image Forces and Motion - Newton's Laws of Motion

Georgia Perimeter College

Objectives

  1. Be able to find the net force on an object.

  2. Be able to state if an object is being accelerated in magnitude, direction, both or neither.
  3. Recognize a state of equilibrium.
  4. State and explain all three Laws of Motion by Sir Isaac Newton.
  5. Point out and correct common misconceptions related to forces and motions.
  6. Explain correctly the difference between weight and mass, and the measurements on scales used to weigh objects.
  7. Recognize that the motion of an object in a two dimensional (x-y) plane is equivalent to two independent motions along the x and y directions;
  8. Describe the motion of a projectile falling freely in the presence of the earth’s gravitational acceleration;
  9. Apply the equations of motion at a constant acceleration to the free fall motion of an object.
This section addresses, in whole or in part, the following Georgia GPS standard(s):
  • SKP2. Students will investigate different types of motion.
    1. Sort objects into categories according to their motion. (straight, zigzag, round and round, back and forth, fast and slow, and motionless)
    2. Push, pull, and roll common objects and describe their motions.
  • SKP3. Students will observe and communicate effects of gravity on objects.
    1. Recognize that some things, such as airplanes and birds, are in the sky, but return to earth.
    2. Recognize that the sun, moon, and stars are in the sky, but don’t come down.
    3. Explain why a book does not fall down if it is placed on a table, but will fall down if it is dropped.
  •  S2P3. Students will demonstrate changes in speed and direction using pushes and pulls.
    1. Demonstrate how pushing and pulling an object affects the motion of the object.
    2. Demonstrate the effects of changes of speed on an object. 
  • S4P3. Students will demonstrate the relationship between the application of a force and the resulting change in position and motion on an object.
    1. Identify simple machines and explain their uses (lever, pulley, wedge, inclined plane, screw, wheel and axle).
    2. Using different size objects, observe how force affects speed and motion.
    3. Explain what happens to the speed or direction of an object when a greater force than the initial one is applied.
    4. Demonstrate the effect of gravitational force on the motion of an object.
  • S8P3. Students will investigate relationship between force, mass, and the motion of objects.
    a. Determine the relationship between velocity and acceleration.
    b. Demonstrate the effect of balanced and unbalanced forces on an object in terms of gravity, inertia, and friction.

This section addresses, in whole or in part, the following Benchmarks for Scientific Literacy:
  • Things move in many different ways, such as straight, zigzag, round and round, back and forth, and fast and slow.
  • The way to change how something is moving is to give it a push or a pull.
  • Changes in speed or direction of motion are caused by forces.
  • The greater the force is, the greater the change in motion will be. The more massive an object is, the less effect a given force will have.
  • An unbalanced force acting on an object changes its speed or direction of motion, or both. If the force acts toward a single center, the object's path may curve into an orbit around the center.
  • The change in motion of an object is proportional to the applied force and inversely proportional to the mass.
  • Whenever one thing exerts a force on another, an equal amount of force is exerted back on it.

This section addresses, in whole or in part, the following National Science Education Standards:
  • The position of an object can be described by locating it relative to another object or the background.
  • An object's motion can be described by tracing and measuring its position over time.
  • The position and motion of objects can be changed by pushing or pulling. The size of the change is related to the strength of the push or pull.
  • The motion of an object can be described by its position, direction of motion, and speed. That motion can be measured and represented on a graph.
  • An object that is not being subjected to a force will continue to move at a constant speed and in a straight line.
  • If more than one force acts on an object along a straight line, then the forces will reinforce or cancel one another, depending on their direction and magnitude. Unbalanced forces will cause changes in the speed or direction of an object's motion.
  • Objects change their motion only when a net force is applied. Laws of motion are used to calculate precisely the effects of forces on the motion of objects. The magnitude of the change in motion can be calculated using the relationship F = ma, which is independent of the nature of the force. Whenever one object exerts force on another, a force equal in magnitude and opposite in direction is exerted on the first object.

The World According to Newton

Introduction

How many of the statements below do you agree with?

       You need force to keep a car moving.

       Friction is an inherent part of an object.

       Going at a steady velocity in a circle around the Earth means there are no accelerations.

       Your weight tells you have much stuff you have.

       Equilibrium is the absence of forces.

       Inertia is what keeps you from getting up in the morning.

