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6.5: The Forces We Typically Experience

According to the expressions we wrote above for the electric and gravitational forces, we might think that we would experience forces in all directions from all of the electrons and protons and mass distributed all around us. In fact, we experience only the gravitational force between us and the Earth, which is directed toward the center of the Earth. We experience very few electrical forces unless we have matter in contact with other matter. What happened to all the long range gravitational forces and electrical forces that must be acting between all of the electrons, protons, and neutrons in our bodies and all of the matter around us?

The answer is fairly simple in both the gravitational case and electrical case, but the reasons for not experiencing the forces are very different in the two cases.

In the case of gravity, all of our atoms do attract all other atoms in our vicinity. However, the gravitational force is a very weak force. Only when there are a very large number of atoms nearby, such as all of the atoms that make up the Earth, is the net force due to the interactions with all of these atoms sufficiently large for us to be aware of it.

Newton showed (by inventing calculus) that the attraction of a mass m to a sphere of mass M is the same as if M were concentrated at the center of the sphere, and the distance from the mass mto the center of the sphere is used in calculation.

The net gravitational force between you and the person sitting next to you is too small to feel, because there are not a sufficient number of atoms in the two of you. However, it is interesting to note, that even though it is extremely small, the universal gravitational constant G is experimentally determined by measuring the attraction of two solid metal spheres a foot or so in diameter hung a foot or so apart.

So, for all practical purposes, we experience only one gravitational force: the force between an object and the center of the Earth. This same force, described bu the same formula, however, also descries the attraction of the planets to our sun, the stars to each other in our galaxy and the attraction of the galaxies to each other in our galaxy cluster. And of course, it describes the attraction of an apple to the Earth, causing it to fall on Newton's head, or so the story goes.

Why don't two objects close together attract or repel each other due to the electrical force? Most objects don't do so, because they are composed of very large numbers of electrically neutral molecule. For every positive proton there is a negative electron, the electrical force that one molecule exerts on another molecule that is more than a short distance away si practically zero. However, because the positive and negative charges— the protons and the electrons—are not exactly in the same locations, molecules do exert attractive forces on nearby molecules. These are the atom-atom forces we encountered in Physics 7A.

What are Contact Forces?

Recall what happens when molecules get pushed very close together. The electrons then exert very large repulsive forces on each other. This is why substances resist compression. When we push on an object, it is the electrical forces between the electrons in the molecules of our skin and the electrons on the atoms at the surface of what we are pushing that are really doing the pushing. And it is the electrical forces holding molecules together that allow us to establish a tension in a stretched wire or cord.

So, we actually do experience electrical forces all the time. But because they are for the most part due to electrically neutral molecules interacting with each other, the net forces are “short range” and are not given by our simple formula. We often describe these electric forces as contact forces. To summarize, the forces that electrical neutral objects exert on each other when they are brought into close proximity really are electric forces, but they are very short range, and are not described by the one-over-r-squared long-range force formula.

Weight of Objects on the surface of the Earth

We directly experience one of the fundamental forces all the time—the gravitational force. We know this force as the weight of an object. In Physics 7A we used the fact that the weight of an object on the surface of the Earth is proportional to the mass of the object with the constant of proportionality, represented by the symbol g, having the value 9.80 N/kg. Now we know where the constant g comes from. Let's compare our two expressions for the gravitational force the earth exerts on an object:

First we write the general gravitational force \( F_G = G \frac{m_1m_2}{r^2}\) in a way that explicitly gives the force that the Earth exerts on an object of mass m located at the surface of the Earth:

\[F_{ Earth \thinspace on \thinspace object} = G \frac{M_E m}{r_{E}^2} \]

Our expression from Physics 7A is 

\[F_{Earth \thinspace on \thinspace object} = m g \]

Comparing these expressions, we see that 

\[ g= G\frac{M_E}{r_{E}^2}\]

and we also see why the expression FEarth on object = mg with g constant, is valid only near the surface of the Earth. (Note: in Part 3, we will treat g as the magnitude of the gravitational field, when we take up the Field Model of electric, magnetic, and gravitational interactions.)

Large Scale Gravity Forces

Our solar system is “held together” by the gravitational force. Our solar system is situated in a particular place in our galaxy due to the action of the gravitational force. When dealing with the gravitational force acting between astronomical bodies, we can’t, of course use the convenient expression FEarth on object = mobjectg  that works for objects on or very near the surface of the Earth. Rather, we have to use the actual masses and separations of the celestial objects in Newton’s universal law of gravitation.

The table below lists useful astronomical parameters for our solar system.

