Vector Mechanics For Engineers
12th Edition
ISBN: 9781259977305
Author: BEER, Ferdinand P. (ferdinand Pierre), Johnston, E. Russell (elwood Russell), Cornwell, Phillip J., SELF, Brian P.
Publisher: Mcgraw-hill Education,
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Chapter 16.2, Problem 16.98P
To determine
(a)
The chance of disk slides.
To determine
(b)
Angular acceleration of the disk.
To determine
(c)
Acceleration of G.
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The 2-mass system shown below depicts a disk which rotates about its center and has rotational
moment of inertia Jo and radius r. The angular displacement of the disk is given by 0. The spring
with constant k₂ is attached to the disk at a distance from the center. The mass m has linear
displacement & and is subject to an external force u. When the system is at equilibrium, the spring
forces due to k₁ and k₂ are zero. Neglect gravity and aerodynamic drag in this problem. You may
assume the small angle approximation which implies (i) that the springs and dampers remain in
their horizontal / vertical configurations and (ii) that the linear displacement d of a point on the
edge of the disk can be approximated by d≈re.
Ө
K2
www
m
4
Cz
777777
Jo
Make the following assumptions when analyzing the forces and torques:
тв
2
0>0, 0>0, x> > 0, >0
Derive the differential equations of motion for this dynamic system. Start by sketching
LARGE and carefully drawn free-body-diagrams for the disk and the…
A linear system is one that satisfies the principle of superposition. In other words, if an input u₁
yields the output y₁, and an input u2 yields the output y2, the system is said to be linear if a com-
bination of the inputs u = u₁ + u2 yield the sum of the outputs y = y1 + y2.
Using this fact, determine the output y(t) of the following linear system:
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=
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U(s)
=
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u(t) = e−2+ sin(t)
=e
Chapter 16 Solutions
Vector Mechanics For Engineers
Ch. 16.1 - Two pendulums, A and B, with the masses and...Ch. 16.1 - Two pendulums, A and B, with the masses and...Ch. 16.1 - Two solid cylinders, A and B, have the same mass m...Ch. 16.1 - A 6-ft board is placed in a truck with one end...Ch. 16.1 - Prob. 16.F2PCh. 16.1 - Two uniform disks and two cylinders are assembled...Ch. 16.1 - Prob. 16.F4PCh. 16.1 - A 60-Ib uniform thin panel is placed in a truck...Ch. 16.1 - A 60-lb uniform thin panel is placed in a truck...Ch. 16.1 - Knowing that the coefficient of static friction...
