Arc of a cylinder - would appreciate help

  • Context: Undergrad 
  • Thread starter Thread starter m32dave
  • Start date Start date
  • Tags Tags
    Arc Cylinder
Click For Summary

Discussion Overview

The discussion revolves around calculating the height of an arc extending from the base of a cylinder and determining the length of a segment across the base. Participants explore the geometry involved in the problem, particularly focusing on the relationship between the arc length, the angle of elevation, and the dimensions of the cylinder.

Discussion Character

  • Exploratory, Technical explanation, Homework-related

Main Points Raised

  • One participant seeks assistance with calculating the height of an arc that is 2.000m long and extends at a 45-degree angle from the base of a cylinder with a diameter of 4.990m.
  • Another participant suggests using Pythagoras' theorem to find the height, proposing that the height equals the base length divided by the square root of 2.
  • A later reply confirms the previous suggestion, indicating that the same reasoning was independently reached by that participant.

Areas of Agreement / Disagreement

There is some agreement on using Pythagoras' theorem for the calculations, but the discussion does not resolve the specific values for height or the segment length, leaving the problem open-ended.

Contextual Notes

The discussion does not clarify the assumptions regarding the definitions of the arc and segment lengths, nor does it address any potential limitations in the application of Pythagoras' theorem in this context.

Who May Find This Useful

Individuals interested in geometry, particularly in applications involving cylindrical shapes and arcs, may find this discussion relevant.

m32dave
Messages
2
Reaction score
0
Would really appreciate help with the following:
Firstly, could someone answer this (simple?) question for something I am trying to make?
Secondly, could you give me the most straightforward formula for working it out if I change the length?

Hope this makes sense.
I have a cylinder. I have an arc exactly 2.000m long extending up from the base of the cylinder at 45 degrees following the elliptical arc. The diameter of the base is 4.990m What is the height of the arc? What is the length of the segment across the base, or the length of the arc around the cylinder base perpendicular to the end of the arc.

Big Thanks
 
Last edited:
Physics news on Phys.org
If you "unroll" a cylinder you get a plane, so you can just use Pitagora's theorem:

height = base length = L/sqrt(2)
 
Petr Mugver said:
If you "unroll" a cylinder you get a plane, so you can just use Pitagora's theorem:

height = base length = L/sqrt(2)

Thanks,for putting it succinctly. I figured the same thing out in my bed last night.
 
In bed- that's where I do my best work!
 

Similar threads

Undergrad Decomposing the arc length of a circular arc segment
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad I need help generating a 2D representation of a curved plane
  • · Replies 5 ·
Replies
5
Views
2K
Undergrad Current's Effect on Electrical Arcs
  • · Replies 9 ·
Replies
9
Views
4K
Undergrad Using the derivative of a tangent vector to define a geodesic
  • · Replies 7 ·
Replies
7
Views
5K
Graduate Computing arc length in Poincare disk model of hyperbolic space
  • · Replies 4 ·
Replies
4
Views
5K
Arc length of vector function - the integral seems impossible
  • · Replies 2 ·
Replies
2
Views
2K
Calculating Arc Length and Area of Cylinder Side
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad [Questions] Modeling a Baseball Pitch Trajectory in 3D Space
  • · Replies 1 ·
Replies
1
Views
2K
Graduate Equation of Curve Using Arc Length and Two Points
  • · Replies 3 ·
Replies
3
Views
9K
Undergrad Diameter of a Galaxy: Calculate Distance/Arc Min?
  • · Replies 9 ·
Replies
9
Views
4K