Physics 122

Dynamics Review

 

It was Galileo who originally asked what caused motion to change but it was Newton who created the laws (three of them) which allow us to describe these changes mathematically. Forces are what cause changes in motion. A force is simply a push or pull. The push or pull could be caused by a person, gravity, electric fields etc.

An extremely important point to remember is that forces are vectors. They have both magnitude and direction. This point will be very important later

Newton's first law which states that:

An object with no net force acting on it remains at rest or moves with constant velocity in a straight line.

The first law is often interpreted as saying that objects resist changes in motion. This resistance to motion changes is often given the name inertia. Objects with large inertia resist changes in motion better than objects with small inertia. So what do we use to measure the inertia of an object? Simply, its mass is a measure of its inertia. It is easier to move a small mass than a large one.

Second Law

The acceleration of a body is directly proportional to the net force on it and inversely proportional to its mass.

Now it's easy to take the second law and derive a formula from it. We simply arrive at:

                                               

where Fnet is the net force measured in what else but newtons! (symbol N)
m is mass (kg)
and a is acceleration (m/s2)

Third Law

When one object exerts a force on a second object, the second object exerts a force on the first that is equal in magnitude but opposite in direction.

This law is sometimes stated as, "For every action there is an equal and opposite reaction." If object A exerts a force on object B then the reaction force is the force that object B exerts on object A. Notice that we always talk about the same two objects when identifying the action-reaction pair.

Types of Forces

Forces can often be classified into two major categories:

  1. contact forces - These occur when one object exerts a force on another through direct contact. An example of this type of force is friction which we will study later.
  2. action-at-a-distance forces - These occur when one object exerts a force on another over a distance. An example of this type of force is the pull of gravity.

Now it is not always clear whether a force belongs in the first or second category since some contact forces look like action-at-a-distance forces at the atomic scale. In addition, just how do action-at-a-distance forces function? We may return to this question at a later time.

Fundamental Forces

So, how many different kinds of forces are there? Physicists believe there is only one fundamental force, but the best they've been able to do so far is describe it in terms of these three:

  1. Gravitational - This attractive force acts between all matter. It is actually the weakest of the fundamental forces.
  2. Electroweak - With the exception of the gravitational force, almost all forces you encounter everyday are some form of the electroweak force. This force used to be known as two separate forces (electromagnetism and the weak) but physicists have fairly recently been able to treat them as one. Examples include magnetic forces, friction and duct tape.
  3. Nuclear (or colour) - This force acts between subatomic particles like quarks. It has nothing to do with the actual colour of the object.

Weight

A guy by the name of Galileo supposedly dropped objects of the Leaning Tower of Pisa and showed that they all accelerated at the same rate regardless of mass. However, even today many people believe otherwise. The fact that air resistance can play a significant role probably contributes to this incorrect idea.

For objects near the surface of the Earth, this acceleration is equal to 9.80 m/s2 (or 9.81 m/s2). Since this acceleration is so special it is given it's own symbol 'g'. Objects that are experiencing ONLY this acceleration and no others are said to be in freefall.

The weight of an object is the gravitational force exerted on it by the Earth (or another planet). It is calculated by using the acceleration due to gravity for that planet. In the case of Earth this acceleration is g.

 

                       

where Fw is the weight (N)
m is the mass (kg)
g is the acceleration due to gravity (for Earth g=9.80 m/s2) Remember that g is positive!

Now instead of writing Fw for the weight we'll usually write W. Makes more sense, doesn't it? So we'll have W = mg.

Remember that force is a vector and therefore weight is a vector. So in which direction does the weight vector point? To be precise the weight vector points toward the center of the planet but for all practical purposes we take this as simply down.

Normal Force

When an object is in contact with a surface, the surface exerts a force on the object that is perpendicular to the surface. This is the force which keeps solid objects from passing through each other. The reason it's called a 'normal' force is that this is the word physicists use to mean perpendicular. (They had to get the word 'normal' into their vocabulary somewhere). The normal force is sometimes denoted by FN but usually just N is used. So if we were to draw the two forces which acted on a book lying on a table it might look like:

The normal force and the weight balance which is why the book doesn't fly off or fall through the table.

Tension

Tension results when you write a physics test! Tension forces result when objects such as ropes, springs, rubber bands etc. are stretched. We usually use the symbol T to distinguish tensions. In the simple case of a rope holding up a mass, the rope stretches just enough so that it provides an upward tension force equal in magnitude to the weight of the object

 Pulleys (not a force)

Pulleys themselves don't create a force. They simply change the direction of a tension force. To pull the cart pictured below requires a tension in the rope

 Friction

Friction is just another force like the ones we looked at in the 'types of forces' section. It acts between surfaces in contact and opposes their motion. Friction is a form of the electroweak force but even today scientists don't have a complete theory as to the inner workings of friction. We do know that its value is dependent on the types of surfaces in contact and the contact force (i.e. the normal force).

One quantity that friction doesn't usually depend on is the surface area in contact. For example, the friction force is the same whether you slide a filing cabinet on its bottom or its side. This seems counter intuitive but it's generally true!

There are two different types of friction:

  1. Static Friction (Fs) - When two objects are at rest relative to each other, this is the force of friction you must overcome in order for them to move. This friction force increases from zero as you apply more and more force to try and move the objects. Eventually you will overcome the friction force and the objects will begin to move relative to each other and we now have to deal with.
  2. Kinetic Friction (Fk) - This is the frictional force that arises because two objects in contact are in relative motion. (Some textbooks call it sliding friction since the objects we'll deal with are always sliding) The value for the kinetic friction is always less than the static value since it is harder to get something moving than it is to keep it moving

We'll only be dealing with kinetic friction since the static value depends on the applied force and is not as easily calculated. So how do we calculate the force of kinetic friction? It's quite simple, actually. Remember that friction only depends on the types of surfaces and the normal force. This leads to this formula:

                            We also use  Ff  = uFn

The quantity N is, of course, the normal force and µk is known as the coefficient of kinetic friction. (The µ is not a u but the Greek letter mu.) The coefficient has no units and it is a measure of the 'roughness' of the surfaces. Its value can range anywhere from .01 to well lubricated surfaces to 1.5 for very rough ones and it is only found through experiment. It is quite difficult to determine consistent values of the coefficient for a particular set of surfaces. Two seemingly identical sets of steel and glass may have different coefficients.