GPS Module 3 - Part 1

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:
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:
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
=

Vectors in the same
direction will add
normally 10 lb
6 lb
16 lb
=
Vectors that are
opposite each other
will subtract 10 lb 6 lb 4 lb
=

Vectors in the same
direction will add
normally 10 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:
mass
accelerationtotal 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 = 1800
2sec
kg m
The 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 = 1800
2sec
kg m
Where 1 n = 1
2sec
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 n
The 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 = 9.8
2sec
m

Weight
W = m g
with g = 9.8
2sec
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 = 9.8
2sec
m

Weight
W = m g
W = ( 8 kg ) ( 9.8 m/sec )
2
with g = 9.8
2sec
m
W = 78.4 kg m/sec
2

Weight
W = m g
W = ( 8 kg ) ( 9.8 m/sec )
2
with g = 9.8
2sec
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 = 9.8
2sec
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

GPS Module 3 - Part 1

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