Ch. 16.1 - Prob. 16.4PCh. 16.1 - A uniform rod BC of mass 4 kg is connected to a...Ch. 16.1 - A 2000-kg truck is being used to lift a 400-kg...Ch. 16.1 - The support bracket shown is used to transport a...Ch. 16.1 - Prob. 16.8PCh. 16.1 - A 20-kg cabinet is mounted on casters that allow...Ch. 16.1 - Prob. 16.10PCh. 16.1 - A completely filled barrel and its contents have a...Ch. 16.1 - A 40-kg vase has a 200-mm-diameter base and is...Ch. 16.1 - Prob. 16.13PCh. 16.1 - Bars AB and BE, each with a mass of 4 kg, are...Ch. 16.1 - At the instant shown, the tensions in the vertical...Ch. 16.1 - Three bars, each of mass 3 kg, are welded together...Ch. 16.1 - Prob. 16.17PCh. 16.1 - Prob. 16.18PCh. 16.1 - Prob. 16.19PCh. 16.1 - The coefficients of friction between the 30-lb...Ch. 16.1 - Prob. 16.21PCh. 16.1 - Prob. 16.22PCh. 16.1 - Prob. 16.23PCh. 16.1 - Prob. 16.24PCh. 16.1 - Prob. 16.25PCh. 16.1 - Prob. 16.26PCh. 16.1 - Prob. 16.27PCh. 16.1 - Solve Prob. 16.27, assuming that the initial...Ch. 16.1 - The 100-mm-radius brake drum is attached to a...Ch. 16.1 - The 180-mm-radius disk is at rest when it is...Ch. 16.1 - Solve Prob. 16.30, assuming that the direction of...Ch. 16.1 - In order to determine the mass moment of inertia...Ch. 16.1 - Prob. 16.33PCh. 16.1 - Each of the double pulleys shown has a mass moment...Ch. 16.1 - Prob. 16.35PCh. 16.1 - Solve Prob. 16.35, assuming that the couple M is...Ch. 16.1 - Gear A weighs 1 lb and has a radius of gyration of...Ch. 16.1 - The 25-lb double pulley shown is at rest and in...Ch. 16.1 - A belt of negligible mass passes between cylinders...Ch. 16.1 - Solve Prob. 16.39 for P=2.00lb .Ch. 16.1 - Disk A has a mass of 6 kg and an initial angular...Ch. 16.1 - Prob. 16.42PCh. 16.1 - Prob. 16.43PCh. 16.1 - Disk B is at rest when it is brought into contact...Ch. 16.1 - Cylinder A has an initial angular velocity of 720...Ch. 16.1 - Prob. 16.46PCh. 16.1 - Prob. 16.47PCh. 16.1 - Prob. 16.48PCh. 16.1 - (a) In Prob. 16.48, determine the point of the rod...Ch. 16.1 - A force P with a magnitude of 3 N is applied to a...Ch. 16.1 - Prob. 16.51PCh. 16.1 - A 250-lb satellite has a radius of gyration of 24...Ch. 16.1 - Prob. 16.53PCh. 16.1 - A uniform semicircular plate with a mass of 6 kg...Ch. 16.1 - Prob. 16.55PCh. 16.1 - Prob. 16.56PCh. 16.1 - The 12-lb uniform disk shown has a radius of r=3.2...Ch. 16.1 - Prob. 16.58PCh. 16.1 - Prob. 16.59PCh. 16.1 - Prob. 16.60PCh. 16.1 - The 400-lb crate shown is lowered by means of two...Ch. 16.1 - Prob. 16.62PCh. 16.1 - Prob. 16.63PCh. 16.1 - A beam AB with a mass m and of uniform...Ch. 16.1 - Prob. 16.65PCh. 16.1 - Prob. 16.66PCh. 16.1 - Prob. 16.67PCh. 16.1 - Prob. 16.68PCh. 16.1 - Prob. 16.69PCh. 16.1 - Solve Prob. 16.69, assuming that the sphere is...Ch. 16.1 - A bowler projects an 8-in.-diameter ball weighing...Ch. 16.1 - Solve Prob. 16.71, assuming that the bowler...Ch. 16.1 - A uniform sphere of radius r and mass m is placed...Ch. 16.1 - A sphere of radius r and mass m has a linear...Ch. 16.2 - A cord is attached to a spool when a force P is...Ch. 16.2 - A cord is attached to a spool when a force P is...Ch. 16.2 - A front-wheel-drive car starts from rest and...Ch. 16.2 - A front-wheel-drive car starts from rest and...Ch. 16.2 - Prob. 16.F5PCh. 16.2 - Prob. 16.F6PCh. 16.2 - Prob. 16.F7PCh. 16.2 - Prob. 16.F8PCh. 16.2 - Show that the couple I of Fig. 16.15 can be...Ch. 16.2 - Prob. 16.76PCh. 16.2 - Prob. 16.77PCh. 16.2 - A uniform slender rod of length L=36 in. and...Ch. 16.2 - Prob. 16.79PCh. 16.2 - Prob. 16.80PCh. 