{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# set5 - Department of Physics The Ohio State University Prof...

This preview shows pages 1–2. Sign up to view the full content.

Department of Physics Prof. R. Bundschuh The Ohio State University Fifth Problem Set for Physics 664 (Theoretical Mechanics) Spring quarter 2004 Important dates: May 11 9:30am-10:18am midterm exam, May 31 no class, Jun 9 9:30am-11:18am final exam Due date: Thursday, May 6 12. Shortest path on a volcano 12 points You are hiking on a volcano given by the equation z = 1 - q x 2 + y 2 . You are at point ( - 1 , 0 , 0) and want to get to the other side, namely to the point (1 , 0 , 0), along the shortest possible path. x y z a) Express the infinitesimal line element d s = d x 2 + d y 2 + d z 2 in cylindrical coordinates ( r, φ, z ) defined by x = r cos φ and y = r sin φ . b) Write down the length of an arbitrary path (specified by r ( φ ), why?) on the volcano as an integral over φ . c) Find a differential equation for the path r ( φ ) of minimal length. d) Solve the differential equation for your hiking problem. [Hint: in order to solve the differential equation, it is helpful to reformulate it in terms of the variable u ( φ ) 1 /r ( φ ).] e) Calculate the length of your path and sketch the path. [Hint:

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 2

set5 - Department of Physics The Ohio State University Prof...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online