Shawn Zhong

Shawn Zhong

 钟万祥
  • Tutorials
  • Mathematics
    • Math 240
    • Math 375
    • Math 431
    • Math 514
    • Math 521
    • Math 541
    • Math 632
    • Abstract Algebra
    • Linear Algebra
    • Category Theory
  • Computer Sciences
    • CS/ECE 252
    • CS/ECE 352
    • Learn Haskell
  • AP Notes
    • AP Microecon
    • AP Macroecon
    • AP Statistics
    • AP Chemistry
    • AP Physics E&M
    • AP Physics Mech
    • CLEP Psycho

Shawn Zhong

 钟万祥
  • Tutorials
  • Mathematics
    • Math 240
    • Math 375
    • Math 431
    • Math 514
    • Math 521
    • Math 541
    • Math 632
    • Abstract Algebra
    • Linear Algebra
    • Category Theory
  • Computer Sciences
    • CS/ECE 252
    • CS/ECE 352
    • Learn Haskell
  • AP Notes
    • AP Microecon
    • AP Macroecon
    • AP Statistics
    • AP Chemistry
    • AP Physics E&M
    • AP Physics Mech
    • CLEP Psycho

Notes

Home / Notes / Page 46

3.6 – Atwood Machines

  • Dec 08, 2017
  • Shawn
  • AP Physics C Mechanics
  • No comments yet
Atwood Machine • Atwood Machine - two objects are connected by a light string over a massless pulley • Ideal pulleys are frictionless and massless (they add no inertia to the system) • Tension is constant in a light string passing over an ideal pulley Solving Atwood Machine Problems 1. Adopt a sign convention for positive and negative motion 2. Draw a free body diagram for each mass 3. Write Newton's Second Law equations for each mass 4. Solve for unknowns Alternate Solution • Analyze the system as a whole Mass and Pulley on a Ramp
Read More >>

4.1 – Work

  • Dec 08, 2017
  • Shawn
  • AP Physics C Mechanics
  • No comments yet
What is Work? • Work is the process of moving an object by applying a force • The object must move for work to be done • The force must cause the movement • Work is a scalar quantity • Units are Joules Work in One Dimension • Only the force in the direction of the displacement contributes to the work done Non-Constant Forces • Work done is the area under the force vs. displacement graph Hooke's Law • The more you stretch or compress a string, the greater the force of the spring • The spring's force is opposite the direction of its displacement from equilibrium • Model this as a linear relationship, where the force applied by the spring is equal to a constant (the spring constant) multiplied by the spring's displacement from its equilibrium (rest) position • F_s=−kx • Slope of the graph gives you the spring constant, k (in N/m) Work Done in Compressing a Spring • A spring obeys Hooke's Law. How much work is done in compressing the spring from equilibrium to some point x? Work Done in Compressing a Non-Linear Spring Work in Multiple Dimensions Work-Energy Theorem Example: Velocity from an F-d Graph • Determine the object's final speed.
Read More >>

4.2 – Energy & Conservative Forces

  • Dec 08, 2017
  • Shawn
  • AP Physics C Mechanics
  • No comments yet
What is Energy? • Energy is the ability or capacity to do work ○ Work is the process of moving an object • Energy is the ability or capacity to move an object Energy Transformations • Energy can be transformed from one type to another • You can transfer energy from one object to another by doing work • Work-Energy Theorem ○ Work done on a system by an external force changes the energy of the system Kinetic Energy • Kinetic Energy is energy of motion ○ The ability or capacity of a moving object to move another object • K=1/2 〖mv〗^2 Potential Energy • Potential Energy (U) is energy an object possesses due to its position or state of being ○ Gravitational Potential Energy (Ug) is the energy an object possesses because of its position in a gravitational field ○ Elastic Potential Energy (Us) ○ Chemical Potential Energy ○ Electric Potential Energy ○ Nuclear Potential Energy • A single object can have only kinetic energy, as potential energy requires an interaction between objects Internal Energy • The internal energy of a system include the kinetic energy of the objects that make up the system and the potential energy of the configuration of the objects that make up the system • Changes in a system's structure can result in changes in internal energy Gravitational Potential Energy (Ug) Conservative Forces • A force in which the work done on an object is independent of the path taken is known as conservative force • A force in which the work done moving along a closed path is zero • A force in which the work done is directly related to a negative change in potential energy (W=-ΔU) Conservative Forces Non-Conservative Forces Gravity Elastic Forces Friction Drag Air Resistance Coulombic Forces Newton's Law of Universal Gravitation • The gravitational force of attraction between any two objects with mass • F_g=−(〖Gm〗_1 m_2)/r^2 r ̂ Force from Potential Energy Summary
Read More >>

