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MOTION
When you travel a certain distance within a certain time the ratio
of the distance to the time is referred to as speed (average
speed actually, since your speed usually varies throughout the trip).
If direction is taken into account then we can upgrade our term
for speed to velocity.
The equation for velocity is v = d / t (or d = v * t or t = d
/ v). So, to find your average velocity if you went 36 meters
(d) in 4 seconds (t) you would just divide 36 m by 4 s and get an
answer of 9 m/s. Or, to find how far you would travel going 7 m/s
(v) for 10 minutes (t) you would multiply 7 m/s by 600 s (10 minutes
* 60 s/min) and get 4200 m (or 4.2 km).
Variations on the velocity equation include solving such problems
as:
If car A travels at 30 m/s and car B travels at 20 m/s and they
are separated by a distance of 40 meters, how many seconds before
car A catches up with car B?
Using t = d / v, we substitute the difference in the two velocities
( v1 - v2 ) for v so the new equation
becomes t = d / ( v1 - v2 ). Solving, t = 40m / ( 30 m/s
- 20 m/s ) or t = 40m / 10 m/s = 4 seconds
Or, if car A is 60 m behind car B (going 25 m/s), how fast must
car A go to catch up to car B in 20 seconds?
The previous equation can be used in a different form to solve
this. t = d / ( v1 - v2 ) becomes
v1 = d / t + v2. Solving, v1 = ( 60 m / 20 s ) + 25 m/s,
or v1 = 3 m/s + 25 m/s = 28 m/s.
Now, when velocity doesn't remain constant but changes with time,
it is called acceleration. Since velocity is considered both
speed and direction, you can accelerate by changing your speed or
by changing your direction. In a later chapter you will see that
forces cause acceleration. This is why you can turn a corner without
changing your speed and feel centripetal force. This type of velocity
change where speed is constant but the direction changes is called
centripetal acceleration (more on this in chapter 7). The equation
for acceleration is a =  v
/ t . The symbol
(greek letter
delta) means "change". v
can be represented as v f - v i (i.e. final velocity minus
initial velocity). Likewise, t
can be represented as t f - t i . So, if your velocity was
a constant 15 m/s for the last 10 seconds and then your velocity
gradually changed to 60 m/s at 15 seconds, the acceleration during
that period of change would be 60 m/s - 15 m/s (change in velocity)
divided by 15 s - 10 s (change in time) or 45 m/s / 5 m/s or finally
9 m/s^2
Restated, every second the velocity changes by increasing
another 9 m/s
or 9 meters per second per second ( i.e. m/s^2 ).
The following list of equations contains several useful variations
of distance, velocity and acceleration relationships.
Click Here for Freefall Lab DEMO- Terminal Velocity
Did you ever think of all the physics involved when you drop a ball
(or an expensive plate)?
FORCE
- A FORCE is a push or pull.
- A NET FORCE will cause an object/mass to accelerate.
- FORCE is measured in NEWTONS in the metric system.
- 1 pound = 4.54 Newtons or .2245 lbs = 1 N
A force can be caused by such things as gravity, magnetism,
electric charges, and nuclear interactions. If chemicals in
a rocket engine react (electric charges), gases expand rapidly
and produce great force. But, if this force isn't greater than
the gravitational force between the rocket and the earth, the
rocket goes nowhere. Likewise, if the force provided by a horse
on a cart isn't greater than the frictional force between the
cart and the ground, the cart also goes nowhere. There must be
a NET FORCE in order for an object/mass to move. A net
force is the result of 2 or more forces acting on the same
object in the same or different directions. If the forces are
all in allignment (in the same linear dimension) then simply adding
the magnitude of the forces is all that is necessary to get the
value of the resulting net force.
NEWTON'S LAWS
- Newton's 1st Law: Objects like to keep doing what they're
doing until interupted by a NET FORCE
(OR An object at rest remains at rest and an object in motion
remains in motion unless acted upon by an outside force)
- Newton's 2nd Law: A NET FORCE causes a mass
to accelerate or F = m x a
- Newton's 3rd Law: For every action there is an equal
and opposite reaction
(the more popular one!)
Newton's 1st Law. When we look at a rock and notice that
it doesn't move, this doesn't suprise us. If it suddenly starts
to move we instantly suspect that a force caused it to move, evil
or otherwise. However, when a rock has been thrown and rolls across
the ground we expect it to eventually stop. We know that frictional
forces were responsible for keeping it from doing what it was
doing (continuing to roll). So, whether sitting motionless or
moving at a constant velocity, the application of a NET FORCE
will change this constant state.
Newton's 2nd Law focuses on this NET FORCE causing
the change of state called acceleration.
The equation F = m x a can be rewritten in the form F
/ m = a or F / a = m. This simple proportional equaution
simple implies the obvious. The larger the net force, the greater
the object accelerates and the greater the mass, the less the
it accelerates. F is force in Newtons, m is mass
in kilograms and a is acceleration.
Newton's 3rd Law is the more popular, but probably the
least understood of the 3 laws. The confusion probably arises
from the misunderstanding of the term equal and opposite
reaction. The diagram below should help clear up some
of this confusion. Notice that the compressed spring between the
2 different masses pushes equally in both directions but the effect
of the same force on the different masses causes
different accelerations (nothing equal and opposite about
that!). However, since the reaction is a combination of both
mass and acceleration they end up being equal. The same force
on a smaller mass causes a greater acceleration and the same force
on a larger mass causes less acceleration. The product of mass
& acceleration is the same for both, but in opposite directions.
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The force of gravity on earth (neglecting the opposing force
of air friction) will cause ANY mass to accelerate at 9.8
m/s^2. Of course a feather has a tremendous air friction to
mass ratio so this is why we must add the phrase neglecting
friction. Now you might think that because a mass is bigger
it will fall faster, but if you remember Newton's 2nd Law, the
bigger the mass the slower it accelerates. However, the force
of gravity is greater on the greater mass (it weighs more) increasing
proportionately with bigger masses.
F / M = F / M ..... 196 N / 20 kg = 19.6 N / 2 kg = 9.8
m/s^2 !!!
This is where we make the distinction between mass and weight.
Mass is just the amount of matter measured in kilograms. Weight
is the gravitational Force (usually caused by the earth)
on the mass. To convert mass into weight just substitute
9.8 m/s^2 for a in F = m x a.
MOMENTUM
Momentum (p) is a product of the mass
and velocity of an object (p = m x v). If an object
has no velocity then it has no momentum. Also, if the object is
moving to the left it would have a negative momentum due to the
vector (direction) nature of velocity. The Law of Conservation
of Momentum concludes that the sum of all momentums
before and after a collision are equal (m1v1
+ m2v2 + ... = m1'v2' + m2'v2' + ...).
Click
Here for Interactive Shockwave Momentum Demo!
Click
Here for another great Airtrack Demo!
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