VECTOR MECHANIC
12th Edition
ISBN: 9781264095032
Author: BEER
Publisher: MCGRAW-HILL HIGHER EDUCATION
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Chapter 16.2, Problem 16.133P
To determine
The smallest constant acceleration that the driver can maintain if the car’s door is to close and latch.
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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
B
y(t)
100 L
y(0) = 20 kg
2 L/min
1 L/min
Figure Q1 - Mixing problem for interconnected tanks
Determine the mass of salt in each tank at time t > 0:
Analytically (hand calculations)
Chapter 16 Solutions
VECTOR MECHANIC
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 - Prob. 16.1FBPCh. 16.1 - Prob. 16.2FBPCh. 16.1 - Prob. 16.3FBPCh. 16.1 - The 400-lb crate shown is lowered by means of two...Ch. 16.1 - A 60-lb 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 - A loading car is at rest on a track forming an...
Ch. 16.1 - A 2100-lb rear-wheel-drive tractor carries a 900...Ch. 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 - Solve Prob. 16.9, assuming that the casters are...Ch. 16.1 - Prob. 16.11PCh. 16.1 - Prob. 16.12PCh. 16.1 - The retractable shelf shown is supported by two...Ch. 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 - Members ACE and DCB are each 600 mm long and are...Ch. 16.1 - A prototype rotating bicycle rack is designed to...Ch. 16.1 - The control rod AC is guided by two pins that...Ch. 16.1 - The coefficients of friction between the 30-lb...Ch. 16.1 - Prob. 16.21PCh. 16.1 - Prob. 16.22PCh. 16.1 - For a rigid body in translation, show that the...Ch. 16.1 - For a rigid body in centroidal rotation, show that...Ch. 16.1 - It takes 10 min for a 2.4-Mg flywheel to coast to...Ch. 16.1 - The rotor of an electric motor has an angular...Ch. 16.1 - The 10-in.-radius brake drum is attached to a...Ch. 16.1 - The 10-in.-radius brake drum is attached to a...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 - The flywheel shown has a radius of 20 in., a...Ch. 16.1 - Each of the double pulleys shown has a mass moment...Ch. 16.1 - Two disks A and B, of mass mA = 2 kg and mB = 4...Ch. 16.1 - Two disks A and B, of mass mA = 2 kg and mB = 4...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 - Prob. 16.40PCh. 16.1 - Disk A has a mass of 6 kg and an initial angular...Ch. 16.1 - Prob. 16.42PCh. 16.1 - Disk A has a mass mA = 4 kg, a radius rA = 300 mm,...Ch. 16.1 - Disk B is at rest when it is brought into contact...Ch. 16.1 - Prob. 16.45PCh. 16.1 - Prob. 16.46PCh. 16.1 - For a rigid body in plane motion, show that the...Ch. 16.1 - A uniform slender rod AB rests on a frictionless...Ch. 16.1 - Prob. 16.49PCh. 16.1 - Prob. 16.50PCh. 16.1 - Prob. 16.51PCh. 16.1 - A 250-lb satellite has a radius of gyration of 24...Ch. 16.1 - A rectangular plate of mass 5 kg is suspended from...Ch. 16.1 - Prob. 16.54PCh. 16.1 - A drum with a 200-mm radius is attached to a disk...Ch. 16.1 - A drum with a 200-mm radius is attached to a disk...Ch. 16.1 - The 12-lb uniform disk shown has a radius of r =...Ch. 16.1 - Prob. 16.58PCh. 16.1 - Prob. 16.59PCh. 16.1 - 16.60 and 16.61The 400-lb crate shown is lowered...Ch. 16.1 - Prob. 16.61PCh. 16.1 - Two uniform cylinders, each of weight W = 14 lb...Ch. 16.1 - Prob. 16.63PCh. 16.1 - Prob. 16.64PCh. 16.1 - A uniform slender bar AB with a mass m is...Ch. 16.1 - Prob. 16.66PCh. 16.1 - 16.66 through 16.68A thin plate of the shape...Ch. 16.1 - 16.66 through 16.68A thin plate of the shape...Ch. 16.1 - A sphere of radius r and mass m is projected along...Ch. 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 - Prob. 16.72PCh. 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 - Prob. 16.5CQCh. 16.2 - Prob. 16.6CQCh. 16.2 - Prob. 16.7CQCh. 16.2 - Prob. 16.5FBPCh. 16.2 - Two identical 4-lb slender rods AB and BC are...Ch. 16.2 - Prob. 16.7FBPCh. 16.2 - Prob. 16.8FBPCh. 