Vector Mechanics for Engineers: Statics and Dynamics
11th Edition
ISBN: 9780073398242
Author: Ferdinand P. Beer, E. Russell Johnston Jr., David Mazurek, Phillip J. Cornwell, Brian Self
Publisher: McGraw-Hill Education
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Textbook Question
Chapter 5.1, Problem 5.8P
Locate the centroid of the plane area shown.
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6/86 The connecting rod AB of a certain internal-combustion engine weighs 1.2 lb with mass center at G
and has a radius of gyration about G of 1.12 in. The piston and piston pin A together weigh 1.80 lb. The
engine is running at a constant speed of 3000 rev/min, so that the angular velocity of the crank is
3000(2)/60 = 100л rad/sec. Neglect the weights of the components and the force exerted by the gas in
the cylinder compared with the dynamic forces generated and calculate the magnitude of the force on the
piston pin A for the crank angle 0 = 90°. (Suggestion: Use the alternative moment relation, Eq. 6/3, with B
as the moment center.)
Answer
A = 347 lb
3"
1.3"
B
1.7"
PROBLEM 6/86
6/85 In a study of head injury against the instrument panel of a car during sudden or crash stops where
lap belts without shoulder straps or airbags are used, the segmented human model shown in the figure is
analyzed. The hip joint O is assumed to remain fixed relative to the car, and the torso above the hip is
treated as a rigid body of mass m freely pivoted at O. The center of mass of the torso is at G with the initial
position of OG taken as vertical. The radius of gyration of the torso about O is ko. If the car is brought to a
sudden stop with a constant deceleration a, determine the speed v relative to the car with which the
model's head strikes the instrument panel. Substitute the values m = 50 kg, 7 = 450 mm, r = 800 mm, ko
= 550 mm, 0 = 45°, and a = 10g and compute v.
Answer
v = 11.73 m/s
PROBLEM 6/85
Chapter 5 Solutions
Vector Mechanics for Engineers: Statics and Dynamics
Ch. 5.1 - 5.1 through 5.9 Locate the centroid of the plane...Ch. 5.1 - 5.1 through 5.9 Locate the centroid of the plane...Ch. 5.1 - 5.1 through 5.9 Locate the centroid of the plane...Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - 5.1 through 5.9 Locate the centroid of the plane...Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Prob. 5.7PCh. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Locate the centroid of the plane area shown.
Ch. 5.1 - Prob. 5.11PCh. 5.1 - Locate the centroid of the plane area shown.Ch. 5.1 - Prob. 5.13PCh. 5.1 - 5.10 through 5.15 Locate the centroid of the plane...Ch. 5.1 - Prob. 5.15PCh. 5.1 - PROBLEM 5.16 Determine the y coordinate of the...Ch. 5.1 - Show that as r1 approaches r2, the location of the...Ch. 5.1 - Prob. 5.18PCh. 5.1 - Prob. 5.19PCh. 5.1 - Prob. 5.20PCh. 5.1 - Prob. 5.21PCh. 5.1 - The horizontal x-axis is drawn through the...Ch. 5.1 - PROBLEM 5.23 The first moment of the shaded area...Ch. 5.1 - Prob. 5.24PCh. 5.1 - Prob. 5.25PCh. 5.1 - Prob. 5.26PCh. 5.1 - A thin, homogeneous wire is bent to form the...Ch. 5.1 - Prob. 5.28PCh. 5.1 - The frame for a sign is fabricated from thin, flat...Ch. 5.1 - The homogeneous wire ABCD is bent as shown and is...Ch. 5.1 - The homogeneous wire ABCD is bent as shown and is...Ch. 5.1 - Prob. 5.32PCh. 5.1 - Knowing that the distance h has been selected to...Ch. 5.2 - 5.34 through 5.36 Determine by direct integration...Ch. 5.2 - 5.34 through 5.36 Determine by direct integration...Ch. 5.2 - 5.34 through 5.36 Determine by direct integration...Ch. 5.2 - 5.37 through 5.39 Determine by direct integration...Ch. 5.2 - 5.37 through 5.39 Determine by direct integration...Ch. 5.2 - Prob. 5.39PCh. 5.2 - 5.40 and 5.41 Determine by direct integration the...Ch. 5.2 - 5.40 and 5.41 Determine by direct integration the...Ch. 5.2 - 5.42 Determine by direct integration the centroid...Ch. 5.2 - 5.43 and 5.44 Determine by direct integration the...Ch. 5.2 - 5.43 and 5.44 Determine by direct integration the...Ch. 5.2 - 5.45 and 5.46 A homogeneous wire is bent into the...Ch. 5.2 - 5.45 and 5.46 A homogeneous wire is