PEARSON ETEXT ENGINEERING MECH & STATS
15th Edition
ISBN: 9780137514724
Author: HIBBELER
Publisher: PEARSON
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Chapter 8, Problem 73P
To determine
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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 8 Solutions
PEARSON ETEXT ENGINEERING MECH & STATS
Ch. 8 - F81. Determine the friction developed between the...Ch. 8 - F82. Determine the minimum force P to prevent the...Ch. 8 - Prob. 3FPCh. 8 - F84. If the coefficient of static friction at...Ch. 8 - F85. Determine the maximum force P that can be...Ch. 8 - F86. Determine the minimum coefficient of static...Ch. 8 - F87. Blocks A, B, and C have weights of 50 N, 25...Ch. 8 - F88. If the coefficient of static friction at all...Ch. 8 - Prob. 9FPCh. 8 - Determine the maximum force P the connection can...
Ch. 8 - The mine car and its contents have a total mass of...Ch. 8 - Prob. 4PCh. 8 - The automobile has a mass of 2 Mg and center of...Ch. 8 - The automobile has a mass of 2 Mg and canter of...Ch. 8 - Prob. 9PCh. 8 - Determine the angle at which the applied force P...Ch. 8 - Prob. 12PCh. 8 - The car has a mass of 1.6 Mg and center of mass at...Ch. 8 - The log has a coefficient of state friction of, s...Ch. 8 - The spool of wire having a weight of 300 Ib rests...Ch. 8 - The spool of wire having a weight of 300 Ib rests...Ch. 8 - Prob. 20PCh. 8 - The uniform thin pole has a weight of 30 Ib and a...Ch. 8 - The uniform pole has a weight of 30 Ib and a...Ch. 8 - The friction pawl is pinned at A and rests against...Ch. 8 - Two blocks A and B have a weight of 10 Ib and 6...Ch. 8 - Two blocks A and B have a weight of 10 Ib and 6...Ch. 8 - Determine the smallest force P that must be...Ch. 8 - The man having a weight of 200 Ib pushes...Ch. 8 - The uniform hoop of weight W is subjected to the...Ch. 8 - Determine the maximum horizontal force P that can...Ch. 8 - Determine the minimum force P needed to push the...Ch. 8 - Prob. 41PCh. 8 - Prob. 42PCh. 8 - Prob. 51PCh. 8 - Prob. 52PCh. 8 - Determine the smallest couple moment that can be...Ch. 8 - If P=250 N, determine the required minimum...Ch. 8 - Determine the minimum applied force P required to...Ch. 8 - Prob. 67PCh. 8 - Prob. 68PCh. 8 - Prob. 71PCh. 8 - Prob. 72PCh. 8 - Prob. 73PCh. 8 - Prob. 74PCh. 8 - Prob. 81PCh. 8 - Determine the horizontal force P that must be...Ch. 8 - A 180-lb farmer tries to restrain the cow from...Ch. 8 - The 100-lb boy at A is suspended from the cable...Ch. 8 - Prob. 87PCh. 8 - Determine the force P that must be applied to the...Ch. 8 - Prob. 93PCh. 8 - Prob. 98PCh. 8 - Prob. 99PCh. 8 - Blocks A and B have a mass of 7 kg and 10 kg,...Ch. 8 - The uniform bar AB is supported by a rope that...Ch. 8 - Prob. 102PCh. 8 - A 10-kg cylinder D, which is attached to a small...Ch. 8 - Prob. 106PCh. 8 - The collar bearing uniformly supports an axial...Ch. 8 - The collar bearing uniformly supports an axial...Ch. 8 - The floor-polishing machine rotates at a constant...Ch. 8 - Prob. 110PCh. 8 - Prob. 111PCh. 8 - Prob. 116PCh. 8 - The collar fits loosely around a fixed shaft that...Ch. 8 - Prob. 119PCh. 8 - Prob. 120PCh. 8 - Solve Prob. 8-120 if the force P is applied...Ch. 8 - Prob. 122PCh. 8 - Prob. 123PCh. 8 - Prob. 125PCh. 8 - The bell crank fits loosely into a 0.5-in-diameter...Ch. 8 - The bell crank fits loosely into a 0.5-in-diameter...Ch. 8 - Prob. 129PCh. 8 - R81. The uniform 20-lb ladder rests on the rough...Ch. 8 - R82. The uniform 60-kg crate C rests uniformly on...Ch. 8 - R83. A 35-kg disk rests on an inclined surface for...Ch. 8 - Prob. 4RPCh. 8 - Prob. 6RPCh. 8 - Prob. 7RPCh. 8 - The hand cart has wheels with a diameter of 80 mm....
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