Engineering Mechanics: Dynamics
8th Edition
ISBN: 9781118885840
Author: James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher: WILEY
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Chapter 6.9, Problem 213RP
To determine
The speed of rack.
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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 6 Solutions
Engineering Mechanics: Dynamics
Ch. 6.4 - Prob. 1PCh. 6.4 - In Prob. 6/1, if the plate is given a horizontal...Ch. 6.4 - The driver of a pickup truck accelerates from rest...Ch. 6.4 - A passenger car of an overhead monorail system is...Ch. 6.4 - The uniform box of mass m slides down the rough...Ch. 6.4 - The uniform slender bar of mass m and length L is...Ch. 6.4 - Prob. 7PCh. 6.4 - The frame is made from uniform rod which has a...Ch. 6.4 - Prob. 9PCh. 6.4 - Determine the value of P which will cause the...
Ch. 6.4 - The uniform 5-kg bar AB is suspended in a vertical...Ch. 6.4 - Prob. 12PCh. 6.4 - Prob. 13PCh. 6.4 - Prob. 14PCh. 6.4 - Prob. 15PCh. 6.4 - Prob. 16PCh. 6.4 - The 1650-kg car has its mass center at G....Ch. 6.4 - Prob. 18PCh. 6.4 - A cleated conveyor belt transports solid...Ch. 6.4 - The thin hoop of negligible mass and radius r...Ch. 6.4 - Determine the magnitude P and direction θ of the...Ch. 6.4 - The mine skip has a loaded mass of 2000 kg and is...Ch. 6.4 - The block A and attached rod have a combined mass...Ch. 6.4 - The homogeneous rectangular plate weighs 40 lb and...Ch. 6.4 - A jet transport with a landing speed of 200 km/h...Ch. 6.4 - Prob. 26PCh. 6.4 - Prob. 27PCh. 6.4 - The 30,000-lb concrete pipe section is being...Ch. 6.4 - Determine the maximum counterweight W for which...Ch. 6.4 - The 1800-kg rear-wheel-drive car accelerates...Ch. 6.4 - The experimental Formula One race car is traveling...Ch. 6.4 - Two pulleys are fastened together to form an...Ch. 6.4 - The uniform 20-kg slender bar is pivoted at O and...Ch. 6.4 - The figure shows an overhead view of a...Ch. 6.4 - The uniform 100-kg beam is freely hinged about its...Ch. 6.4 - The motor M is used to hoist the 12,000-lb stadium...Ch. 6.4 - Prob. 38PCh. 6.4 - Each of the two drums and connected hubs of 8-in....Ch. 6.4 - Determine the angular acceleration and the force...Ch. 6.4 - The uniform 5-kg portion of a circular hoop is...Ch. 6.4 - The 30-in. slender bar weighs 20 lb and is mounted...Ch. 6.4 - The half ring of mass m and radius r is welded to...Ch. 6.4 - The uniform plate of mass m is released from rest...Ch. 6.4 - The uniform slender bar AB has a mass of 8 kg and...Ch. 6.4 - Prob. 46PCh. 6.4 - Prob. 47PCh. 6.4 - Prob. 48PCh. 6.4 - Prob. 49PCh. 6.4 - Prob. 50PCh. 6.4 - Prob. 51PCh. 6.4 - Prob. 52PCh. 6.4 - Prob. 53PCh. 6.4 - Prob. 54PCh. 6.4 - The solid cylindrical rotor B has a