With the possible exception of the last one, everything above is a false statement.  Surprised?  The misconceptions about Forces are astoundingly widespread.

Here’s the main point of this chapter.  If you keep this in mind, you will be smarter than most other people you know, and definitely ahead of your students:

Forces cause CHANGES in motion.  You need forces to speed you up, slow you down, overcome other forces that resist your motion, turn you, make you spin, stop you from spinning, make you change direction and even to make you stand still. 

You do not need forces to move at a steady speed but if you keep the same speed yet change direction, like a moon around a planet, then you have a force acting on you anyway. 

You are ALWAYS under the influences of forces, but if forces act on you such that they cancel each other out, it only APPEARS like there are no forces on you but trust me, they are there.

 

 

Vocabulary

 

 

Force

Mass

Acceleration

Equilibrium

Net Force

Friction force

Normal force

Gravity

Weight

g

 

Inertia

Units of Mass

Units of force

Units of acceleration

British system

Metric system

Magnitude

Direction

Action

Reaction


 

What are Forces?

 

We need to separate forces from the effects of forces.

 

In everyday language, forces are pushes or pulls on an object

 

Generally, said object doesn’t care what the source of the push or pull is, it just reacts to the force.  More precisely, it reacts to the SUM of all the forces acting on it at one instant. 

 

Link to lesson on force

 

   


Forces have TWO values 

You know what a push or pull is. 

And you know that pushes and pulls have a direction. 

You push forward on a door, it opens. 

You pull it towards you to close it.    

You know that pushes and pulls have an amount. 

There are strong pushes and weak ones, ditto for pulls. 

 

So forces have two qualities:
    1.  An amount (or magnitude)

    2.  A direction.

 

We can indicate directions with various pairs of values, such as in versus out, right versus left, up versus down, positive versus negative, or use angular measures in degrees, most often from 0 to 360.

 


Forces in the same line

A strong push to the right pushes some slowpoke out of your way.  His push back at you cancels out your push towards him. 

 

You pull forward on the reins of a horse that you are leading, the recalcitrant horse pulls backwards on you.  His pull being more than yours, you move towards him, not vice versa. 

 

In the first case, think of these not as 2X amount of force summed from X amount in both directions but think instead of one force as +1X in one direction and –1X force in the other.  The directions were opposite so they have opposite signs but since  the magnitudes are equal (1), the sum of +1 and -1 equals zero. Nobody moves.  

 

The second case has directions opposite and magnitudes unequal (+1X and -2Y, the + and – indicating direction and the 1 and 2 as force magnitudes); the Sum is -1Y.  You had better have some sugar handy for your close encounter with Mr. Horsey.

 

The point here is that you can’t just equate the values or magnitudes of the forces. 

1 + 1 does not always = 2. 

You need to account for the direction of the force, in this case, positive and negative (forward versus back, up versus down, inwards versus outwards, etc.)

 


Forces along perpendicular lines still equal ONE TOTAL FORCE

You need to know about their directions and (here’s the Big Point), only forces in the same line affect each other (add together in both positive and negative ways). 

 

A force that is perpendicular to another force doesn’t affect the other force’s effect.  Some guy pulls you forward and another one pulls to the right, you will move in both directions.

 

But ultimately, if you add all the ‘left-right forces’ into one sum total force in this direction, and do the same with the ‘up-down forces’ into a second total force in this direction, you can finally add these up and get some single equivalent sum force (magnitude) in ONE single equivalent direction. 

 

Take a classroom of kids into a circle around you, give each one a rope to you and have them pull.  In general, their forces will cancel out but if you do move, you will move in ONE direction, just as if the one kid in that position did all the pulling.  You and slowpoke don’t move because there is no TOTAL NONZERO force on you two.

The total nonzero force is called the Net Force and it has a single magnitude value and a single direction.

 

Finally, it is not a given that you end up with a force of magnitude X and direction whatever.  If the forces are opposite in direction but equal in amount, the Net force is zero.  There are still individual forces on you, they just happen to cancel out in sum because of the directional aspects. 

 

This is called equilibrium

 


 1 Forces mean motions change

 

Push on a ball, it goes from stationary to moving.  Do the same push on a car and little or nothing happens.  Clearly, a push CAN accomplish something, but what is the difference?

 

This stumped the ancient sages and still stumps people today, though it shouldn’t.

