Manual Dynamics of Motion - Level III (Dynamics of Motion System)

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  1. chapter and author info
  2. Unit 3 Dynamics: Forces and Motion - MS. TAYLOR'S SCIENCE CLASSES
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  4. Course Introduction; Angular Velocity; Angular Acceleration
  5. Kinematics and dynamics analysis of the main motion system of reciprocating machine tools

Exerting a force on an object will cause that object to accelerate.

Try pushing your finger against a wall. By doing this, you are said to exert a force on the wall. You will feel the wall 'pushing' back on you. The wall is said to exert a force on you. The force you exert on the wall always equals the force with which the wall exerts on you Newton's Third Law.

Because the wall is heavy, the force you exert on it does not move the wall noticeably. However, being much lighter, you will be probably be moved by the force that the wall exerts on you. Try it!

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A force can be applied to an object in different directions. Force is said to be a vector quantity. Exerting a force on an object causes the object to accelerate. The same force applied on objects of different masses causes different accelerations in each object. We observe that a force applied on a light object causes greater acceleration than the same force applied on a heavier object. We also observe that the acceleration of an object is proportional to the force exerted on it. In the SI unit system, force is measured in Newtons.

The weight of an object is defined as the gravitational force acting on the object, and is dependent on the mass of the body. Note that the acceleration due to gravity or acceleration of free-fall, usually denoted by g is taken as the constant 9. The direction of that force weight is always toward the center of this planet.

In rough terms, an apple weighs approximately one Newton. Viscosity of a fluid is a measure of its resistance to flow. Objects drag fluid along near its surface. The faster the object moves, the bigger the viscous drag. From Wikibooks, open books for an open world. Dynamics is the study of why objects move, and the effects of forces on moving objects. Mass will resist changes in motion. Category : Book:A-level Physics. Hidden category: Requests for expansion.

Unit 3 Dynamics: Forces and Motion - MS. TAYLOR'S SCIENCE CLASSES

Namespaces Book Discussion. The most important thing to realize is that this relationship involves not only changes in the magnitude of the momentum or of the velocity but also in their direction. If the mass is constant, then Eq. Thus we must understand that a change in a velocity, or an acceleration, has a wider meaning than in common language: The velocity of a moving object can change by its speeding up, slowing down when it slows down, we say it accelerates with a negative acceleration , or changing its direction of motion.

In order to make our language more precise, we shall make one further definition in our use of the words speed and velocity.

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Ordinarily we think of speed and velocity as being the same, and in ordinary language they are the same. But in physics we have taken advantage of the fact that there are two words and have chosen to use them to distinguish two ideas. We carefully distinguish velocity, which has both magnitude and direction, from speed, which we choose to mean the magnitude of the velocity, but which does not include the direction. Suppose, for example, that at a certain instant an object is moving as shown in Fig.

In Eq. Next, suppose that, because of the action of a force, the velocity changes to some other direction and a different magnitude, as shown in Fig. Let us consider a simple example.

A falling body moves horizontally without any change in horizontal motion, while it moves vertically the same way as it would move if the horizontal motion were zero. If an object is accelerating, some agency is at work; find it. Our program for the future of dynamics must be to find the laws for the force. Newton himself went on to give some examples. In the case of gravity he gave a specific formula for the force. In the case of other forces he gave some part of the information in his Third Law, which we will study in the next chapter, having to do with the equality of action and reaction. Again we find that the motion in the horizontal direction is at constant velocity.

As another example, let us suppose that we have been able to build a gadget Fig.

Course Introduction; Angular Velocity; Angular Acceleration

If we forget about gravity, which is of course balanced out by the initial stretch of the spring, and talk only about excess forces, we see that if we pull the mass down, the spring pulls up, while if we push it up the spring pulls down. This machine has been designed carefully so that the force is greater, the more we pull it up, in exact proportion to the displacement from the balanced condition, and the force upward is similarly proportional to how far we pull down. Now let us try to analyze just what Eq. If we can answer this question our problem is solved, for then we can start with the given condition and compute how it changes for the first instant, the next instant, the next instant, and so on, and in this way we gradually evolve the motion.

Why does the object move at all? Therefore the velocity which is zero starts to change, because of the law of motion. Once it starts to build up some velocity the object starts to move up, and so on. Now what about the velocity?

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And how are we going to find the acceleration? That is where the law of dynamics comes in. The law of dynamics tells us what the acceleration is. But Eq. The velocity changes a little bit because of the force, and the position changes a little bit because of the velocity. Now let us really solve the problem.

Kinematics and dynamics analysis of the main motion system of reciprocating machine tools

However, for practical purposes there are some little tricks by which we can increase the accuracy. Then to go through a reasonable total time interval would take a lot of cycles of computation. This can be done if we make a subtle improvement in the technique of the analysis. But the velocity when? The velocity at the beginning of the time interval is one velocity and the velocity at the end of the time interval is another velocity. Our improvement is to use the velocity halfway between. If we know the speed now, but the speed is changing, then we are not going to get the right answer by going at the same speed as now.

The same considerations also apply to the velocity: to compute the velocity changes, we should use the acceleration midway between the two times at which the velocity is to be found. Now we are ready to carry through our calculation. We just fill in the various spaces in the table one by one. This table now gives us a very good idea of the motion: it starts from rest, first picks up a little upward negative velocity and it loses some of its distance.


The acceleration is then a little bit less but it is still gaining speed. Thus the speed decreases. The agreement is within the three significant figure accuracy of our calculation! The above analysis is very nice for the motion of an oscillating spring, but can we analyze the motion of a planet around the sun? Let us see whether we can arrive at an approximation to an ellipse for the orbit. We shall suppose that the sun is infinitely heavy, in the sense that we shall not include its motion. At a given moment it is at some position in space. To analyze this further we must find out what acceleration will be produced by this force.