mass of 43 kg...Ch. 6.4 - Prob. 56PCh. 6.4 - Prob. 57PCh. 6.4 - The uniform slender bar is released from rest in...Ch. 6.4 - Prob. 59PCh. 6.4 - Prob. 61PCh. 6.4 - The uniform steel I-beam has a mass of 300 kg and...Ch. 6.4 - The gear train shown operates in a horizontal...Ch. 6.4 - Prob. 64PCh. 6.4 - Prob. 65PCh. 6.4 - Prob. 66PCh. 6.4 - The uniform 72-ft mast weighs 600 lb and is hinged...Ch. 6.4 - The robotic device consists of the stationary...Ch. 6.4 - Prob. 69PCh. 6.4 - Prob. 70PCh. 6.5 - The uniform slender bar rests on a smooth...Ch. 6.5 - The 64.4-lb solid circular disk is initially at...Ch. 6.5 - Prob. 73PCh. 6.5 - Prob. 74PCh. 6.5 - Prob. 75PCh. 6.5 - Prob. 76PCh. 6.5 - Prob. 77PCh. 6.5 - Determine the angular acceleration of each of the...Ch. 6.5 - The solid homogeneous cylinder is released from...Ch. 6.5 - The 30-kg spool of outer radius ro = 450 mm has a...Ch. 6.5 - Repeat Prob. 6/80 for the case where the cable...Ch. 6.5 - The fairing which covers the spacecraft package in...Ch. 6.5 - Prob. 83PCh. 6.5 - Prob. 85PCh. 6.5 - The system of Prob. 6/20 is repeated here. If the...Ch. 6.5 - Prob. 87PCh. 6.5 - Prob. 88PCh. 6.5 - Prob. 89PCh. 6.5 - Prob. 90PCh. 6.5 - Prob. 91PCh. 6.5 - The truck, initially at rest with a solid...Ch. 6.5 - Prob. 93PCh. 6.5 - The uniform rectangular 300-lb plate is held in...Ch. 6.5 - Prob. 96PCh. 6.5 - Prob. 97PCh. 6.5 - Prob. 98PCh. 6.5 - The yo-yo has a mass m and a radius of gyration k...Ch. 6.5 - Prob. 100PCh. 6.5 - Prob. 101PCh. 6.5 - Prob. 102PCh. 6.5 - Prob. 103PCh. 6.5 - Prob. 104PCh. 6.5 - The connecting rod AB of a certain...Ch. 6.5 - Prob. 107PCh. 6.5 - The four-bar mechanism lies in a vertical plane...Ch. 6.5 - The Ferris wheel at an amusement park has an even...Ch. 6.6 - The slender rod of mass m and length l has a...Ch. 6.6 - The log is suspended by the two parallel 5-m...Ch. 6.6 - The assembly is constructed of homogeneous slender...Ch. 6.6 - Prob. 114PCh. 6.6 - Prob. 115PCh. 6.6 - The uniform semicircular bar of radius r = 75 mm...Ch. 6.6 - The homogeneous rectangular crate weighs 250 lb...Ch. 6.6 - The 24-lb disk is rigidly attached to the 7-lb bar...Ch. 6.6 - The two wheels of Prob. 6/78, shown again here,...Ch. 6.6 - The 15-kg slender bar OA is released from rest in...Ch. 6.6 - The light circular hoop of radius r contains a...Ch. 6.6 - Prob. 122PCh. 6.6 - The figure shows an impact tester used in studying...Ch. 6.6 - Prob. 124PCh. 6.6 - Prob. 125PCh. 6.6 - Prob. 126PCh. 6.6 - Prob. 127PCh. 6.6 - The uniform 40-lb bar with attached 12-lb wheels...Ch. 6.6 - Prob. 129PCh. 6.6 - The wheel consists of a 4-kg rim of 250-mm radius...Ch. 6.6 - The uniform slender bar ABC weighs 6 lb and is...Ch. 6.6 - Prob. 133PCh. 6.6 - The system is released from rest when the angle θ...Ch. 6.6 - The uniform 12-lb disk pivots freely about a...Ch. 6.6 - Prob. 137PCh. 6.6 - Prob. 138PCh. 6.6 - Prob. 139PCh. 6.6 - Prob. 140PCh. 6.6 - Prob. 141PCh. 6.6 - Prob. 142PCh. 6.6 - The homogeneous solid semicylinder is released...Ch. 6.6 - A small experimental vehicle has a total mass m of...Ch. 6.6 - Prob. 147PCh. 6.6 - The open square frame is constructed of four...Ch. 6.7 - The load of mass m is supported by the light...Ch. 6.7 - The uniform slender bar of mass m is shown in its...Ch. 6.7 - Prob. 151PCh. 6.7 - Prob. 152PCh. 6.7 - Prob. 153PCh. 6.7 - The load of mass m is given an upward acceleration...Ch. 6.7 - The cargo box of the food-delivery truck for...Ch. 6.7 - The sliding block is given a horizontal...Ch. 6.7 - Prob. 157PCh. 6.7 - Prob. 158PCh. 6.7 - Prob. 159PCh. 6.7 - Prob. 160PCh. 6.7 - The mechanical tachometer measures the rotational...Ch. 6.7 - Prob. 162PCh. 6.7 - Prob. 163PCh. 6.7 - Prob. 164PCh. 6.7 - Prob. 165PCh. 6.7 - Prob. 166PCh. 6.9 - Prob. 167RPCh. 6.9 - Prob. 168RPCh. 6.9 - Prob. 169RPCh. 6.9 - The frame of mass m is welded together from...Ch. 6.9 - Prob. 171RPCh. 6.9 - The cable drum has a mass of 800 kg with radius of...Ch. 6.9 - Prob. 173RPCh. 6.9 - Prob. 174RPCh. 6.9 - Prob. 175RPCh. 6.9 - Prob. 176RPCh. 6.9 - Prob. 177RPCh. 6.9 - The wad of clay of mass m is initially moving with...Ch. 6.9 - Prob. 179RPCh. 6.9 - Prob. 180RPCh. 6.9 - Prob. 181RPCh. 6.9 - Prob. 182RPCh. 6.9 - Prob. 183RPCh. 6.9 - Two small variable-thrust jets are actuated to...Ch. 6.9 - Prob. 185RPCh. 6.9 - Each of the two 300-mm uniform rods A has a mass...Ch. 6.9 - Prob. 187RPCh. 6.9 - The slender bar of mass m and length l is released...Ch. 6.9 - Prob. 189RPCh. 6.9 - Prob. 190RPCh. 6.9 - Prob. 191RPCh. 6.9 - Prob. 192RPCh. 6.9 - Prob. 193RPCh. 6.9 - Prob. 194RPCh. 6.9 - The 165-lb ice skater with arms extended...Ch. 6.9 - Prob. 196RPCh. 6.9 - Prob. 197RPCh. 6.9 - The body of the spacecraft weighs 322 lb on earth...Ch. 6.9 - Prob. 199RPCh. 6.9 - Prob. 200RPCh. 6.9 - Prob. 201RPCh. 6.9 - The uniform cylinder is rolling without slip with...Ch. 6.9 - Prob. 203RPCh. 6.9 - The 30-kg wheel has a radius of gyration about its...Ch. 6.9 - The mass m is traveling with speed v when it...Ch. 6.9 - Prob. 206RPCh. 6.9 - Prob. 207RPCh. 6.9 - Prob. 208RPCh. 6.9 - The nose-wheel assembly is raised by the...Ch. 6.9 - Prob. 210RPCh. 6.9 - Prob. 211RPCh. 6.9 - Prob. 212RPCh. 6.9 - Prob. 213RPCh. 6.9 - Prob. 214RPCh. 6.9 - Prob. 215RPCh. 6.9 - Prob. 216RPCh. 6.9 - Prob. 217RPCh. 6.9 - Prob. 218RPCh. 6.9 - Prob. 219RPCh. 6.9 - Prob. 220RPCh. 6.9 - The slender rod of mass m1 and length L has a...Ch. 6.9 - Prob. 222RPCh. 6.9 - Prob. 226RPCh. 6.9 - Prob. 228RPCh. 6.9 - Prob. 229RPCh. 6.9 - Prob. 230RP
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