 

Forces cause a change in the status of the motion of an object.  As you should remember from the course module on the Motion of Objects, a change in motion is an acceleration, a change in velocities.  A change in velocities equals a speed up or slow down but it is NOT a steady state. 

 

A steady velocity means the object has no force on it.  A steady velocity can be forwards, backwards, or even the special case of no motion at all (it is still a steady value, right??)

As long as the value or direction is unchanged, no forces are being applied.

 

So let’s make an equation: 

A = F (acceleration equals force). 

Well, not quite true.  Remember the force on the ball and the car?  What was the critical difference between them? It wasn’t the value of the force, nor its direction.  It was something, some property of the pushed objects. Both can roll (though in different ways) so it isn’t shape.  Give up?  It’s the mass.  The same push on the heavy object (Car) made a dramatically smaller acceleration.  If for fun we say that the Force on the ball has a value of 1 and the acceleration is a value of 1, then the value of the acceleration on the car is much much less because the motion change was less.  Since F didn’t change, but A did, both had to have been reduced by some net effect, reduced by the mass of the car.  Thus our equation becomes Acar = F/m(car).

 

Let’s rewrite this to get rid of the division.  Now it is F = m*a (mass times acceleration).  This is Newton’s Second Law.  A force applied to a small mass gets you a big acceleration (the ball moves a lot),  The same force to a large mass must have acceleration reduced (car moves little) else the equation is not in balance.

 

Here’s the conceptual point.  You get motion changes out of forces applied, the amount of change controlled inversely by the mass of the object involved. When forces act in the same direction as velocity, you get speeding up or slowing down. And if there is no motion change, there is no force.  It is not F = m*v (mass times velocity), but F = m*a.

 

Link to lesson on mass

 

Get a wheeled vehicle that you can have empty or filled.  Examples are wheelbarrows and shopping carts.  (I’ll pretend to use the shopping cart). Practice pushing the empty vehicle with your hands such that you always apply the same amount force.  See how far the cart goes.  If the wheels are well lubricated so that there is minimal friction.  You should have the cart go about the same distance from you each push.  You will also see (and show to students) that the cart’s speed goes from zero to some value when you push it (a positive acceleration) and then go back to zero (a negative acceleration).

 

Now put something into the cart—cans, kids, books, whatever.  Push the cart with the same amount of force.  Because there is additional mass, your acceleration will be less (more mass balanced by less acceleration = same force).  If you want to get the same accelerations you had before (making the cart go the same distance is your proxy measurement here even though distance isn’t acceleration), you will have to add more force for each extra mass.

 

Forces have units.  In metrics, we call force values in newtons, named after Sir Isaac.  It is abbreviated as N or Nt.  Mass is in kilograms.  If you have problems in grams, convert to kilograms first.

 


Newton’s Second Law is that the total external force on an object is equal to the object’s mass multiplied by the acceleration experienced by the object, or F = ma.
 

 


 

Forces change motion in two ways

 

But we’ve only talked about forces in one direction, forward-back.  Recall that forces have directions as well as magnitudes.  So what happens if the motion is in one direction at some speed, but the force is applied from the side?  Then the direction of motion will change for sure. Sometimes the velocity amount does too, but it doesn’t have to.

 

Consider a little girl running steadily in a straight line, about to pass you.  You and the child momentarily grab hands and what happens?  The kid’s motion changes in direction, but the speed doesn’t.  Your sideway force changed which way she was heading.  What would happen if you held on?  The child would circle you but her little feet would keep the speed value.  If you let go, the child would no longer circle you but would keep going as well.  So forces can speed things up (or slow things down), or change the direction, or both.  Perpendicular forces to the direction of travel change those directions for sure, speeds sometimes.  Parallel forces speed things up or slow them down. 

 


1.

3  The force of gravity and its effect on YOU

 

Gravity is a force that pulls on you down to the center of Earth.  Or it would if the ground didn’t stop you.  We’ll talk about what gravity IS in a later section; here we concentration on what it DOES.

 

Gravity is a force that brings matter together.  You and the Earth have matter. If you push upwards, gravity brings you back down.  (Actually, you pull each other together but that F=ma thing, with your widely different m’s, generates very different a’s, and yours is much more noticeable than Earth’s).

 

All things with matter generate gravity, but the Earth is far more massive so the gravity of a flower, you, a local building, don’t seem all that obvious.