4.3 – Conservation of Energy

  • Dec 08, 2017
  • Shawn
  • AP Physics C Mechanics
  • No comments yet
Conservation of Mechanical Energy • Consider a single conservative force doing work on a closed system • ∵W_F=ΔK, W_F=−ΔU • ∴ΔK+ΔU=0 • ∴K_i+U_i=K_f+U_f Non-Conservative Forces • Non-conservative forces change the total mechanical energy of a system, but not the total energy of a system • Work done by a non-conservative force is typically converted to internal (thermal) energy • E_total=K+U+W_NC • E_mecℎ=K+U 2002 Free Response Question 3 2007 Free Response Question 3 2010 Free Response Question 1 2013 Free Response Question 1
Read More >>

4.4 – Power

  • Dec 08, 2017
  • Shawn
  • AP Physics C Mechanics
  • No comments yet
Defining Power • Power is the rate at which work is done • Power is the rate at which a force does work • Units of power are joules/second, or watts • P_avg=ΔW/Δt • P=dW/dt=(F ⃗⋅dr ⃗)/dt=F ⃗⋅(dr ⃗)/dt=F ⃗⋅v ⃗ 2003 Free Response Question 1
Read More >>
  • 1
  • …
  • 44
  • 45
  • 46
  • 47
  • 48
  • …
  • 84

Search

  • Home Page
  • Tutorials
  • Mathematics
    • Math 240 – Discrete Math
    • Math 375 – Linear Algebra
    • Math 431 – Intro to Probability
    • Math 514 – Numerical Analysis
    • Math 521 – Analysis I
    • Math 541 – Abstract Algebra
    • Math 632 – Stochastic Processes
    • Abstract Algebra @ 万门大学
    • Linear Algebra @ 万门大学
    • Category Theory
  • Computer Sciences
    • CS/ECE 252 – Intro to Computer Engr.
    • CS/ECE 352 – Digital System Fund.
    • Learn Haskell
  • Course Notes
    • AP Macroeconomics
    • AP Microeconomics
    • AP Chemistry
    • AP Statistics
    • AP Physics C: E＆M
    • AP Physics C: Mechanics
    • CLEP Psychology
  • 2048 Game
  • HiMCM 2016
  • 登峰杯 MCM

WeChat Account

Categories

  • Notes (418)
    • AP (115)
      • AP Macroeconomics (20)
      • AP Microeconomics (23)
      • AP Physics C E＆M (25)
      • AP Physics C Mechanics (28)
      • AP Statistics (19)
    • Computer Sciences (2)
    • Mathematics (300)
      • Abstract Algebra (29)
      • Category Theory (7)
      • Linear Algebra (29)
      • Math 240 (42)
      • Math 375 (71)
      • Math 514 (18)
      • Math 521 (39)
      • Math 541 (39)
      • Math 632 (26)
  • Projects (2)
  • Tutorials (11)

Archives

  • October 2019
  • May 2019
  • April 2019
  • March 2019
  • February 2019
  • December 2018
  • November 2018
  • October 2018
  • September 2018
  • July 2018
  • May 2018
  • April 2018
  • March 2018
  • February 2018
  • January 2018
  • December 2017
  • November 2017
  • October 2017
  • September 2017
  • August 2017
  • July 2017
  • June 2017

WeChat Account

Links

RobeZH's thoughts on Algorithms - Ziyi Zhang
Copyright © 2018.      
TOP