Engineering Mechanics: Statics & Dynamics (14th Edition)
14th Edition
ISBN: 9780133915426
Author: Russell C. Hibbeler
Publisher: PEARSON
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Chapter 16.6, Problem 92P
To determine
The velocity of the point
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2. Express the following complex numbers in rectangular form.
(a) z₁ = 2еjл/6
(b) Z2=-3e-jπ/4
(c) Z3 =
√√√3e-j³/4
(d) z4 = − j³
A prismatic beam is built into a structure. You can consider the boundary conditions at A and B to be
fixed supports. The beam was originally designed to withstand a triangular distributed load, however,
the loading condition has been revised and can be approximated by a cosine function as shown in the
figure below. You have been tasked with analysing the structure. As the beam is prismatic, you can
assume that the bending rigidity (El) is constant.
wwo cos
2L
x
A
B
Figure 3: Built in beam with a varying distributed load
In order to do this, you will:
a. Solve the reaction forces and moments at point A and B.
Hint: you may find it convenient to use the principal of superposition.
(2%)
b. Plot the shear force and bending moment diagrams and identify the maximum shear force
and bending moment.
(2%)
c. Develop an expression for the vertical deflection. Clearly state your expression in terms of x.
(1%)
Question 1: Beam Analysis
Two beams (ABC and CD) are connected using a pin immediately to the left of Point C. The pin acts
as a moment release, i.e. no moments are transferred through this pinned connection. Shear forces
can be transferred through the pinned connection. Beam ABC has a pinned support at point A and a
roller support at Point C. Beam CD has a roller support at Point D. A concentrated load, P, is applied
to the mid span of beam CD, and acts at an angle as shown below. Two concentrated moments, MB
and Mc act in the directions shown at Point B and Point C respectively. The magnitude of these
moments is PL.
Moment Release
A
B
с
°
MB = PL
Mc=
= PL
-L/2-
-L/2-
→
P
D
Figure 1: Two beam arrangement for question 1.
To analyse this structure, you will:
a) Construct the free body diagrams for the structure shown above. When constructing your
FBD's you must make section cuts at point B and C. You can represent the structure as three
separate beams. Following this, construct the…
Chapter 16 Solutions
Engineering Mechanics: Statics & Dynamics (14th Edition)
Ch. 16.3 - When the gear rotates 20 revolutions, it achieves...Ch. 16.3 - The flywheel rotates with an angular velocity of ...Ch. 16.3 - The flywheel rotates with an angular velocity of (...Ch. 16.3 - The bucket is hoisted by the rope that wraps...Ch. 16.3 - A wheel has an angular acceleration of = (0.5 )...Ch. 16.3 - For a short period of time, the motor turns gear A...Ch. 16.3 - Prob. 1PCh. 16.3 - The angular acceleration of the disk is defined by...Ch. 16.3 - The disk is originally rotating at 0 = 12 rad/s....Ch. 16.3 - Prob. 4P