 

The rate that gravity changes your motion is measured by the acceleration it produces on you (and everything else).  Things fall at an acceleration rate of 9.8 meters per second, per second. 

 

That is, your velocity (speed) changes as you move towards the Earth at an increasing amount of 9.8 meters per second every second (and abbreviated as 9.8 m/s2).  In one second, you are moving from no motion to 9.8 meters per second.  After two seconds, your velocity has grown to 19.6 meters per second.  After three seconds, it is 29.4 meters per second.  After that, you probably won’t care.  (In British units, it is 32 feet per second per second, 32 ft/sec2). 

 

Notice that nothing was said about mass.  Whether you are a teacher as anorexically thin as a model, or as solid as an oak table, you will both fall at the same rate.

 


Hands-on activity

Here’s a demonstration that shows that mass has no affect on how fast things fall.

 

Find two solid balls of different masses.  Considering that most solids have about the same density, different sizes of solid balls will work well, too.  You can use a billiard ball and a marble for example.  Other kinds of balls that work here are ball bearings and balls as big as bowling balls.  But, don’t use hollow balls, like basketballs or ping pong balls as they add the additional force of non-negligible friction.  Other balls that are not smooth, like golf balls or soccer balls, also add friction.

 

Take the two balls and roll them down an incline, such as a long piece of wood at a small angle from the horizontal.  If you start them at the same time, they will arrive at the bottom at the same time.  You can have students, if not you, weigh them to show how much different mass they have.  Then it should be clear that mass has no affect on how something falls.

 

Note:  young students often insist that one ball arrived before the other.  Sometimes it is the fact that they hear multiple thumps when the balls arrive at the bottom but they mistake the multiple thumps of the bouncing balls for the thumps of the heavy balls versus lighter balls.  Also, when they predict which ball would arrive first, some do the usual misconception that heavier equates to faster while some will do the opposite, that the heavier one is inhibited in some way so the lighter one will be faster.  Challenge them to explain themselves, and then the results when they agree that both balls arrived together.  Final note:  balls massively different in size WILL arrive at different times because the bigger ball has the larger circumference and covers the ground more easily.

 

One additional aid here.  It can be more instructive if you roll the balls down an incline that has side walls.  Then they can race along opposite sidewalls (any friction is equally applied).  I used a flat table-top hockey gameboard from a 14-in-1 game table that had small walls on all sides.  It was instructive also to see that they bounced back upwards equally, in an equal number of increasing smaller bounces!  Remember this when you do the section on energy conservation, and loss.

 

Further proof can usually be found by taking the solid balls to some height and releasing them simultaneously, to see them arrive on the ground at the same time.  A movie camera that can take high speed movies, and play them back one frame at a time is good project for students to see the simultaneity of their falling.

But mass does change the amount of force needed to pull you at that rate of fall.  A little mass, a little force.  A lot of mass, a lot of force.  Same rate of fall though.

 

So we measure the amount of gravity FORCE on you by measuring your WEIGHT.  The more mass you have, the more force there is, the more you weigh.

 

Recall that F = ma. 

 

That “a” is the constant, 9.8. 

 

So the force of gravity is strictly proportional to mass. 

 

The bathroom scale measures weight but that is just your mass multiplied by the rate of gravity.  Since that is a constant, we give that “a” and its value a special symbol of its own. 

 

9.8 m/s2 is known as g, as in gravity’s rate of acceleration

 

For every kilogram of mass (every kilogram of stuff), gravity’s force = m*a, or 1kg*gm/s2, or 9.8 Newton’s of weight

 

5 kilos?  49 Newtons (or 49N). 

 

For those of us stuck in British units, g = 32 ft/sec2, mass is in ‘slugs’(!) and one slug yields one pound of force or weight.  If you weigh 200 pounds like I do, you have a mass of 200/32, or 6.25, slugs.  Well, it gives me an excuse to be sluggish….

When you weigh yourself on a bathroom scale (or veggies at the market on a hanging scale), the result is weight, the amount of force that gravity is pulling down on you or the carrots.  But in some countries they use kilogram scales.  Kilogram is mass!  Asking for a kilo of bologna is not using a weigh value.  But since weight and mass ARE PROPORTIONAL, that’s okay, as long as you know which is which. 

Weight/mass = g, which is a constant. 