  \(Mass(kg)\) \(Radius(km)\) \(Orbital Radius(km)\)
\(SUN\) \(1.99 \times 10^{30}\) \(696,000\) \(n/a\)
\(EARTH\) \(5.98 \times 10^{24}\) \(6,370\) \(1.50 \times 10^8\)
\(MOON\) \(7.35 \times 10^{22}\) \(1,738\) \(3.85 \times 10^5\)
\(MARS\) \(6.42 \times 10^{23}\) \(3,407\) \(2.28 \times 10^8\)
\(VENUS\) \(4.87 \times 10^{24}\) \(6,050\) \(1.08 \times 10^8\)

Everyday Forces that Result from the Electric Force

Most of the forces we experience, other than weight, are ultimately due to the electrical force. But as we previously mentioned, these forces are due to the collective action of a vast number of oppositely charged particles, whose individual forces almost cancel out. When a spring is stretched, electrical forces acting between atoms of the metal are responsible for the restoring force that causes the spring to resist being stretched or compressed. The forces that bind atoms into molecules are electrical in nature, arising from the interaction of the various electrons and protons of the atoms that make up the molecules.

Historically, many names have been given to different kinds of forces, all of which are fundamentally electrical in nature. In Physics 7A we studied the force due to the pair-wise potential acting between particles. We will mention several others here, along with some useful conventions for dealing with them. It is worthwhile to remember, however, that fundamentally they are all due to the same basic interaction—the electric force between charged particle

Forces Exerted by Springs—Hooke's Law

Robert Hooke (a contemporary of Isaac Newton) discovered in 1676 that the force exerted by many stretched springs is proportional to the elongation or compression of the spring and in the opposite direction to the elongation or compression. The constant of proportionality depends on the way the particular spring is made (its material, size, number of coils, etc.). We used this model for springs extensively in Physics 7A. In equation form we express the force exerted by a spring as

\[ F_{by \: spring} = -kx . \]

More on the Contact Force

In a certain sense all objects behave like springs. When we place a book on a table, the earth pulls down on the book and the table pushes up. Why does the table push up? Well, the table behaves like a spring. The book pushing down on the table compresses the table a very slight amount, so the table pushes back. As the table becomes more and more compressed, it pushes back harder and harder. This process continues until the force exerted by the table equals the weight of the book. Then the two forces are in balance and the book becomes stationary.

It is frequently useful to “break up” the contact force into two components, one perpendicular and one parallel to the surface.

Perpendicular Component of the Contact Force:

This spring-like force that the table exerts is called the perpendicular contact forceor in some textbooks it is called the normal force. ( Here "normal" means "perpendicular.") This force is always perpendicular to the surface of the object exerting it. In our example of the book still pull straight down on the mass. The perpendicular component of the contact force would not be straight up, but rather it would be perpendicularto the table surface. The forces acting on the book would then not be in balance, and if there were no friction, the book would slide on the non-level table. We will often add a perpendicular sign to the subscript to designate the perpendicular component of the contact force; e.g., the perpendicular contact force the table exerts on book would be designated as \(F_{\perp \thinspace table \: on \: book}\) .

Parallel Component of the Contact Force:

Frictional forces between solid objects are exerted parallel to their surfaces. These forces arise because the molecules on one surface are attracted to the molecules of the other surface where they come into contact. We call these parallel contact forces.

It is sometimes useful (and conventional) to separately talk about the case when the surfaces are not moving with respect to each other and when they are. The former is called static frictionthe latter, kinetic or sliding friction.

In general, frictional forces act in a direction opposite to the motion, but this is not always the case; the direction can be determined only through analysis of the specific case under study. We use a parallel symbol to indicate the parallel component of the contact force. Using our previous example the parallel contact force exerted by the table on the book would be written as \(F_{\parallel \thinspace table \: on \: book}\).

Total Contact Force:

Both perpendicular and parallel contact forces can be present at the same time. They are, after all, simply the total contact force resolved into two perpendicular components. In the case of the mass sitting on a rough-surfaced table whose surface is not horizontal, both perpendicular and parallel contact forces are present; the total contact force balances the force exerted by the Earth, if the mass is indeed stationary.

Drag Forces

As we will see when we study fluids, when a fluid flows through a pipe, the inside surface of the pipe slows down the fluid adjacent to it. Conversely, when an object moves through a gas or liquid, there are drag or viscous forces retarding the motion of the object. These forces point in a direction opposite to the velocity of the object. Thus, when a car moves down the highway at high speed, the air exerts a drag force on the car, sometimes called air friction. This is force exerted on the car by air is directed "Backwards", opposite to the direction the car is moving.