Forces

The Physics Hypertextbook™
© 1998-2008 by Glenn Elert -- A Work in Progress
All Rights Reserved -- Fair Use Encouraged

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Discussion

Truth is ever to be found in simplicity,
& not in ye multiplicity & confusion of things.
Isaac Newton. Treatise on the Apocalypse.

The first chapter of this book dealt with the topic of kinematics -- the mathematical description of motion. With the exception of falling bodies and projectiles (which involve some mysterious thing called gravity) the factors affecting this motion were never discussed. It is now time to expand our studies to include the quantities that affect motion -- mass and force. The mathematical description of motion that includes these quantities is called dynamics.

Many introductory textbooks often define a force as "a push or a pull". This is a reasonable informal definition to help you conceptualize a force, but it is a terrible operational definition. What exactly is "a push or a pull"? How would you measure such a thing? Most importantly, how does "a push or a pull" relate to the other quantities already defined in this book?

Physics, like mathematics, is axiomatic. Each new topic begins with elemental concepts, called axioms, that are so simple that they cannot be made any simpler or are so generally well understood that an explanation would not help people to understand them any better. The two quantities that play this role in kinematics are distance and time. No real attempt was made to define either of these quantities formally in this book (so far) and none was needed. Nearly everyone on the planet knows what distance and time mean.

So a force is "a push or a pull". That's a pretty poor definition even for an informal definition. How about we build up the concept of force with real world examples? Here we go …

• Forces that act on all objects.
  • Weight
    The force of gravity acting on an object due to its mass. An object's weight is directed downward, toward the center of the gravitating body; like the earth or moon, for example.
• Forces associated with solids.
  • Normal
    The force between two solids in contact that prevents them from occupying the same space. The normal force is directed perpendicular to the surface. A "normal" in mathematics is a line perpendicular to a curve or surface; thus the name "normal force".
  • Friction
    The force between solids in contact that resists their sliding across one another. Friction is directed opposite the direction of relative motion or the intended direction of motion of either of the surfaces.
  • Tension
    The force exerted by an object being pulled upon from opposite ends like a string, rope, cable, chain, etc. Tension is directed along the axis of the object. (Although normally associated with solids, liquids and gases can also be said exert tension in some circumstances.)
  • Elasticity
    The force exerted by an object under deformation (typically tension or compression) that will return to its original shape when released like a spring or elastic band. Elasticity, like tension, is directed along an axis (although there are exceptions to this rule).
• Forces associated with fluids. Fluids include liquids (like water) and gases (like air).
  • Buoyancy
    The force exerted on an object immersed in a fluid. Buoyancy is usually directed upward (although there are exceptions to this rule).
  • Drag
    The force that resists the motion of an object through a fluid. Drag is directed opposite the direction of motion of the object relative to the fluid.
  • Lift
    The force that a moving fluid exerts as it flows around an object; typically a wing or wing-like structure, but also golf balls and baseballs. Lift is generally directed perpendicular to the direction of fluid flow (although there are exceptions to this rule).
  • Thrust
    The force that a fluid exerts when expelled by a propeller, turbine, rocket, squid, clam, etc. Thrust is directed opposite the direction the fluid is expelled.
• Forces associated with physical phenomena.
  • Electrostatic Force
    The attraction or repulsion between charged bodies. Experienced in everyday life through static cling and in school as the explanation behind much of elementary chemistry.
  • Magnetic Force
    The attraction or repulsion between magnetic bodies. Experienced in everyday life through magnets and in school as the explanation behind why a compass needle points north. (Actually, magnetism is the attraction or repulsion between charged bodies in motion, but this description is good enough for now. Electricity and magnetism are dealt with more thoroughly in later chapters.)
• Fundamental forces. All the forces in the universe can be explained in terms of the following four fundamental interactions.
  • Gravity
    The interaction between objects due to their mass. Weight is the name for the force of gravity.
  • Electromagnetism
    The interaction between objects due to their charge. All the forces discussed above except weight are electromagnetic in origin.
  • Strong Nuclear Interaction
    The interaction between subatomic particles with "color" (an abstract quantity that has nothing to do with human vision). This is the force that holds protons and neutrons together in the nucleus and holds quarks together in the protons and neutrons. It cannot be felt outside of the nucleus.
  • Weak Nuclear Interaction
    The interaction between subatomic particles with "flavor" (an abstract quantity that has nothing to do with human taste). This force, which is many times weaker than the strong nuclear interaction, is involved in certain forms of radioactive decay.
• Fictitious forces. These are apparent forces that objects experience in an accelerating coordinate system like an accelerating car, airplane, spaceship, elevator, or amusement park ride. Fictitious forces are not authentic forces in the sense that they do not arise from an external object, but rather as a consequence of trying to keep up with a changing environment.
  • Centrifugal Force
    The force experienced by all objects in a rotating coordinate system that seems to pull them away from the center of rotation.
  • Coriolis Force
    The force experienced by moving objects in a rotating coordinate system that seems to deflect them at right angles to their direction of motion.
  • "G Force"
    Not really a force (or even a fictitious force) but rather an apparent gravity-like acceleration experienced by objects in an accelerating coordinate system.
• Generic forces. When you don't know what to call a force, you can always give it a generic name like …
  • Push
  • Pull
  • Force
  • Applied Force

