ENGINEERING MECHANICS: STATICS
14th Edition
ISBN: 9780135681879
Author: HIBBELER
Publisher: PEARSON
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Chapter 8.2, Problem 54P
Determine the greatest angle θ so that the ladder does not slip when it supports the 75-kg man in the position shown. The surface is rather slippery, where the coefficients of static friction at A and B is, μs = 0.3.
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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 8 Solutions
ENGINEERING MECHANICS: STATICS
Ch. 8.2 - Determine the friction force at the surface of...Ch. 8.2 - Determine M to cause impending motion of the...Ch. 8.2 - Determine the force P to move block B.Ch. 8.2 - Determine the force P needed to cause impending...Ch. 8.2 - Determine the friction developed between the 50-kg...Ch. 8.2 - Determine the minimum force P to prevent the 30-kg...Ch. 8.2 - Determine the maximum force P that can be applied...Ch. 8.2 - If the coefficient of static friction at contact...Ch. 8.2 - Determine the maximum force P that can be applied...Ch. 8.2 - Prob. 6FP
Ch. 8.2 - Blocks A, B, and C have weights of 50 N, 25 N, and...Ch. 8.2 - If the coefficient of static friction at all...Ch. 8.2 - Using the coefficients of static friction...Ch. 8.2 - Determine the maximum force P the connection can...Ch. 8.2 - The tractor exerts a towing force T=400 lb....Ch. 8.2 - Prob. 3PCh. 8.2 - The winch on the truck is used to hoist the...Ch. 8.2 - The automobile has a mass of 2 Mg and center of...Ch. 8.2 - The automobile has a mass of 2 Mg and canter of...Ch. 8.2 - The block brake consists of a pin-connected lever...Ch. 8.2 - The block brake consists of a pin-connected lever...Ch. 8.2 - Prob. 9PCh. 8.2 - Prob. 10PCh. 8.2 - Determine the maximum weight W the man can lift...Ch. 8.2 - The block brake is used to stop the wheel from...Ch. 8.2 - If a torque of M=300 Nm is applied to the...Ch. 8.2 - The car has a mass of 1.6 Mg and center of mass at...Ch. 8.2 - Prob. 15PCh. 8.2 - The 180-Ib man climbs up the ladder and stops at...Ch. 8.2 - The 180-Ib man climbs up the ladder and stops at...Ch. 8.2 - The spool of wire having a weight of 300 Ib rests...Ch. 8.2 - Prob. 19PCh. 8.2 - The ring has a mass of 0.5 kg and is resting on...Ch. 8.2 - A man attempts to support a stack of books...Ch. 8.2 - The tongs are used to lift the 150-kg crate, whose...Ch. 8.2 - The beam is supported by a pin at A and a roller...Ch. 8.2 - The uniform thin pole has a weight of 30 Ib and a...Ch. 8.2 - The uniform pole has a weight of 30 Ib and a...Ch. 8.2 - The block brake is used to stop the wheel from...Ch. 8.2 - Solve Prob. 8-26 if the couple moment M0 is...Ch. 8.2 - A worker walks up the sloped roof that is defined...Ch. 8.2 - Prob. 29PCh. 8.2 - Two blocks A and B have a weight of 10 Ib and 6...Ch. 8.2 - Two blocks A and B have a weight of 10 Ib and 6...Ch. 8.2 - Determine the smallest force P that must be...Ch. 8.2 - The man having a weight of 200 Ib pushes...Ch. 8.2 - The uniform hoop of weight W is subjected to the...Ch. 8.2 - Prob. 35PCh. 8.2 - Determine the minimum force P needed to push the...Ch. 8.2 - Prob. 37PCh. 8.2 - The coefficient of static friction between the...Ch. 8.2 - Determine the smallest coefficient of static...Ch. 8.2 - Prob. 40PCh. 8.2 - If the coefficient of static friction at A and B...Ch. 8.2 - The 100-kg disk rests on a surface for which, B =...Ch. 8.2 - Investigate whether the equilibrium can be...Ch. 8.2 - Prob. 44PCh. 8.2 - The beam AB has a negligible mass and thickness...Ch. 8.2 - It is supported at one end by a pin and at the...Ch. 8.2 - Crates A and B weigh 200 Ib and 150 Ib,...Ch. 8.2 - Two blocks A and B, each having a mass of 5 kg,...Ch. 8.2 - The uniform crate has a mass of 150 kg. If the...Ch. 8.2 - The uniform crate has a mass of 150 kg. If the...Ch. 8.2 - Beam AB has a negligible mass and thickness, and...Ch. 8.2 - Beam AB has a negligible mass and thickness, and...Ch. 8.2 - Determine the smallest couple moment