Find the largest clockwise couple C that can be...Ch. 7 - The test specimen AB is placed in the grip of a...Ch. 7 - The coefficient of static friction between the...Ch. 7 - The uniform bars AB and BC are connected with a...
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