 


Friction force

Another common everyday force is friction

Friction is actually due not to gravity but to another natural force to be discussed in detail later, electromagnetic force.  At atomic scales, gravity isn’t important but the positive and negative charges of the parts of the atoms (and of molecular fragments) are strong.  When two things gets close enough, the attraction and repulsion of these charges takes over.

Friction is the interaction of big macroscopic things when they are microscopically close.  The attractions draw things together, the repulsions push them apart, but these pulls and pushes are forces felt as friction.  Thus friction is always a resistance to the motion of things.  These interactions never help motion, they inhibit it.  So if your shoe is sliding forward, friction slows it down.

Friction is a force that resists motion and only occurs when things slide or roll against each other.

Link to lesson on friction

Here is a good place to show friction and gravity together.  Remember the solid balls experiment above?  Now do this with equally sized (and, if you can, equally massive) balls, like a ping pong ball and a similar-sized solid ball, or a bowling ball and equally sized inflated ball.  See if they too arrive at the bottom of the incline (or a long fall down in the air) at the same time.  When they don’t ask what could affect the balls that counteracts gravity?  Make sure you have students see that we are watching TWO SIMULTANEOUS forces at work!

Friction is proportional to the gravitational force of the moving object as it pushes down on the source material of the friction.  For objects just sitting still, friction is the force that resists you making the object move in the first place.  Thus, to make or keep something moving requires a sideways force greater than the friction that is resisting the motion.

We have two forces then at work.  The forward moving push or pull against the resisting force of friction.  Remember what we said about forces in the same line of direction?  Add them together keeping track of the positive and negative signs. 

With friction we have two little quirks. 

1.  First, you get NO effect until you overcome friction.  The amount of friction grows with the amount of applied force until the maximum friction force is reached.  Any additional force moves the object.  So if the friction is –f in value and direction, the SUM total force is +X – f.

2.  Second quirk.  The amount of friction is proportional to two values, the weight of the mass being moved and a physical parameter μ (pronounced Mu, a Greek letter), called the coefficient of friction, and it depends entirely on the nature of the frictional object. 

In fact, this “Mu” value is entirely empirical, it is a measured quantity, with some range, and is still not predictable. 

Mu lies between 0 and 1 but is usually closer to the former.  So even though the friction force acts in the (opposite) direction of motion, it depends on the perpendicular force of gravity!

Friction can be non-horizontal too.  Dropping things in air or water begets frictional forces from the fluid.  Dropping a rock and a feather clearly shows that the feather is affected by friction from the air!  To show that friction is an additional force and that gravity is still there, drop a hammer and a feather outside into a patch of dirt (so you don’t damage any flooring or the hammer!) and then show the movie clip of an Apollo astronaut on the moon dropping a feather and hammer.  In the absence of air friction, the hammer and feather fall at the same rate and land at the same time.

http://www1.jsc.nasa.gov/er/seh/feather.html
http://apolloera.blogspot.com/2006/10/apollo-15-hammerfeather-gravity.html

http://video.google.com/videoplay?docid=6926891572259784994
 

Friction comes in several forms.  The friction is always greater in trying to move a stationary object than the friction felt by a sliding object.  The Normal force is still the same but the coefficients are different.  As the surface gets more inclined, the Normal force gets smaller.  Things stuck on an incline (like a ramp) move when the friction force is smaller than the force of gravity, and that comes the Normal force on the incline is smaller, too.    

Sliding friction is always greater than rolling friction, often by a factor of 100 times or more. That’s why people use carts and dollies with wheels to move things; it’s easier than sliding!

Want to weight less?  Change your normal force.  Fix a bathroom scale to a large, strong piece of wood or metal with a nailed framework or some other strong method.  Have someone, if not yourself, stand on the scale and get the weight.  Then step off.  Raise one end of the long wood so the scale is on an angle.  Weigh again.  It should be a little less. 

Continue raising the angle and taking measurements but be sure to have helpers keeping the person being weighed from harm, to catch them if they slip off.  You only need a few small angles (no more than 30 degrees for most) to prove the point, and to make the students predict what the Normal force will be when the board and scale is vertical.

Here’s a web simulation that will diagram out all the forces on an object sitting on an inclined plane.  http://www.schulphysik.de/ntnujava/forceDiagram/forceDiagram.html

 


Friction and Inertia

Why does a car need to have your foot on the gas pedal to keep going?  Doesn’t that go against what was said above, that steady motion requires no extra force? Doesn’t the engine provide force to the tires, hence to the road? 

