Download Physics - Park High School

Independent Study:
Advanced Physics
Fall 2016
Max Serafin
Overview
This class focused on material from the Mechanics
section of the AP Physics C Exam
(calculus-based physics)
Topics Covered
Topics included:
Vectors
Kinematics
Newton’s Laws
Work, Energy, and Power
Linear Momentum
Rotational Motion
This presentation will provide both a brief overview of each topic, as well as a
real-world application
Vectors Overview
A vector is a quantity that has both a direction and a
magnitude, versus a quantity that does not have
direction, such as a constant or scalar.
Some common examples of vectors in physics
include displacement, velocity, acceleration, force,
momentum, and electric and magnetic fields.
Vectors cont.
Vectors are very useful for describing anything that has
both magnitude and directional qualities.
They are commonly used in navigation to describe
position on coordinate axes.
They can also be used to describe more recognizable
quantities such as wind
ex: 25mph NNW (25 mph is magnitude, NNW is
direction)
Vectors cont.
This graphic shows the
use of vectors to
describe the movement
of air on Earth
Each vector has
specific direction, and
the more powerful
winds have longer
vectors (greater
magnitude)
Kinematics Overview
Kinematics is the study of an object’s motion in space
Common aspects of kinematics include:
Position
Speed
Velocity
Acceleration
Displacement
Momentum
Kinematics cont.
Basic kinematics and fundamentals of calculus go
hand in hand.
The relationship between an object’s position,
velocity, and acceleration can very easily be
calculated using calculus
Kinematics cont.
This graphic shows how
as the car accelerates at
a constant speed, it’s
velocity increases in a
linear fashion, and the
position increases as a
quadratic
The graphs can be
derived from each other
using both derivation and
integration
Newton’s Laws Overview
While kinematics describes how things move,
Newton’s Laws describe why they move in such a
way
This is often called the study of dynamics
There are three main laws that form the basis of
dynamics, commonly known as “Newton’s Laws of
Motion”
Newton’s Laws cont.
The First Law (Law of Inertia)
“An object in motion will continue in its state of
motion unless compelled to change by a net force
impressed upon it.”
Newton’s Laws cont.
The Second Law
Newton’s Second Law predicts what will happen if a force does act
on an object
Essentially, it says that if a force acts on an object, the objects
velocity will change (or the object will acceleration)
The acceleration of the object will be directly proportional to the
strength of the net force and inversely proportional to the object’s
mass
This gives the commonly known formula: Force = mass x
acceleration or F = ma
Newton’s Laws cont.
The Third Law
“For every action, there is an equal, but opposite
reaction.”
The Third Law describes that if a force acts on
something, an equal force is returned in the
opposite direction
Newton’s Laws cont.
Newton’s Laws can be found almost anywhere, but some examples include:
First Law
A hockey puck sliding on ice, a ball kicked in space
Second Law
Pushing an empty cart vs. a full cart. (More force required to push the full cart
because it has more mass)
Third Law
If a balloon is let go, the air rushes downward, pushing the balloon up into the air
When jumping off a diving board, you push the board down, and it springs back up
and pushes you into the air
Work, Energy, and Power
Overview
This unit covers topics including force, energy, power
work, and the Law of Conservation of Energy
Work, Energy, and Power
cont.
Work is described as the application of a force over a
certain distance, which results in a change in energy
Work can be calculated by taking the integral of a
Force vs. distance graph between two positions
Work, Energy, and Power
cont.
Energy has two primary forms: kinetic and potential.
Kinetic energy is energy that an object possess by
virtue of motion
Potential energy is independent of motion and stems
from an object’s position.
Ex: A ball rolling on the ground has kinetic energy,
while a ball being held above your head has potential
energy by way of gravity
Work, Energy, and Power
cont.
Law of Conservation of Energy
This law states that an object has a value known as
it’s mechanical energy that equals the sum of it’s
kinetic and potential energy
As long as no nonconservative forces (friction) act on
an object, it’s final mechanical energy must equal it’s
initial mechanical energy
Work, Energy, and Power
cont.
Power is the rate at which work gets done (or energy
is transferred)
Power = Work / Time
Power is measured in watts
Cars often use horsepower instead, which is equal to
about 746 watts
Linear Momentum
Overview
Linear momentum is a vector quantity (denoted p)
that is the product of mass and velocity
p = mv
Linear Momentum cont.
If you instead find the product of force and the time in
which it acts, the result is a different vector quantity
known as impulse (denoted J)
J = F * time
Impulse can also be found by taking the integral of a
force vs. time graph between two time points
Linear Momentum cont.
Linear momentum, especially the Conservation of
Linear Momentum, is often used when working with
collisions
Ex: car crashes, hitting a ball, playing pool
An elastic collision occurs when kinetic energy is
conserved, while an inelastic collision occurs when
kinetic energy in a system changes
Rotational Motion Overview
This section covers objects in motion, but also
introduces rotation (studying the motion of objects
that are spinning)
Rotational Motion cont.
The same concepts apply to rotational motion as well,
but in some instances their is now an angular
component that accounts for the rotation
i.e angular velocity, angular acceleration, angular
momentum
inertia, kinetic energy, work, and power are also
present
Rotational Motion cont.
There is however, a new dynamic known as torque
Torque describes how effectively a force can produce
angular acceleration
(how much a force acting on an object causes that
object to rotate)
Rotational Motion cont.
The most common example of torque relates to
automobiles
A car’s torque specs relate to the maximum amount
of torque that the internal combustion engine can
produce.
A car that has more torque can (in theory) accelerate
faster
Evaluation
Overall, I was not entirely satisfied with this independent
study. Although the material was not overly difficult, the
learning experience was not very enlightening. Several
factors contributed to this.
Attempting to take a primarily lab-based science class
individually is extremely difficult and definitely not as
rewarding.
Due to scheduling, I was not able to take the class during
the prep periods of my advisor, so I was on my own for the
majority of the semester.
Evaluation cont.
I have several suggestions to improve this course
A) Make sure an advisor is available at the same
time
B) If possible, I believe that taking this course with
2 or 3 other people would be extremely beneficial.
Not only would it provide grounds for collaboration
and teamwork, but it also opens up the possibility
of group labs.
Resources
Listed below are the various texts that I used
“Cracking the AP Physics C Exam 2015 Edition” -Princeton
Review
“Fundamentals of Physics Vol. 1” - Halliday, Resnick, Walker
“Physics Principles and Problems” - Zitzewitz, Haase, Harper
“Physics in Minutes” - Sparrow
“Physics- An Illustrated History of the Foundations of Science”
- Jackson
Image Sources
http://maretbccalculus2007-2008.pbworks.com/f/graphs2.bmp
https://upload.wikimedia.org/wikipedia/en/c/c8/Wind_diagram.jpg
http://image.shutterstock.com/z/stock-photo-black-hockey-puck-on-ice-rink-39167347.jpg
http://previews.123rf.com/images/graphego/graphego1012/graphego101200010/8390759Stylized-icons-of-empty-and-full-shopping-cart--Stock-Photo.jpg
https://lindajohnsonleadership.files.wordpress.com/2013/09/a-boy-jumps-off-a-diving-007.jpg
https://www.albert.io/blog/wp-content/uploads/2016/06/800px-Billard.jpg
http://www.asawicki.info/Mirror/Car%20Physics%20for%20Games/Car%20Physics%20for%2
0Games_files/tc_torques.png
https://qph.ec.quoracdn.net/main-qimg-23220e830c9728eeddd887b08ca8ee3dc?convert_to_webp=true