GPS Module 3 - Part 1

Ch 3: Newton’s Laws

Chapter 3 - Newton’s Laws

Newton’s 1st Law:

If an object is left alone with no outside influences, then it will have a velocity that remains constant.

Or a more popular wording: “An object at rest tends to stay at rest and an object in motion tends to stay in motion”.


Newton’s 1st Law:


Constant velocity implies both constant speed and direction.


Newton’s 1st Law:



The constant speed can be zero. For example, an object at rest tending to stay at rest.


Newton’s 1st Law:



The constant speed can be zero.

Moving objects that are truly isolated from all outside influences should ‘coast’ forever in a straight line, but objects isolated that well are virtually impossible to find. Most moving objects will gradually slow down and stop due to frictional forces.


Newton’s 1st Law:


Moving objects that are truly isolated from all outside influences should ‘coast’ forever in a straight line, but objects that well isolated are virtually impossible to find. Most moving objects will gradually slow down and stop due to frictional forces.

This part is tricky. That’s why the Ancient Greeks missed it - they thought the natural state of motion was for all things to stop. Newton’s 1st Law is obvious for objects at rest. Look around the room and you will see many things just sitting there and you don’t expect them to start moving without some cause.


Newton’s 1st Law:


Moving objects that are truly isolated from all outside influences should ‘coast’ forever in a straight line, but objects that well isolated are virtually impossible to find. Most moving objects will gradually slow down and stop due to frictional forces.

But moving things don’t seem to coast forever. The real world is complicated, with many different things going on at the same time . Part of the challenge (and success) of the sciences is to pull apart all the intertwined variables to see what causes what. By looking at situations where friction and air resistance are reduced, one gets closer and closer to seeing Newton’s 1st Law fully in action for moving objects. An object slipping on slick ice or a puck on an air hockey table suggest that truly free objects would tend to keep coasting. Space travel is the best example. A few of our space probes have left the solar system and are coasting (at tens of thousand of miles per hour) in very close (the sun does tug on them a tiny bit still) to a straight line and constant speed for decades now


Newton’s 1st Law:


Inertia is just another name for this tendency of objects to not change their state of motion.


Force:

A force is a ‘push’ or ‘pull’ of one object on another.

Before moving on the Newton’s 2nd Law, we need to introduce an important and basic term in physics.

Sometimes it is the most basic terms that are the hardest to define. Some examples will be helpful. The part about ‘one object on another’ is significant. Objects exert forces on each other. If you can’t identify the object pushing and the object being pushed on, that might be a clue that the situation does not involve a force.


Force:


Pushing a box with your hand

Examples:


Force:



Examples:

Pulling a box with a rope

The force exerted by a long skinny element such as a wire, rope or chain is also called a tension


Force:



Examples:

The force of support that keeps objects from falling is called the normal force

Pulling a box with a rope

The force exerted by a long skinny element such as a wire, rope or chain is also called a tension


Force:


Friction is the force that keeps one object from sliding across another

Examples:


Force:


Friction is the force that keeps one object from sliding across another

Examples:

Gravity is the force exerted by the earth on objects near the surface that pulls these objects downward


So ‘force’ is the broad term and then there are many names of specific kinds of force – such as gravity, friction, and tension.

Gravity is the force exerted by the earth on objects near the surface that pulls these objects downward

Until the example of gravity, all the other forces involved actual physical contact between the two objects in question. In fact, that was originally a criticism of the idea of a gravitational ‘force’. It seemed like a ghost-like action at a distance. Other fundamental forces such as the electric force or magnetic force have this same feature of kicking in even before the objects actually touch (that’s why magnets are fun to play with). Later the idea of a ‘force field’ was introduced for these cases. Despite these exceptions, it is still a good rule of thumb in this class is that forces typically involve contact between the objects.


Force is a vector quantity

Full vector addition is beyond the scope of this class, but we can handle a couple simple case:

Vectors in the same direction will add normally 10 lb

6 lb

16 lb=



6 lb

16 lb=

Vectors that are opposite each other will subtract 10 lb 6 lb 4 lb

=





6 lb

16 lb=

Vectors that are opposite each other will subtract 10 lb 6 lb 4 lb

=

Vectors at arbitrary angles are more complex (we will not deal with this case).

10 lb

6 lb

14.7 lb=




Newton’s 2nd Law:

If a single force (or a non-zero sum of forces if there are more than one) acts on an object, then that object will accelerate in the same direction as the force.


Newton’s 2nd Law:

If a single force (or a non-zero sum of forces if there are more than one) acts on an object, then that object will accelerate in the same direction as the force.

F = m a

The amount of the acceleration depends on the mass of the object according to:

massaccelerationtotal force


How large of a force is required to accelerate a 1500 kg car at 1.2 m/sec ?

Example 3.1:

2



Example 3.1:

2

It is important for doing word problems to be able to recognize the units for our key quantities. Note; the question does not say a ‘mass of 1500 kg’ or an ‘acceleration of 1.2 m/sec2’, you just need to know a kg number is a mass and a m/sec2 number must be an acceleration.

A question involving force, mass, and acceleration sounds like a candidate for Newton’s 2nd Law.



Example 3.1:

2

F = m a



Example 3.1:

2

F = m a

F = ( 1500 kg ) ( 1.2 m/sec )2 Plug in the givens



Example 3.1:

2

F = m a

F = ( 1500 kg ) ( 1.2 m/sec )2

F = 18002sec

kg mThe number part is straight-forward, but we are getting new units combinations (pretty typical for a new formula).

Units are a bit messy too, but there is nothing to simplify or cancel here.

So we do the next best thing: abbreviate!



