Finding the Path of a Ball on Tilted Triangle Table

Click For Summary

Homework Help Overview

The problem involves a ball of mass m being released from a point on a tilted triangular table defined by its vertices. The objective is to determine where the ball will fall off the table, considering there are no friction or external forces acting on it.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the initial conditions and the geometry of the problem, with one suggesting to analyze the vector with the largest negative z component to determine the ball's path. Others question the assumption that the ball will roll towards a specific vertex and explore the implications of maximizing the z-coordinate as the ball moves.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the ball's trajectory and questioning the assumptions made about its path. Some guidance has been offered regarding the vector analysis, but no consensus has been reached on the exact approach to take.

Contextual Notes

There is a lack of clarity regarding the equation of the plane formed by the vertices of the triangle, which is crucial for determining the ball's path. Additionally, the absence of friction and external forces is a significant constraint in the analysis.

RyanGray
Messages
2
Reaction score
0

Homework Statement



The vertices of a tilted triangle table are (0,0,9), (5,3,7), (4,7,6) and I need to determine where the a ball of mass m falls off of the table. There is no friction or outside forces. The ball is released from point (0,0,9).

2. The attempt at a solution
I'm not sure how to start.. I was thinking of breaking it into 2 components but it doesn't seem to work out. Any help would be appreciated.
 
Physics news on Phys.org
While on the table, the ball will follow the vector with largest (negative) z component. You should be able to determine from that where the ball leaves the table.
 
wouldnt that vector = <4-0, 7-0, 6-9> = <4, 7, -6> ?
 
Last edited:
You are assuming that the ball will roll from vertex (0, 0, 9) to vertex (4, 7, 6)? Why? Why wouldn't it roll toward the other vertex. Or someplace in between?

If the ball rolls from (0, 0, 9) to the point (x, y, z) then it rolls along vector <x, y, z-9>. You want maximize z- 9 for (x, y, z) on the plane. What is the equation of that plane?
 

Similar threads

Replies
2
Views
1K
  • · Replies 12 ·
Replies
12
Views
3K
  • · Replies 5 ·
Replies
5
Views
4K
  • · Replies 1 ·
Replies
1
Views
3K
  • · Replies 21 ·
Replies
21
Views
3K
Replies
14
Views
3K
  • · Replies 14 ·
Replies
14
Views
2K
  • · Replies 62 ·
3
Replies
62
Views
10K
  • · Replies 11 ·
Replies
11
Views
3K
  • · Replies 9 ·
Replies
9
Views
2K