Three boxes rest side-by-side on a smooth, horizontal floor. Their masses are 5.0-kg, 3.0-kg, and 2.0-kg, with the 3.0-kg mass in the center
A force of 50 N pushes on the 5.0-kg mass, which pushes against the other two masses.
(a) Draw the free-body diagrams for each of the masses.
(b) What is the contact force between the 5.0-kg mass and the 3.0-kg mass?
(c) What is the contact force between the 3.0-kg and the 2.0-kg mass?
(a) The following forces act on the 5.0-kg mass: the force due to gravity, normal force, contact force between 5.0-kg mass and 3.0-kg mass, the force of 50 N pushing on the mass. The following forces act on the 3.0-kg force: the force due to gravity, normal force, contact force between the 5.0-kg mass and the 3.0- kg mass, the contact force between the 3.0-kg mass and the 2.0-kg mass. The following forces act on the 2.0-kg mass: the force due to gravity, normal force, contact force between the 3.0-kg mass and the 2.0-kg mass.
(b) 25 N
(c) 10 N
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Is often called the fully-implicit form of the one-dimensional transient conduction difference equation because all quantities in the equation, except for the temperatures in the energy storage term, are evaluated at the new time step, m + 1. In an alternate form called Crank-Nicholson, these quantities are evaluated at both time step m and m + 1 and then averaged. This averaging significantly improves the accuracy of the numerical solution relative to the fully-implicit form without increasing the complexity of the solution method. Derive the one-dimensional transient conduction difference equation in the Crank-Nicholson form.
GIVEN One-dimensional transient conduction difference equation in the implicit form FIND (a) The Crank-Nicholson form of the difference equation
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