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Related Concept Videos

Statically Indeterminate Problem Solving01:16

Statically Indeterminate Problem Solving

344
Statically indeterminate problems are those where statics alone can not determine the internal forces or reactions. Consider a structure comprising two cylindrical rods made of steel and brass. These rods are joined at point B and restrained by rigid supports at points A and C. Now, the reactions at points A and C and the deflection at point B are to be determined. This rod structure is classified as statically indeterminate as the structure has more supports than are necessary for maintaining...
344
Dot Product: Problem Solving01:21

Dot Product: Problem Solving

329
The dot product is a powerful tool in problem-solving involving vectors, given that the dot product of two vectors is the product of their magnitudes and the cosine of the angle between them measured anti-clockwise. Solving problems involving the dot product requires understanding its properties and developing a step-by-step process to solve them. Here are the main steps to follow when solving any general problem involving the dot product:
Identify the problem: Start by reading the problem and...
329
Potential Due to a Polarized Object01:29

Potential Due to a Polarized Object

351
A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...
351
Thin-Walled Hollow Shafts01:15

Thin-Walled Hollow Shafts

157
In analyzing a thin-walled hollow shaft subjected to torsional loading, a segment with width dx is isolated for examination. Despite its equilibrium state, this segment faces torsional shearing forces at its ends. These forces are quantitatively described by the product of the longitudinal shearing stress on the segment's minor surface and the area of this surface, leading to the concept of shear flow. This shear flow is consistent throughout the structure, indicating a uniform distribution...
157
Temperature Dependent Deformation01:12

Temperature Dependent Deformation

132
In a nonhomogeneous rod made up of steel and brass, restrained at both ends and subjected to a temperature change, several steps are involved in calculating the stress and compressive load. Due to the problem's static indeterminacy, one end support is disconnected, allowing the rod to experience the temperature change freely. Next, an unknown force is applied at the free end, triggering deformations in the rod's steel and brass portions. These deformations are then calculated and added...
132
Gravitation Between Spherically Symmetric Masses01:14

Gravitation Between Spherically Symmetric Masses

814
The gravitational potential energy between two spherically symmetric bodies can be calculated from the masses and the distance between the bodies, assuming that the center of mass is concentrated at the respective centers of the bodies.
814

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Related Experiment Video

Updated: May 15, 2025

Visually Based Characterization of the Incipient Particle Motion in Regular Substrates: From Laminar to Turbulent Conditions
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Analytical sphere-thin rod interaction potential.

Junwen Wang1,2,3, Shengfeng Cheng4,5,6,7

  • 1Department of Mechanical Engineering, Virginia Tech, Blacksburg, VA, 24061, USA.

The European Physical Journal. E, Soft Matter
|April 7, 2025
PubMed
Summary
This summary is machine-generated.

We derived an analytical solution for sphere-rod interactions using the Lennard-Jones potential. Adhesion scales with the sphere

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Area of Science:

  • Computational physics and physical chemistry
  • Materials science and nanotechnology

Background:

  • Understanding interatomic and intermolecular forces is crucial for predicting material properties and interactions at the nanoscale.
  • The Lennard-Jones potential is a widely used model for describing van der Waals interactions between atoms and molecules.

Purpose of the Study:

  • To derive a compact analytical form for the interaction potential between a sphere and a thin rod.
  • To investigate the adhesion forces between these two objects using the derived potential.

Main Methods:

  • Integration approach treating both sphere and rod as continuous media of material points.
  • Summation of pairwise Lennard-Jones 12-6 potentials between material points on the sphere and rod.
  • Derivation of expressions for resultant force and torque, and analysis of asymptotic limits.

Main Results:

  • A compact analytical form for the sphere-rod interaction potential was obtained.
  • Expressions for resultant force and torque were derived.
  • For large spheres and long rods, equilibrium separation is approximated as a + 0.787σ, and adhesion scales with √a.

Conclusions:

  • The derived analytical potential provides an accurate method for studying sphere-rod interactions.
  • The findings offer insights into adhesion mechanisms relevant to nanoparticle assembly and surface interactions.