Posted on Categories:Theoretical mechanics, 物理代写, 理论力学

# 物理代写|理论力学代写Theoretical Mechanics代考|PHYS354 Forces

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## 物理代写|理论力学代写Theoretical Mechanics代考|Forces

At the beginning of this chapter we recognized as the elementary task of each physical theory, in particular the Classical Mechanics, to derive conclusions from preformulated postulates (basis definitions, axioms). The axioms and the fundamental definition of mass are now available. The law of motion (2.42) and (2.43), respectively, have become the principal dynamical equation of Classical Mechanics. This equation is to be solved. As a rule, mathematically that means, for a given force $\mathbf{F}$, one has to solve a differential equation of second order.

More precise than the term force in this connection is, strictly speaking, the concept of the
‘Force Field’
$$\mathbf{F}=\mathbf{F}(\mathbf{r}, \dot{\mathbf{r}}, t) .$$

## 物理代写|理论力学代写Theoretical Mechanics代考|Theorem of Kinetic Energy

To each space point a force that acts on the mass point is assigned, which in general can even be time dependent and, additionally, may depend on the particle velocity. Dependence on acceleration $\ddot{\mathbf{r}}$, however, will not appear.

All the matter is built by elementary constituents (molecules, atoms, nucleons, electrons, …). Therefore, in the last analysis each force can be traced back to the interactions between these elementary constituents. To do this in all detail, however, is beyond the framework of Classical Mechanics which only asks for the consequences and not for the elementary causes of the forces. Normally one restricts oneself to mathematically as simple as possible and empirically reasoned model representations
Some frequently used examples are listed in the following:
(a) Weight, Gravitational Force
Each body is ‘heavy’. $1 \mathrm{~m}^3$ of iron is ‘heavier’ than $1 \mathrm{~cm}^3$ of iron. By this everyday experience a new material quantity is documented which is denoted as
gravitational (heavy) mass $m_h$.
It manifests itself in the ‘gravitational force’
$$\mathbf{F}_g=m_h \mathbf{g},$$
which acts on a stationary (motionless) mass point in the gravitational field of the earth. $g$ close to the earth’s surface is a nearly constant vector always pointing downwards in direction to the earth’s center. If we define this direction as the negative $x_3$ direction of a Cartesian coordinate system then we write
$$\mathbf{g}=-(0,0, g) ; \quad g=9.81 \mathrm{~m} \mathrm{~s}^{-2} \text { ‘gravity acceleration’. }$$

## 物理代写|理论力学代写Theoretical Mechanics代考|Forces

$$\mathbf{F}=\mathbf{F}(\mathbf{r}, \dot{\mathbf{r}}, t)$$

## 物理代写|理论力学代写Theoretical Mechanics代考|Theorem of Kinetic Energy

(a) 重量，重力

$$\mathbf{F}_g=m_h \mathbf{g}$$

$$\mathbf{g}=-(0,0, g) ; \quad g=9.81 \mathrm{~m} \mathrm{~s}^{-2} \text { ‘gravity acceleration’. }$$

## MATLAB代写

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