mPEC Forum

ถามโจทย์ปัญหา => ถามโจทย์ปัญหากลศาสตร์ => Topic started by: phys_pucca on July 01, 2005, 09:00:51 AM



Title: CLASSICAL MECHANICS SECOND YEAR STUDENTS EPISODE III
Post by: phys_pucca on July 01, 2005, 09:00:51 AM
กระทู้สำหรับผู้ที่ไม่พอใจโจทย์ข้อที่มาตั้งเอาไว้ อาจเป็นเพราะยากหรือง่ายเกินไป
   จะสามารถเอาโจทย์มา โพส เองและแสดงวิธีทำเองได้เลยครับ
                                           >:A    PHYSICS NEVER DIE


Title: Two sticks and a wall
Post by: I am wathan on July 01, 2005, 04:16:21 PM
(http://einstein.sc.mahidol.ac.th/~u4705180/mpec/03_12_e.JPG)


Title: Re: CLASSICAL MECHANICS SECOND YEAR STUDENTS EPISODE III
Post by: pattyphys on July 01, 2005, 04:34:55 PM
Patty,  
Here we go again.Under construction.


Title: Re: CLASSICAL MECHANICS SECOND YEAR STUDENTS EPISODE III
Post by: I am wathan on July 01, 2005, 06:08:40 PM
Computer room is closed.  :(
See again on Monday.


Title: Re: CLASSICAL MECHANICS SECOND YEAR STUDENTS EPISODE III
Post by: I am wathan on July 04, 2005, 10:42:39 AM
Wait for figure!!!

Consider the lower stick. Let the junction between two sticks be the fulcrum.
We get
\begin{array}{rcl}N_{b,y}L& = &\rho gL\frac{L}{2} \\ N_{b,y}& = &\rho g\frac{L}{2}\end{array}

Consider vertical forces on two sticks.
\begin{array}{rcl}N_{t,y}+N_{b,y}& = &\rho gL(1+\sec{\theta}) \\ N_{t,y}& = &\rho gL(1+\sec{\theta})-N_{b,y} \end{array}

Substitue N_{b,y}. Then
\begin{array}{rcl}N_{t,y}& = &\rho gL\left( \frac{1}{2}+\sec{\theta} \right) \\ & = &\rho gL\left( \frac{2+\cos{\theta}}{\cos{\theta}}\right) \end{array}

Consider the upper stick. Let the junction between two sticks be the fulcrum (again).
\begin{array}{rcl}N_{t,y}\cos{\theta}L\sec{\theta}+N_{t,x}\sin{\theta}L\sec{\theta}& = &\rho gL\sec{\theta}\cos{\theta}\frac{L}{2}\sec{\theta} \\ N_{t,y}\cos{\theta}+N_{t,x}\sin{\theta}& = &\rho g\frac{L}{2} \\ N_{t,x}& = &\rho g\frac{L}{2}-N_{t,y}\cos{\theta}\end{array}

Substitue N_{t,y}. Then
N_{t,x}=-\rho gL\left( \frac{\cos{\theta}+1}{2\sin{\theta}}\right)


 :laugh: Typing \LaTeX is very fun.


Title: Re: CLASSICAL MECHANICS SECOND YEAR STUDENTS EPISODE III
Post by: I am wathan on July 04, 2005, 10:48:44 AM
If \theta \rightarrow 0, then \sin{\theta} \rightarrow 0
So that, N_{t,x} \rightarrow -\infty

If \theta \rightarrow \pi/2, then \cos{\theta} \rightarrow 0
So that, N_{t,y} \rightarrow \infty