Isaac Newton (1642-1727) England. Did most of the work during the plague years of 1665 & 1666. Philosophiæ Naturalis Principia Mathematica (The Mathematical Principles of Natural Philosophy) published in 1687 (20+ year lag!) at Halley's expense.

Lex. I.   Law I. Corpus omne perſeverare in ſtatu ſuo quieſcendi vel movendi uniformiter in directum, niſi quatennus illud a viribus impreſſi cogitur ſtatum suum mutare.   Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.     Projectilia perſeverant in motibus ſuis, niſi quatenus a reſiſtentia aëris retardantur, & vi gravitatis impelluntur deorſum. Trochus, cujus partes cohærendo perpetuo retrahunt ſeſe a motibus rectilineis, non ceſſat rotari, niſi quatenus ab aëre retardantur. Majora autem planetarum & cometarum corpora motus ſuos & progreſſivos & circulares in ſpatiis minus reſiſtentibus factos conſervant diutius.   Projectiles continue in their motions, so far as they are not retarded by the resistance of the air, or impelled downwards by the force of gravity. A top, whose parts by their cohesion are continually drawn aside from rectilinear motions, does not cease its rotations, otherwise than it is retarded by the air. The greater bodies of the planets and comets, meeting with less resistance in freer spaces, persevere in their motions both progressive and circular for a much longer time.

(Newton, interpreted by Elert)

An object at rest tends to remain at rest and an object in motion tends to continue moving with constant velocity unless compelled by a net external force to act otherwise.

This rather complicated sentence says quite a bit. A common misconception is that moving objects contain a quantity called "go" (or something like that -- in the old days they called it "impetus") and they eventually stop since they run out of "go".

If no forces act on a body, its speed and direction of motion remain constant.

Motion is just as natural a state as is rest.

Motion (or the lack of motion) doesn't need a cause, but a change in motion does.

Definitio. III.   Definition III. Materiæ vis insita est potentia resistendi, qua corpus unumquodque, quantum in se est, perseverat in statu suo vel quiescendi vel movendi uniformiter in directum.   The vis insita, or innate force of matter, is a power of resisting, by which every body endeavours to persevere in its present state, whether it be of rest, or of moving uniformly forward in a right line. …   …       Definitio. IV.   Definition IV. Vis impressa est actio in corpus exercita, ad mutandum ejus statum vel quiescendi vel movendi uniformiter in directum.   An impressed force is an action exerted upon a body, in order to change its state, either of rest, or of moving uniformly forward in a right line.       Consistit hæc vis in actione sola, neque post actionem permanet in corpore. Perserverat enim corpus in statu omni novo per solam vim inertiæ. Est autem vis impresa diversarum originum, ut ex ictu, ex pressione, ex vi centripeta.   This force consists in the action only; and remains no longer in the body when the action is over. For a body maintains every new state it acquires, by its vis inertiæ only. Impressed forces are of different origins as from percussion, from pressure, from centripetal force.

In general, inertia is resistance to change. In mechanics, inertia is the resistance to change in velocity or, if you prefer, the resistance to acceleration.

In general, a force is an interaction that causes a change. In mechanics, a force is that which causes a change in velocity or, if you prefer, that which causes an acceleration.

When more than one force acts on an object it is the net force that is important. Since force is a vector quantity, use geometry instead of arithmetic when combining forces.

External force: For a force to accelerate an object it must come from outside it. You can't pull yourself up by your own bootstraps. Anyone who says you can is literally wrong.

