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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