Finding the Path of a Ball on Tilted Triangle Table

In summary, the goal is to determine where a ball of mass m will fall off of a tilted triangle table, given the vertices (0,0,9), (5,3,7), and (4,7,6). There is no friction or outside forces, and the ball is released from point (0,0,9). It is suggested to break the problem into two components and determine the vector with the largest (negative) z component, which would indicate the direction of the ball's roll. However, it is also noted that the ball could potentially roll towards another vertex or somewhere in between. To find the point where the ball leaves the table, the equation of the plane formed by the three vertices must be considered.
  • #1
RyanGray
2
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.
 
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  • #2
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.
 
  • #3
wouldnt that vector = <4-0, 7-0, 6-9> = <4, 7, -6> ?
 
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  • #4
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?
 

FAQ: Finding the Path of a Ball on Tilted Triangle Table

How do you determine the trajectory of a ball on a tilted triangle table?

To determine the trajectory of a ball on a tilted triangle table, you will need to consider the angle of the tilt, the initial velocity of the ball, and the force of gravity. These factors will help you calculate the path of the ball as it rolls down the table.

What are the key factors that affect the path of a ball on a tilted triangle table?

The key factors that affect the path of a ball on a tilted triangle table are the angle of the tilt, the initial velocity of the ball, and the force of gravity. Other factors such as the surface of the table and air resistance may also play a role.

Can the path of a ball on a tilted triangle table be predicted accurately?

The path of a ball on a tilted triangle table can be predicted with a high degree of accuracy by using mathematical equations and physics principles. However, external factors such as friction and imperfections in the table surface may slightly affect the actual path of the ball.

How does the angle of the tilt affect the path of a ball on a tilted triangle table?

The angle of the tilt greatly affects the path of a ball on a tilted triangle table. The steeper the angle, the faster the ball will roll down the table and the shorter the distance it will travel. A shallower angle will result in a slower speed and a longer distance traveled by the ball.

Are there any real-world applications for understanding the path of a ball on a tilted triangle table?

Understanding the path of a ball on a tilted triangle table has various real-world applications, such as in sports like billiards or golf where the trajectory of a ball is crucial for success. It can also be applied in engineering and design to determine how objects will move on inclined surfaces.

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