bent into the...Ch. 5.2 - A homogeneous wire is bent into the shape shown....Ch. 5.2 - 5.48 and 5.49 Determine by direct integration the...Ch. 5.2 - Prob. 5.49PCh. 5.2 - Prob. 5.50PCh. 5.2 - Determine the centroid of the area shown when a =...Ch. 5.2 - Prob. 5.52PCh. 5.2 - 5.53 Determine the volume and the surface area of...Ch. 5.2 - Determine the volume and the surface area of the...Ch. 5.2 - Prob. 5.55PCh. 5.2 - Prob. 5.56PCh. 5.2 - Prob. 5.57PCh. 5.2 - Prob. 5.58PCh. 5.2 - Prob. 5.59PCh. 5.2 - Determine the capacity, in liters, of the punch...Ch. 5.2 - Determine the volume and total surface area of the...Ch. 5.2 - Prob. 5.62PCh. 5.2 - Determine the total surface area of the solid...Ch. 5.2 - Prob. 5.64PCh. 5.2 - The shade for a wall-mounted light is formed from...Ch. 5.3 - 5.66 and 5.67 For the beam and loading shown,...Ch. 5.3 - Prob. 5.67PCh. 5.3 - Prob. 5.68PCh. 5.3 - Prob. 5.69PCh. 5.3 - Prob. 5.70PCh. 5.3 - Prob. 5.71PCh. 5.3 - 5.68 through 5.73 Determine the reactions at the...Ch. 5.3 - 5.68 through 5.73 Determine the reactions at the...Ch. 5.3 - Determine (a) the distance a so that the vertical...Ch. 5.3 - Prob. 5.75PCh. 5.3 - 5.76 Determine the reactions at the beam supports...Ch. 5.3 - Prob. 5.77PCh. 5.3 - The beam AB supports two concentrated loads and...Ch. 5.3 - For the beam and loading of Prob. 5.78, determine...Ch. 5.3 - The cross section of a concrete dam is as shown....Ch. 5.3 - Prob. 5.81PCh. 5.3 - The dam for a lake is designed to withstand the...Ch. 5.3 - Prob. 5.83PCh. 5.3 - 5.84 An automatic valve consists of a 9 × 9-in....Ch. 5.3 - 5.85 An automatic valve consists of a 9 × 9-in....Ch. 5.3 - Prob. 5.86PCh. 5.3 - The 3 4-m side of an open tank is hinged at its...Ch. 5.3 - Prob. 5.88PCh. 5.3 - A 0.5 0.8-m gate AB is located at the bottom of a...Ch. 5.3 - Prob. 5.90PCh. 5.3 - Prob. 5.91PCh. 5.3 - Prob. 5.92PCh. 5.3 - Prob. 5.93PCh. 5.3 - Prob. 5.94PCh. 5.3 - The square gate AB is held in the position shown...Ch. 5.4 - Consider the composite body shown. Determine (a)...Ch. 5.4 - Prob. 5.97PCh. 5.4 - Prob. 5.98PCh. 5.4 - Prob. 5.99PCh. 5.4 - Prob. 5.100PCh. 5.4 - Prob. 5.101PCh. 5.4 - Prob. 5.102PCh. 5.4 - Prob. 5.103PCh. 5.4 - For the machine element shown, locate the y...Ch. 5.4 - For the machine element shown, locate the x...Ch. 5.4 - 5.106 and 5.107 Locate the center of gravity of...Ch. 5.4 - 5.106 and 5.107 Locate the center of gravity of...Ch. 5.4 - A corner reflector for tracking by radar has two...Ch. 5.4 - A wastebasket, designed to fit in the corner of a...Ch. 5.4 - Prob. 5.110PCh. 5.4 - Prob. 5.111PCh. 5.4 - Prob. 5.112PCh. 5.4 - Prob. 5.113PCh. 5.4 - A thin steel wire with a uniform cross section is...Ch. 5.4 - The frame of a greenhouse is constructed from...Ch. 5.4 - Locate the center of gravity of the figure shown,...Ch. 5.4 - PROBLEM 5.117 Locate the center of gravity of the...Ch. 5.4 - A scratch awl has a plastic handle and a steel...Ch. 5.4 - Prob. 5.119PCh. 5.4 - PROBLEM 5.120 A brass collar, of length 2.5 in.,...Ch. 5.4 - Prob. 5.121PCh. 5.4 - Prob. 5.122PCh. 5.4 - Prob. 5.123PCh. 5.4 - Prob. 5.124PCh. 5.4 - PROBLEM 5.125 Locate the centroid of the volume...Ch. 5.4 - PROBLEM 5.126 Locate the centroid of the volume...Ch. 5.4 - Prob. 5.127PCh. 5.4 - Prob. 5.128PCh. 5.4 - PROBLEM 5.129 Locate the centroid of the volume...Ch. 5.4 - Prob. 5.130PCh. 5.4 - Prob. 5.131PCh. 5.4 - PROBLEM 5.132 The sides and the base of a punch...Ch. 5.4 - Locate the centroid of the section shown, which...Ch. 5.4 - Prob. 5.134PCh. 5.4 - Prob. 5.135PCh. 5.4 - Alter grading a lot, a builder places four stakes...Ch. 5 - 5.137 and 5.138 Locate the centroid of the plane...Ch. 5 - 5.137 and 5.138 Locate the centroid of the plane...Ch. 5 - Prob. 5.139RPCh. 5 - Prob. 5.140RPCh. 5 - Prob. 5.141RPCh. 5 - Prob. 5.142RPCh. 5 - Determine the reactions at the supports for the...Ch. 5 - A beam is subjected to a linearly distributed...Ch. 5 - Prob. 5.145RPCh. 5 - Prob. 5.146RPCh. 5 - An 8-in.-diameter cylindrical duct and a 4 8-in....Ch. 5 - Three brass plates are brazed to a steel pipe to...
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