Well, yes, it does.  The engine indeed does do that.  Why does it need to?  Because the road is providing friction.  If you take your foot off the gas pedal, you eventually slow down to a halt.  Friction is the culprit, the perpetrator, the villain here.  If there was no friction to slow the car, you wouldn’t need to push on the gas pedal. 

The engine is providing just enough force to overcome the friction.  The two forces cancel out and you move steadily.  No extra forces, no acceleration.  No imbalance of engine force and friction force, no slowing down or speeding up.

You may recall that when two forces in equal but opposite directions add up to a sum of zero, they haven’t gone away.  It’s just a special case we called equilibrium.

What if you could get rid of all the friction?  No roadway resistance, no air drag, no engine parts rubbing against each other?  Then you wouldn’t need to keep on the gas pedal, would you?  And the car would keep going.

It was this fact that made Aristotle and the ancients get mechanics and dynamical physics wrong.  They said a vehicle comes to stop because the natural state of moving things is…not moving.  But that’s not the case.  The natural case is to keep moving just as you are; it’s those extra frictional forces the ancients didn’t recognize as separate from the natural motion that get in the way.

This natural tendency to keep moving is called Inertia

Anything moving will stay that way—exactly that way--unless something (a force of any kind) acts on it.  Something not moving is going to stay that way….because not moving is just a case of velocity = 0 instead of another number!  Put a force on it, it speeds up from zero to go forward or backward.  Put a force on something with velocity not equal zero, same thing…it goes more forward (faster!) or more backwards (slower) as long as that force is applied.

This is the essence of Newton’s first law, the Law of Inertia.  An object at rest or in motion will remain in that state unless an external force is applied to the object. 

Thus the car would remain in motion at a constant speed unless a force is applied.  The engine force applying to the ground through the wheels is an applied force.  So is ground friction (in the other direction), air friction or drag, and so on.  It is inertia plus force, Aristotle!


Newton’s First Law, the Law of Inertia, is that an object at rest or in motion will remain in the same state of rest or motion unless acting on by a force. 
 

Inertia is a fun but difficult thing to demonstrate.  Here’s a couple of things to try:

The old magician’s trick of pulling the table cloth out from under tableware.  I suggest you use children’s toy plates and plastic cups for safety!  If you pull very quickly and very horizontally, the toy place setting won’t have time to react to any frictional forces pulling on them and should remain in place.  But I suggest you practice this a lot before trying to demonstrate it!

This may be easier…..place an index card over a glass and set a coin on top of the index card.  With your thumb and forefinger, quickly flick the card sideways off the glass.  Observe that the card goes horizontally away but since you applied no force to the coin, it just stays there until gravity takes over and it falls.  If you pull the card slowly, instead, the coin has friction on it holding it in place so its inertia is overcome by the friction force, and it moves with the card.

An everyday example of inertia is motion in a moving vehicle.  What happens when the car or school bus turns to the right?  Your body appears to move to the left…but it doesn’t.  It is still moving straight ahead, it is the bus that has changed its direction.  Better yet, go straight in your vehicle.  Hit the break, your inertia continues your forward motion until the seatbelt stops you.  Hit the gas, and you move backwards into the seat because your inertia hasn’t yet changed to keep up with the car.  Why does a toy fall out of a suddenly moving wagon?  Because its inertia hasn’t yet been changed to keep up with the wagon!  Try these demos in class with small carts, wagons, and wheeled skateboard, but be sure to take all safety measures if you use kids! Don’t be a crash test dummy!!

 


Action and reaction

Some equilibrium situations are a case of action and reaction.  An action is what a force does to an object.  The reaction is what the object does back to the force.

You know that gravity is pulling you down.  It is accelerating your motion towards Earth’s center.  Yet why do you not sink a few thousand miles downwards?  Why is your motion zero when there is a force acting on you downwards? 

If you answered, there must be an equilibrium between gravity and some other force, collect a prize!  But what other force is there?  It must be an upwards force, equal in magnitude to your downward weight.  This is sometimes called the Normal force, not because it is everyday ‘normal’ but because Normal is an old term for perpendicular.  Normal forces are perpendicular to surfaces and in this case, perpendicular to Earth’s surface.  THIS Normal force is the reaction force of the ground pushing up against your weight downwards (the action).  The two are equal in magnitude but opposite in direction so they cancel out and you stand on the ground.