that can be...Ch. 8.2 - Determine the greatest angle so that the ladder...Ch. 8.2 - The wheel weights 20 lb and rests on a surface for...Ch. 8.2 - Prob. 56PCh. 8.2 - The man has a weight of 200 lb, and the...Ch. 8.2 - Prob. 1CPCh. 8.2 - Prob. 4CPCh. 8.2 - Explain how to find the maximum force this man can...Ch. 8.4 - Determine the largest angle that will cause the...Ch. 8.4 - If the beam AD is loaded as shown, determine the...Ch. 8.4 - The wedge is used to level the member. Determine...Ch. 8.4 - Prob. 61PCh. 8.4 - If P=250 N, determine the required minimum...Ch. 8.4 - Determine the minimum applied force P required to...Ch. 8.4 - If the coefficient of static friction between all...Ch. 8.4 - Determine the smallest force P needed to lift the...Ch. 8.4 - Prob. 66PCh. 8.4 - If the clamping force at G is 900 N, determine the...Ch. 8.4 - If a horizontal force of F = 50 N is applied...Ch. 8.4 - Prob. 69PCh. 8.4 - If the force F is removed from the handle of the...Ch. 8.4 - Prob. 71PCh. 8.4 - If the clamping force on the boards is 600 lb,...Ch. 8.4 - Prob. 73PCh. 8.4 - The square-threaded bolt is used to join two...Ch. 8.4 - The shaft has a square-threaded screw with a lead...Ch. 8.4 - If couple forces of F=35 N are applied to the...Ch. 8.4 - Prob. 77PCh. 8.4 - The device is used to pull the battery cable...Ch. 8.4 - Determine the clamping force on the board A if the...Ch. 8.4 - If the required clamping force on the board A is...Ch. 8.4 - If a horizontal force of P = 100 N is applied...Ch. 8.4 - Determine the horizontal force P that must be...Ch. 8.5 - A cylinder having a mass of 250 kg is to be...Ch. 8.5 - A cylinder having a mass of 250 kg is to be...Ch. 8.5 - A 180-lb farmer tries to restrain the cow from...Ch. 8.5 - The 100-lb boy at A is suspended from the cable...Ch. 8.5 - The 100-lb boy at A is suspended from the cable...Ch. 8.5 - Prob. 88PCh. 8.5 - A cable is attached to the 20-kg plate B, passes...Ch. 8.5 - Prob. 90PCh. 8.5 - Prob. 91PCh. 8.5 - Determine the force P that must be applied to the...Ch. 8.5 - Prob. 93PCh. 8.5 - Determine the weight of the cylinder if the...Ch. 8.5 - If slipping does not occur at the wall, determine...Ch. 8.5 - The coefficient of static friction between the...Ch. 8.5 - Prob. 97PCh. 8.5 - Show that the frictional relationship between the...Ch. 8.5 - The wheel is subjected to a torque of M = 50 N m...Ch. 8.5 - Using the coefficients of static friction...Ch. 8.5 - If the coefficient of static friction between the...Ch. 8.5 - Idler pulley A, and motor pulley B. If the motor...Ch. 8.5 - Using the coefficient of static friction...Ch. 8.5 - Determine the smallest counterclockwise twist or...Ch. 8.5 - Determine the largest angles so that the cord...Ch. 8.5 - Determine the smallest stretch of the spring...Ch. 8.8 - If the coefficient of static is, s = 0.3,...Ch. 8.8 - Prob. 108PCh. 8.8 - Prob. 109PCh. 8.8 - Prob. 110PCh. 8.8 - Prob. 111PCh. 8.8 - Prob. 113PCh. 8.8 - Prob. 114PCh. 8.8 - Prob. 115PCh. 8.8 - Prob. 116PCh. 8.8 - Prob. 117PCh. 8.8 - If the coefficient of static friction is. k....Ch. 8.8 - If the coefficient of static friction between the...Ch. 8.8 - If the coefficient of kinetic friction between the...Ch. 8.8 - if the force P is applied horizontally to the...Ch. 8.8 - Prob. 122PCh. 8.8 - Prob. 123PCh. 8.8 - Prob. 124PCh. 8.8 - Prob. 125PCh. 8.8 - The bell crank fits loosely into a 0.5-in-diameter...Ch. 8.8 - Prob. 127PCh. 8.8 - The vehicle has a weight of 2600 lb and center of...Ch. 8.8 - The tractor has a weight of 16 000 lb and the...Ch. 8.8 - Prob. 130PCh. 8.8 - Prob. 131PCh. 8.8 - The 1.4-Mg machine is to be moved over a level...Ch. 8.8 - Prob. 1RPCh. 8.8 - The uniform 60-kg crate C rests uniformly on a...Ch. 8.8 - A 35-kg disk rests on an inclined surface for...Ch. 8.8 - The cam is subjected to a couple moment of 5N m....Ch. 8.8 - The three stone blocks have weights of, WA =...Ch. 8.8 - Prob. 6RPCh. 8.8 - Prob. 7RPCh. 8.8 - Prob. 8RP
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