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# 物理代考|理论力学代考THEORETICAL MECHANICS代考|PHYS111 Constraint

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## 物理代考|理论力学代考THEORETICAL MECHANICS代考|Flexible cable

An object is often constrained by a flexible cable, which means that the cable provides a reactive force to confine the object. As shown in Fig. 3.1, a ball is hung by a rope on the ceiling. If there is no force from the rope, the ball will go downward to the ground. This fact manifests that a reactive force from the cable must exist to balance the gravity of the ball. We first relieve the constraint, only investigating the object. This process is called isolation, and the object is called a free body now. The force from the rope deviates from the object, along the contraction direction of the rope. We use the symbol $\boldsymbol{T}$ to represent the force, with the meaning of tension.

Similarly, the belt of a wheel can transport some objects from one position to another, and the belt is normally in tension. We analyze the wheel, and it endures the pulling force from the belt, as shown in Fig. 3.2. The tension also deviates from the wheel, along the contraction direction of the belt.

## 物理代考|理论力学代考THEORETICAL MECHANICS代考|Smooth contact surface

As shown in Fig. 3.3, an object is lying on a desk. If there is no supporting force from the desk, the object will go downward to the ground. This means the desk provides a reactive force to ensure the constraint of the object. This kind of constraint is called smooth contact surface constraint, where the friction is neglected. The direction of the reactive force from the contact surface is normal to this surface, pointing inside to the object. The action line of the reactive force can also be determined considering that it is perpendicular to the tangential line of the contact surface. As shown in Fig. 3.4, an object is put on a curved surface. We first relieve the constraint, leaving only a free body. To determine the direction of the reactive force from the curved surface, we can draw the tangential line between the ball and the curved surface. Then the force is vertical to this tangential line.

Figure $3.5$ shows the contact of two gears, where the teeth are contacting with each other to transmit torques. Select one tooth, and it undergoes the force from the neighborhood tooth. Relieving the constraint of the neighborhood tooth, the reactive force of the first tooth is perpendicular to the tangent line of the contact surface, as demonstrated in Fig. 3.6.

Another example is a slender bar put in a trough. There are three contact points which can produce reactive forces. These reactive forces are from the smooth contact surfaces, which can be dictated as the schematic displayed in Fig. 3.7. At point $A$, a point from the bar is contacting with a planar surface, and the tangential line is of the same direction with the surface. Point $B$ is similar to $A$. At point $C$, a point from the trough is contacting with the bar surface, and the tangential line can also be marked.

## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。