Newton’s Third Law of Motion says that for every action there is an equal an opposite reaction. 
 

Link to lesson on Newton's Third Law of Motion

You are weighed downward, the ground reacts upwards. 
You sit on a chair, the chair pushes upwards. 
You walk forward by having the ground react, pushing you forward, to your foot pushing backwards on the ground as an action. 
Don’t believe me?  Walk on ice.  No reaction, you move your foot all you want, you go nowhere but look silly.

The difference here between action-reaction pairs of forces and equilibrium pairs of forces is that there are TWO forces acting on TWO bodies for the former, and TWO (or more) forces acting on ONE body. 

You push on a car, it pushes back on you.  Action-reaction.  But since the car ONLY senses your push (the action force), it feels an unbalanced situation and it accelerates. You don’t accelerate backwards because the car’s force on you is cancelled out by your force on it.  Reaction forces can never exceed the action forces.

Hammer a nail into a board.  The nail feels the action force on it and moves inward.  Where’s the reaction force?  It is the nail pushing back on the hammer…and you feel the hammer bounce back at you.

Stand on roller skates or some other vehicle, holding some balls.  One by one, throw the balls away.  You should roll in the opposite direction.  This is action-reaction, too.  What are the forces involved?  The same thing happens when you step out of boat.  You  go forward, the boat goes backwards, often your forward motion puts you in the water…..

Here’s a more advanced demo.  Have students list all the forces acting in the system to see all the action and reaction pairs.

Hang a mass (such as a 1 or 2 kg mass) from a spring scale.  What are the action and reaction pairs and their measurements?

Answer: The mass has gravity pulling it down with 9.8 or 19.6 Newtons (for 1 or 2 kg).  (The scale may show kilograms so explain that this is a scale that divides the weight by g so that we can show the mass values and use mass as a proxy.)  But since it isn’t falling, there must be an reaction force, which is the pull of the spring scale upwards to balance the force of gravity.  There is also a force upwards, equal to the mass of the scale, caused by whatever is holding the scale up off the floor.  So you have action-reaction pairs between holder and scale, and scale and mass, and an equilibrium situation on scale caused by the balance of the upward holding force and the weight, and on the weight caused by gravity balanced against the spring force upwards.  Each object has two forces on it from external sources, and each force has a paired force against it from action and reaction.

Hang the scale from a second scale. The readings should be different.  The upper scale should have a greater reading because it has to pull up the mass and the lower scale, while the lower scale is unchanged.  Figure out the action reaction pairs for the upper scale, and the equilibrium pairs.

Finally, a demo about action-reaction and rockets. 

Take a long balloon and blow it up.  Seal it temporarily with a clip (paperclip or clamp). Tape a drinking straw to the side of the balloon.  Put a long string through the straw and attach the string to two poles or walls (sort of like a clothesline, stretching across the room). 

Now undo the clip.  Air rushes out (action).  Balloon/rocket moves forward (reaction).  Air inside the balloon is trying to expand under the pressure you put in it by blowing it up.  It tries to expand in all directions.  The sideways expansions are forces that cancel each other out.  But the force of the air moving forward inside the balloon is NOT cancelled out, because the air in the back did escape and isn’t pushing on anything!  So the balloon moves forward.  It is NOT the rocket exhaust the moves the rocket, it’s the force of the exploding fuel pushing towards the rocket’s nose that is unbalanced with any other forces that moves the rocket into space!


Circular motion

When an object moves in a circular path, there is an acceleration which is toward the center of the circle.  This is called centripetal acceleration.

A centripetal force causes circular motion.  When a centripetal force is applied to a moving object, its path curves.  Without the force, the object would fly off in a straight line (from Newton's First Law of Motion) as a result of inertia.  When an object moves along a circular path at a constant speed, acceleration happens without a change in speed.  The acceleration changes the direction of the motion.

A special form of Newton's Second Law governs circular motion.

Fc = mac  = mv2/r

where Fc is the centripetal force in newtons, m is the mass of the moving object, ac is the centripetal acceleration in meters per second squared.  V is the velocity in meters per second, and r is the radius of the circular path of motion.

If you swing an object on a string, the inward centripetal force keeps the object moving in a circular path.  If the string breaks, the object will fly outward in a straight line, tangent to the circle.  This is caused by the removal of the centripetal force.  Motion is in a straight line as required by Newton's First Law of Motion.

