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Unit 4: Motion Class Notes
Speed/velocity
Speed describes how fast an object is moving. To find speed you must measure two quantities:
Distance traveled by an object and the time it takes to travel that distance. The SI unit for speed is
meters per second (m/s). Speed can also be expressed as mi/h or km/h
Speed-need to know
1. Distance Traveled
2. the time it takes to travel that distance
3. SI Units m/s
4. Equation for calculating average speed:
Speed (v) = distance (d) /time (t)
D = v(t)
T=d/v
Speed can be determined by distance-time graph. Need to calculate the slope of a line.
Velocity
Velocity describes both speed and direction. Examples of velocity: Accelerating your car by
hitting the gas pedal or taking a right-hand turn.
1. Equation: d= vt
Newton’s Laws
Newton’s 1st Law Law of Inertia
Newton’s First Law of Motion stated: A body continues at rest or in motion in a straight line with
a constant speed until acted on by a non-zero net force. The tendency of a body to maintain its
status quo is called inertia. Newton’s First Law is often referred to as the Law of Inertia.
An object at rest remains at rest and an object in motion maintain its velocity unless it experiences
an unbalanced force
There are many excellent examples of Newton's first law involving aerodynamics. The motion of
an airplane when the pilot changes the throttle setting of the engine is described by the first law.
The motion of a ball falling down through the atmosphere, or a model rocket being launched up
into the atmosphere are both examples of Newton's first law. The motion of a kite when the wind
changes can also be described by the first law. We have created separate pages which describe
each of these examples in more detail to help you understand this important physical principle.
Inertia is a quality of an object that determines how difficult it is to get that object to move, to stop
moving, or to change directions. Generally, the heavier an object is, the more inertia it has. An
elephant has more inertia than a mushroom. A sumo wrestler has more inertia than a baby. Inertia
is made from the Latin word “inert,” which means “lacking the ability to move”. Inertia isn’t
something people have a grasp of, though, as it’s something you must mathematically calculate
from an object’s mass and size.
Newton’s Second Law
Force (F)= Mass (M) x Acceleration (a)
Force is measured in Newtons (N)
Forces can cause motion. But what exactly is a
force? We can think of a force as a push or a
pull. A force has a direction as well as a
magnitude. A force is a vector quantity which
follows the rules of vector addition and
subtraction. In a diagram, a force can be
represented by an arrow indicating its two
qualities: The direction of the arrow shows the direction of the force (push or pull). The length of
the arrow is proportional to the magnitude (or strength) of the force. The direction of a force is
important for force is a vector. The net force on an object is the
vector sum of all the forces on that object. If the net force is zero an
object's motion will not change.
What are the UNITS of force?
F=ma
A force of ONE unit
will give an object of 1.0 kg mass
an acceleration of 1.0 m/s/s ;
this force is known as
ONE NEWTON (1.0 N) .
1 N = ( 1 kg ) ( 1 m/s/s )
12 N = ( 3 kg ) ( 4 m/s/s )
A force of 12 N could give
a mass of 3 kg
an acceleration of 4 m/s/s
12 N = ( 2 kg ) ( 6 m/s/s )
A force of 12 N could give
a mass of 2 kg
an acceleration of 6 m/s/s .
Net Force = Zero Examples
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This slide shows some rules for the simplified motion of an aircraft. By simplified motion we mean that some of the four
forces acting on the aircraft are balanced by other forces and that we are looking at only one force and one direction at a
time. In reality, this simplified motion doesn't occur because all of the forces are interrelated to the aircraft's speed,
altitude, orientation, etc. But looking at the forces ideally and individually does give us some insight and is much easier to
understand.
In an ideal situation, an airplane could sustain a constant speed and level flight in which the weight would be balanced by
the lift, and the drag would be balanced by the thrust. The closest example of this condition is a cruising airliner. While
the weight decreases due to fuel burned, the change is very small relative to the total aircraft weight. In this situation, the
aircraft will maintain a constant cruise velocity as described by Newton's first law of motion.
If the forces become unbalanced, the aircraft will move in the direction of the greater force. We can compute the
acceleration which the aircraft will experience from Newton's second law of motion
F=m*a
Where a is the acceleration, m is the mass of the aircraft, and F is the net force acting on the aircraft. The net force is the
difference between the opposing forces; lift minus weight, or thrust minus drag. With this information, we can solve for the
resulting motion of the aircraft.
