Dynamics

In this lesson we will answer specific questions related to the causes of motion, such as “What mechanism causes motion?” and “Why do some objects accelerate at a higher rate than others?” We shall then discuss the three basic laws of motion, which are based on experimental observations and were formulated nearly three centuries ago by Isaac Newton. We shall although the force laws are rather simple in form; they successfully explain a wide variety of phenomena and experimental observations. These force laws, together with the laws of motion, are the foundations of classical mechanics

The purpose of classical mechanics is to provide a connection between the acceleration of a body and the forces acting in it.

Keep in mind that classical mechanics deals with objects that are large compared with the dimensions of atoms (~10^-10m) and move at speeds that the much less than the speed of light (3*10⁸m/s).

When you push or pull an object, you exert a force on it. You exert a force when you throw or kick a ball. In these examples, the word forceis associated with the result of muscular activity and some change in the state of motion of an object. Consider a situation in which several forces act simultaneously on an object. In this case, the object will accelerate only if the net force acting on it is not equal to zero. We shall often refer to the net force as the resultant force or unbalanced force. If the net force is zero, the acceleration is zero and the velocity of the object remains constant.

The new approach to motion was later formalized by Newton in a form that come to be known as Newton’s first law of motion:

As object at rest will remain at rest and an object in motion will continue a motion with a constant velocity unless it experiences a net external force (or result force).

We can say that when the resultant force on a body is zero, its acceleration is zero. That is when ΣF = 0, then a = 0.

Newton’s first law is sometimes called the law of inertia and it applies to objects in an inertial frame of reference.

Inertia is the property of matter that relates to the tendency of an object to remain at rest or in uniform motion.

Mass is a term used to measure inertia. The greater the mass of a body, the less it will accelerate (change its nnn of motion) under the action of an applied force.

Newton’s second law

The acceleration of an objects is inversely proportional to its mass.

The Newton’s second law:

The acceleration of an object is directly proportional to the resultant force acting on it and inversely proportional to its mass

Note that if the resultant force is zero, then a = 0, which corresponds to the equilibrium situation where v is equal to a constant. Thus we can relate mass and force through the following mathematical statement of Newton’s second law:

Σ F = ma (1)

You should note that equation (1) is a vector expression and hence is equivalent to the following three component equations:

Σ F_x = ma_x Σ F_y = ma_y Σ F_z = ma_z

To state the law in its most general form, we first define the momentum, p, of a particle as the product of the mass, m and the velocity, u

Дата добавления: 2013-12-13