Ch. 16.3 - The disk is driven by a motor such that the...Ch. 16.3 - A wheel has an initial clockwise angular velocity...Ch. 16.3 - Prob. 7PCh. 16.3 - If gear A rotates with an angular velocity of A =...Ch. 16.3 - Prob. 9PCh. 16.3 - At the instant A = 5 rad/s. pulley A is given a...Ch. 16.3 - The cord, which is wrapped around the disk, is...Ch. 16.3 - The power of a bus engine is transmitted using the...Ch. 16.3 - Prob. 13PCh. 16.3 - The disk starts from rest and is given an angular...Ch. 16.3 - The disk starts from rest and is given an angular...Ch. 16.3 - The disk starts at o = 1 rad/s when = 0, and is...Ch. 16.3 - A motor gives gear A an angular acceleration of A...Ch. 16.3 - A motor gives gear A an angular acceleration of A...Ch. 16.3 - Prob. 19PCh. 16.3 - Prob. 20PCh. 16.3 - Prob. 21PCh. 16.3 - If the motor turns gear A with an angular...Ch. 16.3 - Prob. 23PCh. 16.3 - Prob. 24PCh. 16.3 - Prob. 25PCh. 16.3 - Prob. 26PCh. 16.3 - Prob. 27PCh. 16.3 - Prob. 28PCh. 16.3 - Prob. 29PCh. 16.3 - At the instant shown, gear A is rotating with a...Ch. 16.3 - Determine the distance the load W is lifted in t =...Ch. 16.3 - Prob. 32PCh. 16.3 - Prob. 33PCh. 16.3 - Prob. 34PCh. 16.3 - Prob. 35PCh. 16.3 - Prob. 36PCh. 16.3 - The rod assembly is supported by ball-and-socket...Ch. 16.3 - Prob. 38PCh. 16.4 - The end A of the bar is moving downward along the...Ch. 16.4 - At the instant = 60, the slotted guide rod is...Ch. 16.4 - At the instant = 50, the slotted guide is moving...Ch. 16.4 - At the instant shown, = 60, and rod AB is...Ch. 16.4 - Prob. 43PCh. 16.4 - Determine the velocity and acceleration of the...Ch. 16.4 - Prob. 45PCh. 16.4 - The circular cam rotates about the fixed point O...Ch. 16.4 - Determine the velocity of the rod R for any angle ...Ch. 16.4 - Determine the velocity and acceleration of the peg...Ch. 16.4 - Bar AB rotates uniformly about the fixed pin A...Ch. 16.4 - Prob. 50PCh. 16.4 - Prob. 51PCh. 16.4 - Prob. 53PCh. 16.4 - Prob. 54PCh. 16.4 - Prob. 55PCh. 16.4 - Prob. 56PCh. 16.5 - If roller A moves to the right with a constant...Ch. 16.5 - Prob. 8FPCh. 16.5 - Determine the angular velocity of the spool. The...Ch. 16.5 - If crank OA rotates with an angular velocity of =...Ch. 16.5 - Prob. 11FPCh. 16.5 - Prob. 12FPCh. 16.5 - At the instant shown the boomerang has an angular...Ch. 16.5 - If the block at C is moving downward at 4 ft/s,...Ch. 16.5 - The link AB has an angular velocity of 3 rad/s....Ch. 16.5 - The slider block C moves at 8 m/s down the...Ch. 16.5 - Determine the angular velocity of links AB and BC...Ch. 16.5 - The planetary gear A is pinned at B. Link BC...Ch. 16.5 - If the angular velocity of link AB is AB = 3...Ch. 16.5 - The pinion gear A rolls on the fixed gear rack B...Ch. 16.5 - The pinion gear rolls on the gear racks. If B is...Ch. 16.5 - Determine the angular velocity of the gear and the...Ch. 16.5 - Determine the velocity of point A on the rim of...Ch. 16.5 - Prob. 68PCh. 16.5 - Prob. 69PCh. 16.5 - Prob. 70PCh. 16.5 - Prob. 71PCh. 16.5 - Prob. 72PCh. 16.5 - Prob. 73PCh. 16.5 - Prob. 74PCh. 16.5 - Prob. 75PCh. 16.5 - Prob. 76PCh. 16.5 - Prob. 77PCh. 16.5 - If the ring gear A rotates clockwise with an...Ch. 16.5 - Prob. 79PCh. 16.5 - Prob. 80PCh. 16.6 - Establish the location of the instantaneous center...Ch. 16.6 - Prob. 13FPCh. 16.6 - Prob. 14FPCh. 16.6 - If the center O of the wheel is moving with a...Ch. 16.6 - If cable AB is unwound with a speed of 3 m/s, and...Ch. 16.6 - Prob. 17FPCh. 16.6 - Determine the angular velocity of links BC and CD...Ch. 16.6 - Prob. 81PCh. 16.6 - Determine the angular velocity of link AB at the...Ch. 16.6 - The shaper mechanism is designed to give a slow...Ch. 16.6 - The conveyor belt is moving to the right at v = 8...Ch. 16.6 - The conveyor belt is moving to the right at v = 12...Ch. 16.6 - As the cord