A carnival ride illustrates how this works.  Before the ride begins to turn, the swings hang straight down.  As the ride begins to turn, the swings begin to move outward.  As the ride turns more quickly, the swings begin to move further out.  The swings are being turned by the motor in the center.  At each point, the swing is trying to move in a straight line, but they continue to be turned by the motor in the center.  If the cable on a swing were cut, the swing would fly outward in a straight line.  This natural tendency to keep moving is called inertia.


Photos copyright Pamela J. W. Gore, 2007.

 


Forcing Your Inertia into a New Direction

Let’s try answering those initial questions again….

     You need force to keep a car moving.

No, in an ideal world.  Inertia would keep the car moving straight and at a steady speed except that friction, an additional external force, does slow the car down over time in the real world.  So you do need (in the real world) the force provided by an engine, but to overcome the friction, not to keep the object itself going.

      Friction is an inherent part of an object.

Friction is virtually always ever-present and it is an interaction between the object and its environment but it is not an internal force to the object itself so, No, it is not an inherent part of an object.  

     Going at a steady velocity in a circle around the earth means there are no accelerations.

Definitely No.  Velocity, like force and other properties, has two measurements: magnitude (what we usually think of as speed) and direction.  Something moving with a steady ‘speed’ (7000 miles per second) in orbit is still changing direction, else how would it go around us?  To change direction requires a force even if the magnitude of the ‘speed’ doesn’t change.  

     Your weight tells you have much stuff you have.

No.  “How much stuff” you have is called mass.  However, if you agree that weight divided by the gravitational acceleration “g” is what you meant, then you can find out how much mass you have from your weight, but weight itself is a measurement of force, not mass.  

     Equilibrium is the absence of forces.

No.  There is no circumstance in which you have no forces acting on you.  However, the sum of the forces acting on you may be zero in value so that the effects (accelerations) of the forces acting on you are nil.  This is what equilibrium is, when the sum total of the forces is zero.  

     Inertia is what keeps you from getting up in the morning.

Yes and No.  Yes, in that you (or someone) has to push or pull you up from horizontal to vertical.  No, in that what keeps you getting up in the morning is attitude…..

The key points to know about forces are:

      that they cause change, not continuity.  You speed up, slow down, change direction but you don’t keep going because of forces.

       that changes in motion are accelerations.

       that the resulting accelerations are inversely proportional to mass of the object being affected.

      that all objects are affected by the Sum of all the forces acting on them, the Net force.  A Net force of zero magnitude is a state called equilibrium.

      that in absence of Net Forces, an objects inertia is in control, and inertia is the object’s tendency for continuing its state of motion (moving straight or not moving at all).

      forces in the same direction add up to increase or decrease speed, and forces perpendicular to a motion change the motion’s direction.  The total velocity may increase as well.

      the force of gravity is called weight and equals your mass multiplied by g, the acceleration rate of gravity.

       friction forces are always resistive forces, opposite to motion.

A good review site for all of Newton’s Laws can be found at http://www.physicsclassroom.com/Class/newtlaws/newtltoc.html


 

Review Questions

  1. What is the Net force on an object?


  2. Give an example of an object being accelerated in:


    1. Magnitude only.
    2. Direction only.
    3. Both magnitude and direction.

  3. Explain what a state of equilibrium is and give a credible example of an force equilibrium situation.


  4. State and explain all three Laws of Motion by Sir Isaac Newton.


  5. Give three common misconceptions related to forces and motions and explain why they are not correct, what the fallacy is.


  6. What is your mass?  What is your weight?  What is the difference?


 

Define

Force

Mass

Acceleration

Equilibrium

Net Force

Friction force

Normal force

Gravity

Weight

g

Inertia

Units of Mass

Units of force

Units of acceleration

British system

Metric system

Magnitude

Direction

Action

Reaction


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Content provided by Dr. Larry Krumenaker, Georgia Perimeter College

Linked lessons
courtesy of University System of Georgia Learning Objects Repository for Physics I.

Circular motion content provided by Pamela J.  W. Gore.

Rollercoaster icon from NASA Explores.

Page created by Pamela J.W. Gore
Georgia Perimeter College,
Clarkston, GA

Page created February 8, 2007
Modified March 7, 2007
Modified March 10, 2007
Modified May 27, 2007
Modified March 25, 2009