Engineering Mechanics: Dynamics
8th Edition
ISBN: 9781118885840
Author: James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher: WILEY
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Chapter 4.7, Problem 89P
a)
To determine
The velocity at end
b)
To determine
The velocity at end
c)
To determine
The loss of potential energy
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Problem 1 (30 Points)
Consider the following 2 scenarios. In scenario 1, a mass m slides on a cylindrical surface of radius R. In
scenario 2, a mass m hangs at the end of a thin massless rod of length R. In both scenarios, there is no
friction either on the surface (scenario 1), or at the pivot point of the pendulum (scenario 2). Also in
both scenarios, there is one generalized coordinate, .
R
Scenario 1
R
m
R
g
Scenario 2
m
HINT: In both scenarios, it is much easier to choose your datum for potential energy as the center of the
bowl (scenario 1), or the pivot point of the pendulum (scenario 2).
Part I
a) Determine the Lagrangian for each system. DO NOT FIND THE EQUATIONS OF MOTION (5 points)
b) What can you say about the systems based on the Lagrangian? (2 points)
c) Solve for the equations of motion for both systems. (8 points)
Part II
Now, for scenario 1, introduce an additional coordinate and treat it as a nonholonomic system to
determine the normal force acting on the mass.
a)…
Consider 0.65 kg of N2 at 300 K, 1 bar contained in a rigid tank connected by a valve to another rigid tank holding 0.3 kg of CO2 at 300 K, 1 bar. The valve is opened and gases are allowed to mix, achieving an equilibrium state at 290 K. Determine: (a) the volume of each tank, in m³. (b) the final pressure, in bar. (c) the magnitude of the heat transfer to or from the gases during the process, in kJ. (d) the entropy change of each gas and of the overall system, in kJ/K.
(Read Image) (Answer: ω = 1.10 rad/sec CW)
Chapter 4 Solutions
Engineering Mechanics: Dynamics
Ch. 4.5 - The system of three particles has the indicated...Ch. 4.5 - Prob. 2PCh. 4.5 - Prob. 3PCh. 4.5 - Prob. 4PCh. 4.5 - Prob. 5PCh. 4.5 - Prob. 6PCh. 4.5 - The total linear momentum of a system of five...Ch. 4.5 - Prob. 8PCh. 4.5 - Prob. 9PCh. 4.5 - The monkeys of Prob. 4/9 are now climbing along...
Ch. 4.5 - Prob. 11PCh. 4.5 - Each of the five connected particles has a mass of...Ch. 4.5 - Prob. 13PCh. 4.5 - Calculate the vertical acceleration of the system...Ch. 4.5 - The two small spheres, each of mass m, and their...Ch. 4.5 - Prob. 17PCh. 4.5 - A centrifuge consists of four cylindrical...Ch. 4.5 - The three small spheres are welded to the light...Ch. 4.5 - Prob. 20PCh. 4.5 - The 300-kg and 400-kg mine cars are rolling in...Ch. 4.5 - Prob. 22PCh. 4.5 - The man of mass m1 and the woman of mass m2 are...Ch. 4.5 - The woman A, the captain B, and the sailor C weigh...Ch. 4.5 - Prob. 25PCh. 4.5 - Prob. 26PCh. 4.5 - Prob. 27PCh. 4.5 - Prob. 28PCh. 4.5 - Prob. 29PCh. 4.5 - The carriage of mass 2m is free to roll along the...Ch. 4.5 - Prob. 31PCh. 4.5 - Prob. 33PCh. 4.5 - Prob. 34PCh. 4.5 - Prob. 35PCh. 4.5 - Prob. 36PCh. 4.5 - Prob. 37PCh. 4.5 - Prob. 38PCh. 4.5 - Prob. 39PCh. 4.5 - Prob. 40PCh. 4.5 - Prob. 41PCh. 4.5 - Prob. 42PCh. 4.5 - Prob. 43PCh. 4.5 - The 90° vane moves to the left with a constant...Ch. 4.5 - The pipe bend shown has a cross-sectional area A...Ch. 4.5 - A jet of fluid with cross-sectional area A and...Ch. 4.5 - Prob. 47PCh. 4.5 - Prob. 48PCh. 4.5 - Prob. 49PCh. 4.5 - Prob. 50PCh. 4.5 - Prob. 51PCh. 4.5 - Prob. 52PCh. 4.5 - Prob. 53PCh. 4.5 - Prob. 54PCh. 4.5 - Prob. 55PCh. 4.5 - Prob. 56PCh. 4.5 - Prob. 57PCh. 4.5 - Prob. 58PCh. 4.5 - Prob. 60PCh. 4.5 - Prob. 61PCh. 4.5 - Prob. 62PCh. 4.5 - Prob. 63PCh. 4.5 - Prob. 64PCh. 4.5 - Prob. 65PCh. 4.5 - Prob. 66PCh. 4.5 - Prob. 67PCh. 4.5 - In the figure is shown a detail of the stationary...Ch. 4.7 - When the rocket reaches the position in its...Ch. 4.7 - Prob. 70PCh. 4.7 - Prob. 71PCh. 4.7 - Prob. 72PCh. 4.7 - Prob. 73PCh. 4.7 - Prob. 74PCh. 4.7 - Prob. 75PCh. 4.7 - Prob. 76PCh. 4.7 - Prob. 77PCh. 4.7 - Prob. 78PCh. 4.7 - Prob. 79PCh. 4.7 - Prob. 80PCh. 4.7 - Prob. 81PCh. 4.7 - Prob. 82PCh. 4.7 - Prob. 83PCh. 4.7 - Prob. 84PCh. 4.7 - Prob. 85PCh. 4.7 - Prob. 86PCh. 4.7 - Prob. 87PCh. 4.7 - Prob. 88PCh. 4.7 - Prob. 89PCh. 4.7 - Prob. 90PCh. 4.7 - Prob. 91PCh. 4.7 - Prob. 92PCh. 4.8 - Prob. 93RPCh. 4.8 - For the particle system of Prob. 4/93, determine...Ch. 4.8 - Prob. 95RPCh. 4.8 - Prob. 96RPCh. 4.8 - Prob. 97RPCh. 4.8 - Prob. 98RPCh. 4.8 - Prob. 99RPCh. 4.8 - Prob. 100RPCh. 4.8 - Prob. 101RPCh. 4.8 - Prob. 102RPCh. 4.8 - Prob. 104RPCh. 4.8 - Prob. 105RPCh. 4.8 - Prob. 106RPCh. 4.8 - Prob. 107RPCh. 4.8 - Prob. 108RPCh. 4.8 - Prob. 109RPCh. 4.8 - Prob. 110RPCh. 4.8 - A rope or hinged-link bicycle-type chain of length...
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