Summary

• Newton's first law of motion also known as the law of inertia states that …
  • An object at rest tends to remain at rest and an object in motion tends to continue moving with constant velocity unless acted upon by a net external force.
  • concept-map-1.pdf [pdf]
  • special-principia.html
• In general, inertia is resistance to change.
  In mechanics, inertia is the resistance to change in velocity
  or, if you prefer, the resitance to acceleration.
  • The "normal" state of an object is to continue moving at a constant velocity.
    (A constant velocity of zero -- meaning, at rest for an extended period of time -- is one type of constant velocity.)
  • Objects resist changes in their motion.
  • Objects do not need to be pushed to keep going.
• In general, a force is an interaction that causes a change.
  In mechanics, a force is an interaction that causes a change in velocity
  (or, if you prefer, an interaction that causes acceleration).
  • The motion of an object won't change until a force is exerted from outside the object to cause a change.
  • When more than one force is present, it is the net external force that matters.

Some Common Forces
name/symbol(s)		when/where	direction
weight	W, Fg	due to gravity	down
normal	N, Fn	surfaces in contact	normal to surface
friction	ƒ, Fƒ	surfaces in contact	tangent to surface
tension	T, Ft	strings, ropes, cables, etc	along the axis
elasticity	Fs, Fe	springs, elastic bands, etc.	along the axis
buoyancy	B, Fb	immersed in a fluid	up
drag	R, D, Fd	moving through a fluid	opposite velocity of object
lift	L	moving through a fluid	perpendicular to flow
thrust	T	pushing a fluid	opposite velocity of fluid

Problems

practice

1. Draw a free body diagram of …
   1. a book lying on a level table.
   2. a person floating in still water.
   3. a wrecking ball hanging vertically from a cable.
   4. a helicopter hovering in place.
   Solutions …
   1. Answer it.
   2. Answer it.
   3. Answer it.
   4. Answer it.
2. Draw a free body diagram of a child pushing a wagon on level ground.
   Solution …
   • Answer it.
3. Write something different.
   • Answer it.
4. Write something completely different.
   • Answer it.

conceptual

1. Draw a free body diagram for each of the following situations …
   1. a car that …
      1. accelerates forward,
      2. cruises with a constant velocity, and then
      3. brakes to a stop
   2. a passenger in an elevator that …
      1. ascends from the lobby,
      2. cruises upwards, and then
      3. slows to a stop at the 35th floor
   3. a passenger in an elevator that …
      1. descends from the 35th floor,
      2. cruises downwards, and then
      3. slows to a stop at the lobby
   4. an airplane that …
      1. climbs to cruising altitude,
      2. cruises horizontally, and then
      3. descends to a landing …
      all with a constant velocity
   5. a child pulling a sled by a rope
   6. a home owner pushing a lawn mower
   7. a stationary crate on a ramp inclined 30° to the horizontal
   8. a child pushing a wagon up a ramp inclined 30° to the horizontal
   9. a laboratory pendulum held at an angle …
      1. before and
      2. after …
      being released by a student
2. The physicist and author Dr. John Fontanella in the first chapter of his book The Physics of Basketball claims to have identified "The Final Four". It's more than just a clever reference for fans of college basketball in the US. Mr. Fontanella has identified the four forces that affect the trajectory of a basketball. Determine these four forces and draw a free body diagram for a basketball as it leaves the hands of a player throwing a free throw. Assume a launch angle of 51° with backspin -- an initial condition that Dr. Fontanella says "results in the softest shot".

worksheets

1. The Physics Teacher has published several articles containing free body diagram worksheets. They are available free to members of the American Association of Physics Teachers (AAPT). Everyone else has to pay.
   1. Free-body diagrams revisited — I. James E. Court. The Physics Teacher. Vol. 37, No. 7 (October 1999): 427-433. Note: pages 428-431 are relevant to this topic.
   2. Exercises in drawing and utilizing free-body diagrams. Kurt Fisher. The Physics Teacher. Vol. 37, No. 7 (October 1999): 434-435.
   3. Free-body diagrams. James E. Court. The Physics Teacher. Vol. 31, No. 2 (February 1993): 104-108. Note: Questions 1-19 are relevant to this topic.

Resources

• free body diagrams
  • Free-body diagrams revisited — I. James E. Court. The Physics Teacher. Vol. 37, No. 7 (October 1999): 427-433.
  • Exercises in drawing and utilizing free-body diagrams. Kurt Fisher. The Physics Teacher. Vol. 37, No. 7 (October 1999): 434-435.
  • Free-body diagrams. James E. Court. The Physics Teacher. Vol. 31, No. 2 (February 1993): 104-108.
• historical
  • Principia Mathematica, Isaac Newton (1687)
  • The Mechanical Universe and Beyond (video on demand, login required)
    • Inertia, Galileo risks his favored status to answer the questions of the universe with his law of inertia.
    • Newton's Laws, Newton lays down the laws of force, mass, and acceleration.
• simulations
  • Vector Jockey [exe], a very simple Windows application, but it illustrates Newton's first/second law quite well

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