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Tillery_chapt02_lecture_a.pptxChapter 2 Motion
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Overview
Description
Position
Velocity
Acceleration
Applications
Horizontal motion on land
Falling objects
Compound (2-D) motion
Explanation
Forces
Newton’s laws
Applications
Momentum
Circular motion
Newton’s law of gravitation
Measuring motion
Two fundamental components:
Change in position
Change in time
Three important combinations of length and time:
Speed
Velocity
Acceleration
Speed
Change in position with respect to time
Average speed - most common measurement
Instantaneous speed - time interval approaches zero
Example: average speed
Calculate average speed between trip times of 1 hour and 3 hour
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Velocity
Describes speed (How fast is it going?) and direction (Where is it going?)
Graphical representation of vectors: length = magnitude; arrowheads = direction
Acceleration
Rate at which motion changes over time
Speed can change
Direction can change
Both speed and direction can change
Forces - historical background
Aristotle
Heavier objects fall faster
Objects moving horizontally require continuously applied force
Relied on thinking alone
Galileo and Newton
All objects fall at the same rate
No force required for uniform horizontal motion
Reasoning based upon measurements
Force
A push or pull capable of changing an object’s state of motion
Overall effect determined by the (vector) sum of all forces - the “net force” on the object
Four Fundamental Forces
Gravitational
Act between all objects
Electromagnetic
Act between electrically charged parts of atom
Weak Nuclear Force
Involved in certain nuclear reactions
Strong Nuclear Force
Involved in hold nucleus together
Stronger than electromagnetic and gravitational force
Horizontal motion on land
“Natural motion” question: Is a continuous force needed to keep an object moving?
No, in the absence of unbalanced retarding forces
Inertia - measure of an object’s tendency to resist changes in its motion (including rest)
Balanced and unbalanced forces
Motion continues unchanged without unbalanced forces
Retarding force decreases speed
Boost increases speed
Sideways force changes direction
No force-constant speed in straight line
Force applied against direction of motion
Force applied in same direction as motion
Force applied sideways to direction of motion
Falling objects
Free fall - falling under influence of gravity without air resistance
Distance proportional to time squared
Velocity increases at constant rate
Acceleration due to gravity (g) same for all objects
Compound motion
Three types of motion:
Vertical motion
Horizontal motion
Combination of 1 and 2.
Projectile motion
An object thrown into the air
Basic observations:
Gravity acts at all times
Acceleration (g) is independent of the object’s motion
Projectile motion
Vertical projectile
Slows going up
Stops at top
Accelerates downward
Force of gravity acts downward throughout
Horizontal projectile
Horizontal velocity remains the same (neglecting air resistance)
Taken with vertical motion = curved path
Fired horizontally versus dropped
Vertical motions occur in parallel
Arrow has an additional horizontal motion component
They strike the ground at the same time!
Example: passing a football
Only force = gravity (down)
Vertical velocity decreases, stops and then increases
Horizontal motion is uniform
Combination of two motions = parabola
Three laws of motion
First detailed by Newton (1564 to 1642 AD)
Concurrently developed calculus and a law of gravitation
Published Principia
Essential idea - forces
Newton’s 1st law of motion (1)
“The law of inertia”
Every object retains its state of rest or its state of uniform straight-line motion unless acted upon by an unbalanced force
Inertia resists any changes in motion
Newton’s 2nd law of motion (2)
Forces cause accelerations
Units = Newtons (N)
Proportionality constant = mass
More force, more acceleration
More mass, less acceleration
Examples - Newton’s 2nd
Weight and mass
Mass = quantitative measure of inertia; the amount of matter
Weight = force of gravity acting on the mass
Pounds and newtons measure of force
Kilogram = measure of mass
Newton’s 3rd law of motion
Source of force - other objects
3rd law - relates forces between objects
“Whenever two objects interact, the force exerted on one object is equal in size and opposite in direction to the force exerted on the other object.”
Momentum
Important property closely related to Newton’s 2nd law
Includes effects of both motion (velocity) and inertia (mass)
m = 60.0 kilograms
v = 0.750 meter/second
p = mv
= (60.0 kilograms)(0.750 meter/second)
m = 120.0 kilograms
v = 0.375 meter/second
p = mv
= (120.0 kilograms)(0.375 meter/second)
Conservation of momentum
According to the law of conservation of momentum, the momentum of the expelled gases in one direction equals the momentum of the rocket in the other direction in the absence of external forces.
Impulse
A force acting on an object for some time t
An impulse produces a change in momentum
Applications: airbags, padding for elbows and knees, protective plastic barrels on highways
impulse = Ft
Δp = Ft
Forces and circular motion
Circular motion = accelerated motion (direction changing)
Centripetal acceleration present
Centripetal force must be acting
Centrifugal force - apparent outward tug as direction changes
Centripetal force ends: motion = straight line
Newton’s law of gravitation (1)
Attractive force between all masses
Proportional to product of the masses
Inversely proportional to separation distance squared
Explains why
Provides centripetal force for orbital motion
mass cancels
Newton’s law of gravitation (2)
Earth Satellites
A cannonball shot with sufficient speed from a mountaintop will orbit Earth.
With the correct tangential speed, and above the atmosphere and air friction, satellites follow a circular orbit for long periods of time.
Geosynchronous satellites orbit the earth at an altitude of 36,000 kilometers and have a period of 1 day, so they appear not to move.
Newton’s law of gravitation (3)
Weightlessness
Skydivers and astronauts experience apparent weightlessness because all objects in freefall accelerate with a force of g.
To experience true weightlessness, one would have to travel far from Earth and its gravitational field, and far from the gravitational fields of other planets.