If the weight is decreased while the lift is held constant, the airplane will rise:
Lift > Weight - Aircraft Rises
If the lift is decreased while the weight is constant, the plane will fall:
Weight > Lift - Aircraft Falls
Similarly, increasing the thrust while the drag is constant will cause the plane to accelerate:
Thrust > Drag - Aircraft Accelerates
And increasing the drag at a constant thrust will cause the plane to slow down:
Drag > Thrust - Aircraft Slows
Newton’s 2nd Law and Acceleration
The more mass something has and/or the faster it’s accelerating, the more force it will put on
whatever it hits. F=ma For example, a car colliding at 30 mph will hit a lot harder then a fly
colliding at 30 mph. Conversely, the more mass something has, the more force that’s needed to get
it to accelerate
Newton’s third Law
For every actions force, there is an equal and opposite reaction force. So if you kick a ball the
action force is the force of you kicking it, but the reaction force is the force exerted by the ball on
your foot
All forces occur in action-reaction pairs.
Balloon rockets the air escaping at the back of the balloon has a greater force then if the balloon
was at rest propelling the balloon forward.
Rockets
Calculating Momentum
Weight
All objects fall with the same acceleration, 9.8 m/s/s (which we approximate as nearly 10 m/s/s).
We call this free fall.
When such objects fall, the only force acting on them is their weight, the force of gravity.
The only force on a body in freefall is the force of gravity. We call this its weight.
Since it accelerates at 9.8 m/s/s,
that weight must be:
w = (mass)x (9.8 m/s/s),
w = m(g)
The weight of an object is the force of gravity on that object.
Weight, since it is a force, will be measured in units of newtons (N).
Mass will be measured in kilograms (kg).
Calculating Acceleration
Acceleration is any change in velocity (which can be speed or direction)
Acceleration Lab: Your ball was constantly increasing speed and as such, it was constantly accelerating.
By the way, would it have mattered what the mass of the ball was that you used? No. Gravity
accelerates all things equally. The mass of the ball doesn’t matter but the size of the ball might. If you
used a small ball and a large ball you would probably see differences due to friction and rotational inertia.
The bigger the ball, the more slowly it begins rolling. The mass of the ball, however, does not matter.
Calculating Acceleration:
Acceleration = Final Velocity (Vf) – Initial Velocity (Vi) / Time or a = v/t
If the acceleration is a small value, that means the speed is increasing very gradually. If the acceleration
has a greater value, the object is speeding up more rapidly.
All objects fall to earth at the same acceleration due to the pull of gravity (excluding air
resistance). The formula for gravity (g) is 9.80 m/s2 often rounded up to 10.0 m/s2
Distance (d) = 1 gt2 =
2
2
d =. 5 (gt )
Air resistance is a form of friction. Air resistance is caused by the interaction between the
surface of a moving object and the air molecules; the amount of air resistance on an object depends
on its size and shapes as well as the speed it which it moves. Objects with larger surfaces can
experience greater air resistance. Air resistance also increases with the object’s speed.
Gravitational Force
Gravitational Force is different than the other forms of friction we talked about because the force is
exerted even when the objects are not touching.
Gravitational force depends on mass and distance. Insert Inverse Square Law here:
Force = 1/d2 If the distance between two objects doubles, the gravitational force between the two
will decrease by one-fourth. If the distance tripled, the force will be reduced by one-ninth.
Free Fall Acceleration/Acceleration of Gravity
In the absence of air resistance, all objects near earth’s surface accelerate at the same rate,
regardless of their mass.
This means that is you dropped a 1.5 kg book (approx. 3 lbs) and a 15 kg rock (approx. 30lbs)
from the same height they would hit the ground at about the same time. This happens because of
Newton’s 2nd law: Force = Mass (acceleration). This equation shows that the acceleration of an
object is dependent upon both its mass and the force of gravity. Therefore a heavier object will
experience a greater gravitational force than a lighter object.
Calculating Momentum
All moving objects are said to have momentum. The momentum of an object is dependent upon
its mass. The object with a greater mass will have more momentum and will be more difficult to
change its momentum than an object with less mass. Therefore, to calculate momentum of an
object for an object moving in a straight line:
Momentum (p) = mass (m) x velocity (v)
P = mv
The momentum equation shows that an object with greater mass OR greater velocity will have
more momentum than an object with less mass OR less velocity.
Calculate the momentum of a 6.00 kg bowling bowl moving at 10.0 m/s down the alley
Mass= 6.00 kg
Velocity = 10.0 m/s down the alley
P= 6.00 kg x 10.0 m/s = 60.0 kg x m/s