unravels from the wheels inner hub,...Ch. 16.6 - Prob. 87PCh. 16.6 - If bar AB has an angular velocity AB = 6 rad/s,...Ch. 16.6 - Prob. 89PCh. 16.6 - Prob. 90PCh. 16.6 - Prob. 91PCh. 16.6 - Prob. 92PCh. 16.6 - Prob. 93PCh. 16.6 - Prob. 94PCh. 16.6 - As the car travels forward at 80 ft/s on a wet...Ch. 16.6 - The pinion gear A rolls on the fixed gear rack B...Ch. 16.6 - Prob. 97PCh. 16.6 - If the hub gear H has an angular velocity H = 5...Ch. 16.6 - The crankshaft AB rotates at AB = 50 rad/s about...Ch. 16.6 - Prob. 100PCh. 16.6 - The planet gear A is pin connected to the end of...Ch. 16.7 - Solve Prob. 16-101 if the sun gear D is rotating...Ch. 16.7 - Set up the relative acceleration equation between...Ch. 16.7 - At the instant shown, end A of the rod has the...Ch. 16.7 - Prob. 20FPCh. 16.7 - The gear rolls on the fixed rack B. At the instant...Ch. 16.7 - At the instant shown, cable AB has a velocity of 3...Ch. 16.7 - At the instant shown, the wheel rotates with an...Ch. 16.7 - At the instant shown, wheel A rotates with an...Ch. 16.7 - Bar AB has the angular motions shown. Determine...Ch. 16.7 - At a given instant the bottom A of the ladder has...Ch. 16.7 - At a given instant the top B of the ladder has an...Ch. 16.7 - Prob. 106PCh. 16.7 - At a given instant the roller A on the bar has the...Ch. 16.7 - The rod is confined to move along the path due to...Ch. 16.7 - Member AB has the angular motions shown. Determine...Ch. 16.7 - The slider block has the motion shown. Determine...Ch. 16.7 - At a given instant the slider block A is moving to...Ch. 16.7 - Determine the angular acceleration of link CD if...Ch. 16.7 - The reel of rope has the angular motion shown....Ch. 16.7 - Prob. 114PCh. 16.7 - Prob. 115PCh. 16.7 - The disk has an angular acceleration = 8 rad/s2...Ch. 16.7 - The disk has an angular acceleration = 8 rad/s2...Ch. 16.7 - Prob. 118PCh. 16.7 - Prob. 119PCh. 16.7 - Prob. 120PCh. 16.7 - Prob. 121PCh. 16.7 - If member AB has the angular motion shown,...Ch. 16.7 - If member AB has the angular motion shown,...Ch. 16.7 - The disk rolls without slipping such that it has...Ch. 16.7 - Prob. 125PCh. 16.7 - The slider block moves with a velocity of vB = 5...Ch. 16.8 - The slider block moves with a velocity of vB = 5...Ch. 16.8 - Prob. 129PCh. 16.8 - Prob. 130PCh. 16.8 - Prob. 131PCh. 16.8 - Prob. 132PCh. 16.8 - Water leaves the impeller of the centrifugal pump...Ch. 16.8 - Prob. 134PCh. 16.8 - Prob. 135PCh. 16.8 - Rod AB rotates counterclockwise with a constant...Ch. 16.8 - Prob. 137PCh. 16.8 - Collar B moves to the left with a speed of 5 m/s,...Ch. 16.8 - Prob. 139PCh. 16.8 - At the instant shown rod AB has an angular...Ch. 16.8 - Prob. 141PCh. 16.8 - Prob. 142PCh. 16.8 - Peg B on the gear slides freely along the slot in...Ch. 16.8 - Prob. 144PCh. 16.8 - A ride in an amusement park consists of a rotating...Ch. 16.8 - Prob. 146PCh. 16.8 - If the slider block C is fixed to the disk that...Ch. 16.8 - Prob. 148PCh. 16.8 - Prob. 149PCh. 16.8 - Prob. 150PCh. 16.8 - Prob. 151PCh. 16.8 - Prob. 152PCh. 16.8 - Prob. 4CPCh. 16.8 - Prob. 1RPCh. 16.8 - Starting at (A)0 = 3 nad/s, when = 0, s = 0,...Ch. 16.8 - Prob. 3RPCh. 16.8 - Prob. 4RPCh. 16.8 - Prob. 5RPCh. 16.8 - At the instant shown, link AB has an angular...Ch. 16.8 - Prob. 7RPCh. 16.8 - At the given instant member AB has the angular...
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