Concepts for Unit 4

Concepts for Unit 4: Free Particle Model aka Inertia and Interactions

By Marc Reif

Paradigm: Dry Ice block.
- Dry ice is solid carbon dioxide. Dry ice sublimes, or changes from a solid directly into a gas at room temperature. The dry ice block, when set on the table top, rests on a thin layer of carbon dioxide gas, without contacting the table. Given a tap, the dry ice block accelerates in the direction of the tap. After the tap, it moves at constant velocity in that direction. A dry ice block already moving at constant velocity, given another tap at right angles to the velocity, will accelerate in the direction of the tap, then move at a new, higher constant velocity at an angle to the original velocity. A dry ice block given a constant pull accelerates constantly. A dry ice block given many identical, evenly spaced taps also accelerates constantly.

Dynamics is the scientific study of forces that make things move. The study of forces that affect things but don't move them is called statics. When physicists began to apply the science of forces as developed by Isaac Newton, it caused a revolution in science and technology. This is one of the most significant events in the history of civilization. We begin our explanation of why things move with objects whose motion is described by the constant velocity model, because they are not acted on by a net force.
A force is a push or a pull.
Physicists identify four fundamental forces that affect matter in the universe. Gravity, the electromagnetic force, the strong nuclear force, and the weak nuclear force.
Gravity is an attractive force between any two objects with mass.
The strong nuclear force holds atomic nuclei together.
The weak nuclear force acts in the radioactive decay of some "weakly-interacting" particles. It has (relatively recently) been unified with the electromagnetic force.
The electromagnetic force concerns the attraction between electrons and protons, and the repulsion between electrons and electrons, or the repulsion between protons and protons.
Objects are made of atoms, and atoms are mostly empty space. Why don't two objects pass right through each other, if they're mostly empty space? The structure of the atom and the electromagnetic force give the answer. All atoms have electrons on the outside, and all electrons repel other electrons. Objects are solid because their electrons repel the electrons of other objects. When one object exerts a contact force on the other, it is actually the electromagnetic force of the electrons of the two objects which is interacting.
- Forces that affect objects in our everyday experience may be the result of physical contact between two or more objects, or of non-contact forces. Gravity and the electromagnetic force are the non-contact forces we discuss most often in this course (the strong force and the weak force are the other two non-contact forces). Objects need not be touching for a non-contact force to affect them.
Newton formulated three laws of motion which are the foundation of dynamics and statics.
Newton's first law: An object stays in a state of constant velocity unless acted on by a force. This means the object may move in a straight line at constant speed, or may stay at rest (a state of constant zero velocity). This is the idea of inertia. Inertia refers to the tendency of objects to persist in a state of constant velocity. (Note: be careful with words like force, inertia, momentum, and energy that are used casually in everyday speech but have a specific meaning in physics. Many physics students have had to overcome the belief that they "already know" what these words mean. The upshot: they didn't know what the words mean in physics).
The best measure of the quantity of inertia is mass. Changing the motion of an object with a lot of mass is difficult, so you could say it has a lot of inertia. Physicists distinguish between gravitational mass (the mass as measured by the effect of a gravity field on an object) and inertial mass (the mass as measured by the object's resistance to acceleration). For our purposes, we will consider them to be the same thing (they are extremely close, in any case).
When an object is in contact with a surface, the surface exerts a force perpendicular to itself on the object. We call that force surface or normal force. The force is always perpendicular to the surface. Normal means perpendicular in this context. The normal force is how we experience our weight. If we are not in contact with a surface (falling), then we accelerate towards the center of the earth at g, and we feel weightless.
When a force is exerted on a very rigid object (say a concrete wall), it appears that the object does not move. But how does the wall "know" to push back with an equal and opposite force? The answer is in the molecules. The push on the wall deforms the wall a tiny bit and stretches the molecules, which act like tiny springs, because of the electromagnetic forces holding them together. This tension of the "tiny springs" (molecules) produces force proportional to the push on the wall. That is how the wall "knows" how hard to push back. Push harder, and you stretch the molecules more.
We leave Newton's second law for Unit 5.
- Newton's third law is stated in plain English like this: If an object exerts a force on another object, the second object exerts a force equal in size and opposite in direction on the first object. A physicist once said: "If you punch the wall, the wall punches you back, just as hard." Be careful in the way you state this. As in most physics concepts, the everyday statement of it leaves a lot to be desired in the precision department.
  - Gravitational Force Law
- We determined the amount of gravitational pull on an object (gravitational field strength) by a simple experiment. We suspended known masses from spring scales and graphed the gravitational force as registered on the spring scale. This gave us a rule that can be applied in many situations (the gravitational field strength is surprisingly consistent across the planet)

Memorize this gravitational force "law": when you need to determine the force of gravity on an object, you multiply its mass (in kilograms) by 9.81 N/kg.

Friction (may be presented in Unit 4 or Unit 5)

Friction occurs for two reasons: surfaces, even smooth surfaces, are always microscopically rough, and when the molecules of two objects come in contact they bond together, or "cold weld." The amount of friction is different for different combinations of surfaces. This is because of the different textures and differences in the chemical composition (differences in the arrangements of the electrons and nuclei) of the two materials.
Cold-welding is incomplete. It does not produce a single, "welded-together" object. In general, this is because of the interference of dirt, oil, and oxygen in the air. The dirt and oil are deposited on surfaces and interfere because of their presence. The oxygen reacts with some surfaces to produce a layer of chemical on the surface that does not cold-weld very well.
Sliding (kinetic) friction is a force that occurs when two surfaces are in contact and one is in motion relative to the other. It opposes the direction of motion. Note: not all frictional forces oppose the direction of motion.
We compare the force of sliding friction between two different substances by dividing the amount of force it takes to slide an object on a surface at constant speed by the Normal force on the object. This leads us to a dimensionless quantity we call mu, or the coefficient of friction. The higher the mu, the more friction there is between two surfaces. Many physics books and engineering handbooks contain tables of coefficient of friction for various combinations of substances.
Static friction is higher than kinetic friction for a surface. This is because left over time, the object "sinks in more deeply" and bonds more completely to the surface. A common experience is to slide a heavy object from rest. Once the object is moving, the force you apply to keep it moving is less than the force to start it.
Rolling friction is generally very low (this is the reason ball and roller bearings are used so often). This is because any point on a wheel or ball always contacts a different point on the surface. The two surfaces don't slide. The friction results from the deformation of the surface and the wheel as the wheel moves along.
Objects moving through the air are subject to a drag force. When the gravitational force pulling on a falling object equals the drag force, the object moves at constant velocity. This velocity is called terminal velocity. The drag force is proportional to the square of the velocity of the object (and to the cross-sectional area of the object, the density of the air, and the coefficient of drag). For the exact relationship, consult a college physics book.
The coefficient of drag is analogous to the coefficient of friction. It is a dimensionless quantity that is a measure of how "slippery" an object is in air. Note that a common way of naming drag is to call it air friction.

19 April 2005