Example 3.1:

2

F = m a

F = ( 1500 kg ) ( 1.2 m/sec )2

F = 18002sec

kg m

Where 1 n = 12sec

kg m

F = 1800 n

[‘n’ is short for ‘newton’, which is short for the whole combination]



Example 3.1:

2

F = m a

F = ( 1500 kg ) ( 1.2 m/sec )2

F = 1800 nThe newton is probably not a familiar unit to most of the class. It would be nice to know how big this really is.

Is there an US/British equivalent we can convert to?



Example 3.1:

2

F = m a

F = ( 1500 kg ) ( 1.2 m/sec )2

F = 1800 n Yes! The familiar ‘pound’ is also a unit of force. (Remember weight/gravity is one kind of force, but so is tension, friction, and so on, and they all have the same units).

(1800 n)(1 n)

(0.225 lb)= 405 lbF = After multiplying by a

lb to n conversion factor


405 lb is a pretty big push. But what object actually pushes the car that hard in a forward direction?

Post Analysis:



Post Analysis:

Popular answers in a face-to-face class might include; the engine, the transmission, parts of the drive train, the gas, etc. All of these are important and they are associated with some big forces of pieces of the car on other pieces – but ultimately to accelerate the entire car forward requires a push from another object outside the car itself.

Recalling that, except for fundamental forces like gravity and magnetism, forces usually require contact means that it should be something that is touching the car.

An object not the car that is touching the car – doesn’t leave much...



Post Analysis:

…except the road! The gas, engine, drive train are important, but ultimately all they do is make the wheels turn. If the car is up on blocks or on slick ice, that is all that will happen. But if the tire is pressed against a surface, there will be a tendency for the spinning tire to slip against that surface. A force of friction develops to prevent that slippage. The road literally throws you forward with a large force of friction.

Friction


The road must push on your tires for any acceleration of your car, including taking off from a start, stopping or turning corners and curves. It is not unusual for this force to need to be 200 lb, 300 lb, 500 lb or even a 1000 lb or more. Something to consider next time you’re a driving a bit fast on slick roads – ask yourself “can I get a half a ton of braking force out of this surface”?

Post Analysis:


Weight is another name for the force of gravity.

Weight



Weight

W = m g

There is a simple formula for calculating the weight of an object near the earth’s surface.

with g = 9.82sec

m



Weight

W = m g


with g = 9.82sec

m

Example 3.2: How much does an 8 kg rock weigh?

May appear at first glance as a ‘trick’ question, but the trick is to just know your units. You might be tempted to say ‘8 kg’, but that is a mass and not a weight. If the questions ask ‘how much a 10 lb book weighs, then 10 lb is a good answer. Or ‘what is the mass of a 8 kg book’, then 8kg is a good answer there. But the weight of a 8 kg mass book is not 8 kg, but something you have to calculate from a formula.



Weight

W = m g

W = ( 8 kg ) ( 9.8 m/sec )2


with g = 9.82sec

m




Weight

W = m g

W = ( 8 kg ) ( 9.8 m/sec )2


with g = 9.82sec

m

W = 78.4 kg m/sec 2




Weight

W = m g

W = ( 8 kg ) ( 9.8 m/sec )2


with g = 9.82sec

m

W = 78.4 kg m/sec 2

W = 78.4 n




Weight

W = m g

W = ( 8 kg ) ( 9.8 m/sec )2


with g = 9.82sec

m

W = 78.4 kg m/sec 2

W = 78.4 n [or 17.6 lb]


MassQuantity:

Metric/S.I. units

Units Revisited:

Force

U.S./British units


MassQuantity:

Metric/S.I. units

Units Revisited:

Force

U.S./British units

gram newton (n)


MassQuantity:

Metric/S.I. units

Units Revisited:

Force

U.S./British units pound (lb)

gram newton (n)


People do commonly convert directly between pounds and grams/kilograms, but this is not technically a proper units conversion. Pounds and kilograms are really units for different quantities. A 1 kg object does always weigh about 2.2 lbs near the earth surface, but that relationship contains a gravity ‘g’ factor and would not be true on the moon, where a 1kg object weighs must less than that.

MassQuantity:

Metric/S.I. units

Units Revisited:

Force

U.S./British units pound (lb)

gram newton (n)


MassQuantity:

Metric/S.I. units

Units Revisited:

Force

U.S./British units slug pound (lb)

gram newton (n)


There are US/British units for mass, but they are less commonly used.

MassQuantity:

Metric/S.I. units

Units Revisited:

Force

U.S./British units slug pound (lb)

gram newton (n)

This may seem overly picky, but there are major distinctions between mass and force. Of course, we never really defined mass, which might be helpful at this point.


What is mass anyway?

A good clue is to see where mass first appeared in a formula

F = m a




F = m a

Imagine lining up a bunch of masses (small to large) and poking them all with a 10 lb force. What Newton’s 2nd Law says, is that they do not respond the same. The small ‘m’ will have a large ‘a’ and a large ‘m’ will yield a small ‘a’. In other words small masses are easy to accelerate, while large masses are very difficult to accelerate. So mass is a measure of how an object is to accelerate.


small mass

medium mass

large mass

F=10lb

F=10lb

F=10lb

large acceleration

medium acceleration

small acceleration



F = m a

This is a separate issue from weight. If we did this in deep space, then all three objects could weigh nothing. They could all be floating and weigh zero pounds. But a small mass is still easy to accelerate (poke it and it flies across the ship) and a very large mass is still hard to accelerate (poke it and it just sits there). In other words; a weightless 400 kg refrigerator on a space ship still hurts you if you punch it hard, because it is massive.

So mass is more fundamental: a 1 kg mass is still 1 kg in orbit or on the moon or in deep space, whereas it will weigh different amounts in each place.


small mass

medium mass

large mass

F=10lb

F=10lb

F=10lb

Education

GPS Module 3 - Part 1