Kinetics

Now that we know something about the motion itself through the subject of kinematics, it is good to know something about how these motions are generated and what energy do these moving objects have, etc. through the study of kinetics. Kinetics basically introduces the relationship between the force and mass through Newton's laws.

Momentum (or linear momentum, kg.mps, lbf.sec or N.s) is the product of mass and velocity, p = mv and so it has the same direction as velocity. It can also be defined as the product of force and time p = Ft. According to the law of conservation of momentum, if there is no force applied to an object, its (linear) momentum remains constant. This is in agreement to the Newton's first law of motion that says a particle remains still or keeps a constant speed in motion unless an external unbalanced force is applied to it. Newton's second law of motion says that a particle's acceleration, a, in motion is directly related to the applied force and inversely related to its mass (F = ma). Obviously, the direction of force, velocity, acceleration, and momentum are all the same.

As a result of the above, we may say that since the earth's gravitational field applies a force to any object with mass m and results the object to fall with an acceleration of g = 9.81 m/s2, we call this force as the weight of the object W = mg. What prevents particles to keep their momentum according to the Newton's second law is an external force. One of these that naturally happens is the friction (dynamic friction μk in motion and static friction μs in stationery condition). This page (accessed 09/15/15) has very good illustrations on this matter. that always acts parallel to the contacting surface in the opposite direction, and its magnitude depends on the applied force N and how rough the surface is (shown by coefficient of friction, μ): Ff = μN. There are several scenarios for an object on flat or inclined surface with the associated equations of the acting forces, details of which is very nicely explained in this page (accessed 09/15/15).

If the frictional force is less than the applied force, the object gets out of the stationary status and starts moving. Assume trying to move a couch on sand or on a carpet or on a parket floor. How much push is needed is directly related to the frictional force that prevents the object to move, which is related to the coefficient of friction of the surfaces. Hey, one may say if the coefficient of friction of a surface could be equal to 1 no one could ever move any object on that! Nice, isn't it?! So we know that should be less than 1. It is, though, interesting that when the movement started, then less force is required to keep moving the objects! That is because the coefficient of friction drops after the motion begins, that is the dynamic friction is always less than static friction. It is good to know that these relationships can be presented in different coordinate system and, for example, can be dealt with in only one direction x or y.

Now assume we have a spring attached to the ceiling and we pull it a little and let go. It will oscillate up and down until stays still just like it was. This stillness of the spring is a state of equilibrium and the oscillatory movement is called natural or free vibration. Well, if the force is not removed or repeatedly applied, then we will still have the oscillation and it is called forced vibration, for example, hang a shirt to the end of that spring and let's say there is not air friction. The equations and relationships in this type of periodic motion is also explained in details on this page (accessed 09/15/15). Also, this page (accessed 09/15/15) has almost everything about angular kinetics and rotational motion which is the next subject to learn and get ready for FE. Thanks to whoever created it.

Page updated

Google Sites

Report abuse