Complete Learning Academy
  • Home
  • Programs
    • Summer Programs
    • AP Test Prep Classes
    • ACT Prep Classes
    • SAT Prep Classes
    • Olympiad Classes
    • History & More
    • Reading Writing Math & Science Tutoring
    • Pricing
  • Resources
    • ACT SAT AP AMC Test Dates
    • AP Score Distribution
    • ACT Score Distribution
    • SAT Score Distribution
    • SAT ACT Conversion Table
    • AP Past Exams
    • Math and Science Olympiad Problems
    • College Planning
  • CLA Academic contents
    • Solved Examples
    • YouTube
  • About Us
    • News & Events
    • Engaging our Community
    • Our Staff
    • Job Openings
  • Contact Us
  • CLA Blog
  • 한국어 블로그

The problem #23 of 2015 US Physics Olympiad

6/23/2016

2 Comments

 
The problem #23 of 2015 US Physics Olympiad F=ma Exam generated a bit of controversy as people had slight difficulty dealing with spring that was already compressed at the initial state. The controversy was compounded by some typos in the released solution. The version here might be easier for some people to understand. Please check it and suggest any way to improve it.
Picture
Picture
After deriving all the equation parts in the solution, we can gain physical insight into the situation. We may argue that the mechanical energy of the system can be separated into portion related to the smaller mass that was dropped, and larger mass that already was in sort of equilibrium with the spring, thus be effectively set to zero. It can be viewed that dropping of the smaller mass is what introduced the new mechanical energy into the system, thus we only need to worry about how the smaller mass oscillates within the system as any part of mechanical energy related to the movement of the larger mass will always balance out to zero. Then the oscillating movement of the smaller mass, of which the larger mass will duplicate due to being stuck to the smaller mass, is dependent only on the kinetic energy it introduce to the system ( KE ), gravitational potential energy of the smaller mass( m1 gx), and the additional contraction/extension of the spring induced by the impact of the smaller mass ( ½ k x^2 ), while the gravitational potential energy of the larger mass can be ignored due to existing compression of the spring before the impact.
2 Comments

Hong Kong Advanced Level Examination - Math 4

7/29/2015

0 Comments

 
Picture
Here is downloadable file if you want to print all of them.
hong_kong_advanced_level_examination_math.pdf
File Size: 147 kb
File Type: pdf
Download File

0 Comments

Hong Kong Advanced Level Examination - Math 3

7/28/2015

0 Comments

 
Picture
0 Comments

Hong Kong Advanced Level Examination - Math 2

7/27/2015

0 Comments

 
Picture
0 Comments

Hong Kong Advanced Level Examination - Math 1

7/26/2015

0 Comments

 
This is a slightly modified version of Hong Kong Adavanced Level Examination which was used to test Hong Kong students who wanted to enter colleges. Take a look and enjoy!
Wikepedia link about HKLE.
Picture
0 Comments

Tokyo University Entrance Exam Math Problems 047

6/21/2015

0 Comments

 
Picture
[CLA notes : Try this without using your calculators. ]

0 Comments

Tokyo University Entrance Exam Math Problems 046

6/20/2015

0 Comments

 
Picture
Picture
Picture
[CLA notes : Pay close attentions to the domains for each equations. ]

0 Comments

Tokyo University Entrance Exam Math Problems 045

6/19/2015

0 Comments

 
Picture
[CLA notes : A straight forward min-max problem where you have to be careful of the absolute value in the function. ]

0 Comments

Tokyo University Entrance Exam Math Problems 044

6/18/2015

0 Comments

 
Picture
[CLA notes : The key information to process is what it means for a function to have negative value for certain x value and positive value for different x value. In other word, remember the Intermediate Value Property of a function. ]
0 Comments

Tokyo University Entrance Exam Math Problems 043

6/17/2015

0 Comments

 
Picture
[CLA note : Just keep narrowing down the possibilities. Every clue here is important, and the whole thing is easier than it appears. ]

0 Comments
<<Previous

    Archives

    April 2022
    February 2022
    January 2021
    June 2016
    July 2015
    June 2015
    May 2015
    April 2015
    March 2015
    February 2015
    January 2015

    Author

    Complete Learning Academy

    Categories

    All
    College Preparation
    General
    Mathematics

    RSS Feed

Our Services

AP
ACT
SAT
Math Olympiad & Physics Olympiad
​Reading Writing Math Science
​
​ESL
Daytime SAT ACT AP
​Winter Break Academic Camp

Resources

AP ACT SAT AMC Test Dates
AP Test Score Distribution
ACT Test Score Distribution
SAT Test Score Distribution
SAT ACT Score Conversion Table
AP Past Exams
Math and Science Olympiad Problems
College Planning

Complete Learning Academy

About Us
​Our Staff
​Contact Us
Picture
Copyright ©2021   |   135 Cumberland Rd. Suite #201, Pittsburgh, PA   |   412-701-1011   |   [email protected]                     
Some images are designed by Freepick
  • Home
  • Programs
    • Summer Programs
    • AP Test Prep Classes
    • ACT Prep Classes
    • SAT Prep Classes
    • Olympiad Classes
    • History & More
    • Reading Writing Math & Science Tutoring
    • Pricing
  • Resources
    • ACT SAT AP AMC Test Dates
    • AP Score Distribution
    • ACT Score Distribution
    • SAT Score Distribution
    • SAT ACT Conversion Table
    • AP Past Exams
    • Math and Science Olympiad Problems
    • College Planning
  • CLA Academic contents
    • Solved Examples
    • YouTube
  • About Us
    • News & Events
    • Engaging our Community
    • Our Staff
    • Job Openings
  • Contact Us
  • CLA Blog
  • 한국어 블로그