## Thursday, February 08, 2007

### Motion what does it mean?

You would be surprised by the lack of understanding in physical science. Even w/ simple applications, many don't use any form of Newton's Laws to make sense of things?

Most can't state facts about circles, parabolas, and ellipses. If dealing w/ something that goes in a circle, it might be good to understand what a tangent line is. Perhaps, understanding how projectiles move through the air in a parabolic path. Lastly, it might be good to know that a ellipses is the path any planet makes in space.

How can people say they are a science based person and not understand a formula is an equation that shows a relationship between various quantities. That evaluating a formula consists of substituting numerical values for all but one of the quantities, then solving the resulting equation for the remaining quantity, which is the unknown. You hear they don't buy into formula based systems? How do they measure things?

Don't worry, I am not going into quantum theory and relativity.

There are three fundamental quantities upon which all other quantities in the physical sciences are based: length, mass, and time. The meaning of these terms seems evident all of us, yet define them in the dictionary or written word is quite unsatisfactory. (Try looking them up!)

You will have a debate w/ those who don't understand that we can measure them!!!

The term motion implies a change in an object' position in a given time interval. Motion in the real world is very complicated. For most not easy to understand.

So if we are to understand an object, we first have to understand its position in space.

How do we measure position? First, we need a point in space which is fixed during the object's motion. Then we imagine an x-y coordinate
system to be centered at that point. Such a coordinate system is called a frame of reference. Any point firmly attached to the earth's surface or other fixed objects can be considered the origin of a "frame of reference".

Sometimes an object moves in a circle. In this special case, we indicate position by the angle.

Changes of position, which are vital in the description of motion, can be denoted by specifying one of three possible quantities:

1) The distance, d, that an object travels.
2) The displacement, D, which is a vector quantity whose magnitude is the straight line distance between initial & final positions of an object, and whose direction is the direction from the initial to the final position. Note that displacement is not the same thing a distance. If a object moves from some point A to a point B,distance of 5mm, and then back again, the displacement is zero but the distance travels is 10mm.
3) The angular displacement, which is the change in the angle in the special case of circular motion.

These are basic laws know as Newton's Laws. Newton's laws are laws concerning forces and their relation to motion. For now, we will define a forceas a push or a pull. Since pushing or pulling sometimes causes an object to move, a force is often thought of as that which causes motion.

Newton's Third Law states that if object A exerts a force on object B, then B must exert a force on A equal in magnitude but opposite in direction. This pair of forces is called an action-reaction pair.

This law is often misunderstood. Consider the motion of a car. The tires of a car exert a rearward force on the ground. By Newton's 3rd Law, the ground exerting equal force on the car but in the forward direction. The car moves because the force due to the ground (the unbalanced force) pushes it forward. While it is true that the sum of the action plus reaction forces adds up to zero, the sum of the forces on the car does not add to zero. Hence, the car moves.

Mathematically, we can express many things that can't be seen w/ the eye.

Kinetic energy, is the energy a body possesses because it is moving. We measure work by joules. You have to make more joules to make more speed. For most, we understand at a steady speed, the kinetic energy remains constant. Hence (if there are no hills), the engine uses gas only to overcome friction, not to increase the kinetic energy.

Potential energy is the energy that a body has because of its position. For instance, a body high off the ground has the potential to do work. It can fall and the resulting motion can be harnessed to do work. The potential energy a body has because of height is called gravitational potential energy.

A body at a particular height does not have a unique amount of potential energy. Since a body gains speed as it falls, it is clear that if that body gains more speed that falling at less height, the amount of work it can do depends not only on the initial height but also on how far it falls.

Take a simple device, the pendulum, the higher the pendulum reaches a height from its lowest position, the more the pendulum has potential energy. At the same time its kinetic energy is zero because initially it is not moving know as total energymgh.

As a body moves toward its lowest position, its potential energy decreases. Its kinetic energy must therefore increase so that the total remains constant. At the lowest position, the potential is zero and all of the pendulum's energy is kinetic, making its speed a maximum there.

The maximum speed of the pendulum mg(h+H); quite reasonably, it depends on how high it is pulled up.

What happens to the pendulum after it reaches the bottom of its swing? Its momentum carries it past the bottom and back up again. It gains PE and lose KE, but you also have to add the effect of friction when the pendulum is headed back up.

By the way, if you can't get your pendulum high at the top of the swing, and you drop the mass of the leg behind the lowest point of the pendulum you are just putting the brakes on. For the normal joe & mary, that is 10,000 times per hour you have braked?