16.2 - Prob. 16.81PCh. 16.2 - Prob. 16.82PCh. 16.2 - Prob. 16.83PCh. 16.2 - A uniform rod of length L and mass m is supported...Ch. 16.2 - Prob. 16.85PCh. 16.2 - Prob. 16.86PCh. 16.2 - Prob. 16.87PCh. 16.2 - Two identical 4-lb slender rods AB and BC are...Ch. 16.2 - Prob. 16.89PCh. 16.2 - Prob. 16.90PCh. 16.2 - Prob. 16.91PCh. 16.2 - Prob. 16.92PCh. 16.2 - Prob. 16.93PCh. 16.2 - Prob. 16.94PCh. 16.2 - A homogeneous sphere S, a uniform cylinder C, and...Ch. 16.2 - Prob. 16.96PCh. 16.2 - Prob. 16.97PCh. 16.2 - Prob. 16.98PCh. 16.2 - Prob. 16.99PCh. 16.2 - A drum of 80-mm radius is attached to a disk of...Ch. 16.2 - Prob. 16.101PCh. 16.2 - Prob. 16.102PCh. 16.2 - Prob. 16.103PCh. 16.2 - Prob. 16.104PCh. 16.2 - Prob. 16.105PCh. 16.2 - A 12-in.-radius cylinder of weight 16 lb rests on...Ch. 16.2 - A 12-in.-radius cylinder of weight 16 lb rests on...Ch. 16.2 - Gear C has a mass of 5 kg and a centroidal radius...Ch. 16.2 - Two uniform disks A and B, each with a mass of 2...Ch. 16.2 - Prob. 16.110PCh. 16.2 - Prob. 16.111PCh. 16.2 - Prob. 16.112PCh. 16.2 - Prob. 16.113PCh. 16.2 - A small clamp of mass mBis attached at B to a hoop...Ch. 16.2 - Prob. 16.115PCh. 16.2 - A 4-lb bar is attached to a 10-lb uniform cylinder...Ch. 16.2 - The uniform rod AB with a mass m and a length of...Ch. 16.2 - Prob. 16.118PCh. 16.2 - A 40-lb ladder rests against a wall when the...Ch. 16.2 - A beam AB of length L and mass m is supported by...Ch. 16.2 - End A of the 6-kg uniform rod AB rests on the...Ch. 16.2 - Prob. 16.122PCh. 16.2 - Prob. 16.123PCh. 16.2 - The 4-kg uniform rod ABD is attached to the crank...Ch. 16.2 - The 3-lb uniform rod BD is connected to crank AB...Ch. 16.2 - Prob. 16.126PCh. 16.2 - Prob. 16.127PCh. 16.2 - Prob. 16.128PCh. 16.2 - Prob. 16.129PCh. 16.2 - Prob. 16.130PCh. 16.2 - Prob. 16.131PCh. 16.2 - Prob. 16.132PCh. 16.2 - Prob. 16.133PCh. 16.2 - Prob. 16.134PCh. 16.2 - Prob. 16.135PCh. 16.2 - The 6-kg rod BC connects a 10-kg disk centered at...Ch. 16.2 - In the engine system shown, l=250 mm and b=100 mm....Ch. 16.2 - Solve Prob. 16.137 when =90 .Ch. 16.2 - The 4-lb uniform slender rod AB, the 8-lb uniform...Ch. 16.2 - Prob. 16.140PCh. 16.2 - Two rotating rods in the vertical plane are...Ch. 16.2 - Prob. 16.142PCh. 16.2 - Prob. 16.143PCh. 16.2 - Prob. 16.144PCh. 16.2 - Prob. 16.145PCh. 16.2 - Prob. 16.146PCh. 16.2 - Prob. 16.147PCh. 16.2 - Prob. 16.148PCh. 16.2 - Prob. 16.149PCh. 16.2 - Prob. 16.150PCh. 16.2 - (a) Determine the magnitude and the location of...Ch. 16.2 - Draw the shear and bending-moment diagrams for the...Ch. 16 - A cyclist is riding a bicycle at a speed of 20 mph...Ch. 16 - Prob. 16.154RPCh. 16 - The total mass of the Baja car and driver,...Ch. 16 - Prob. 16.156RPCh. 16 - Prob. 16.157RPCh. 16 - Prob. 16.158RPCh. 16 - A bar of mass m=5 kg is held as shown between four...Ch. 16 - A uniform plate of mass m is suspended in each of...Ch. 16 - Prob. 16.161RPCh. 16 - Two 3-kg uniform bars are connected to form the...Ch. 16 - Prob. 16.163RPCh. 16 - Prob. 16.164RP
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