16.2 - Show that the couple I of Fig. 16.15 can be...Ch. 16.2 - A uniform slender rod of length L = 900 mm and...Ch. 16.2 - A crate of mass 80 kg is held in the position...Ch. 16.2 - A uniform slender rod of length L = 36 in. and...Ch. 16.2 - In Prob. 16.78, determine (a) the distance h for...Ch. 16.2 - An athlete performs a leg extension on a machine...Ch. 16.2 - Prob. 16.81PCh. 16.2 - A turbine disk weighing 50 lb rotates at a...Ch. 16.2 - The 80-lb tailgate of a car is supported by the...Ch. 16.2 - A uniform rod of length L and mass m is supported...Ch. 16.2 - Three stage lights are mounted on a pipe fixture...Ch. 16.2 - An adapted launcher uses a torsional spring about...Ch. 16.2 - A 4-kg slender rod is welded to the edge of a 3-kg...Ch. 16.2 - Prob. 16.88PCh. 16.2 - The object ABC consists of two slender rods welded...Ch. 16.2 - A 3.5-kg slender rod AB and a 2-kg slender rod BC...Ch. 16.2 - A 9-kg uniform disk is attached to the 5-kg...Ch. 16.2 - Derive the equation MC=IC for the rolling disk of...Ch. 16.2 - Prob. 16.93PCh. 16.2 - Prob. 16.94PCh. 16.2 - Prob. 16.95PCh. 16.2 - Prob. 16.96PCh. 16.2 - A 40-kg flywheel of radius R = 0.5 m is rigidly...Ch. 16.2 - Prob. 16.98PCh. 16.2 - 16.98 through 16.101A drum of 80-mm radius is...Ch. 16.2 - 16.98 through 16.101A drum of 80-mm radius is...Ch. 16.2 - 16.98 through 16.101A drum of 80-mm radius is...Ch. 16.2 - 16.102 through 16.105A drum of 4-in. radius is...Ch. 16.2 - 16.102 through 16.105A drum of 4-in. radius is...Ch. 16.2 - 16.102 through 16.105A drum of 4-in. radius is...Ch. 16.2 - 16.102 through 16.105A drum of 4-in. radius is...Ch. 16.2 - 16.106 and 16.107A 12-in.-radius cylinder of...Ch. 16.2 - 16.106 and 16.107A 12-in.-radius cylinder of...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 - A single-axis personal transport device starts...Ch. 16.2 - A hemisphere of weight W and radius r is released...Ch. 16.2 - A hemisphere of weight W and radius r is released...Ch. 16.2 - The center of gravity G of a 1.5-kg unbalanced...Ch. 16.2 - A small clamp of mass mB is attached at B to a...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 - Prob. 16.119PCh. 16.2 - Prob. 16.120PCh. 16.2 - End A of the 6-kg uniform rod AB rests on the...Ch. 16.2 - End A of the 6-kg uniform rod AB rests on the...Ch. 16.2 - End A of the 8-kg uniform rod AB is attached to a...Ch. 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 - The 3-lb uniform rod BD is connected to crank AB...Ch. 16.2 - The test rig shown was developed to perform...Ch. 16.2 - Solve Prob. 16.127 for = 90. 16.127The test rig...Ch. 16.2 - The 4-kg uniform slender bar BD is attached to bar...Ch. 16.2 - The motion of the uniform slender rod of length L...Ch. 16.2 - At the instant shown, the 20-ft-long, uniform...Ch. 16.2 - A driver starts his car with the door on the...Ch. 16.2 - Prob. 16.133PCh. 16.2 - The hatchback of a car is positioned as shown to...Ch. 16.2 - The 6-kg rod BC connects a 10-kg disk centered at...Ch. 16.2 - Prob. 16.136PCh. 16.2 - In the engine system shown, l = 250 mm and b = 100...Ch. 16.2 - Solve Prob. 16.137 when = 90. 16.137In the engine...Ch. 16.2 - The 4-lb uniform slender rod AB, the 8-lb uniform...Ch. 16.2 - The 4-lb uniform slender rod AB, the 8-lb uniform...Ch. 16.2 - Two rotating rods in the vertical plane are...Ch. 16.2 - Two rotating rods in the vertical plane are...Ch. 16.2 - Two disks, each with a mass m and a radius r, are...Ch. 16.2 - A uniform slender bar AB of mass m is suspended as...Ch. 16.2 - A uniform rod AB, of mass 15 kg and length 1 m, is...Ch. 16.2 - The uniform slender 2-kg bar BD is attached to the...Ch. 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 - Prob. 16.152PCh. 16 - A cyclist is riding a bicycle at a speed of 20 mph...Ch. 16 - The forklift truck shown weighs 3200 lb and is...Ch. 16 - The total mass of the Baja car and driver,...Ch. 16 - Identical cylinders of mass m and radius r are...Ch. 16 - Prob. 16.157RPCh. 16 - The uniform rod AB of weight W is released from...Ch. 16 - Prob. 16.159RPCh. 16 - Prob. 16.160RPCh. 16 - A cylinder with a circular hole is rolling without...Ch. 16 - Two 3-kg uniform bars are connected to form the...Ch. 16 - A crate of mass 80 kg is held in the position...Ch. 16 - The Geneva mechanism shown is used to provide an...
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