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A ball trapped in a star


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#1 BMAD

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Posted 13 April 2013 - 03:21 AM

star.png.

A ball  with a 1m diameter starting out in the middle of a 5 pointed star table (outer 5 points - 10m radius..... inner 5 points - 5m radius) has a starting angle of a random value from 0 to 360 degrees. The ball is now set loose and travels around the table.

Now how many sides on average will have been hit once the ball has travelled 1000m ?
Also, where are the most likely points that the ball will end up?

To make things even more wonderfully confusing, the star rotates at an ever increasing speed of half a revolution for every 10 metres the ball has travelled. These speed increases are in incremental 'jumps'. Observe:
0 revolutions per 10 metres of ball travel: (when the ball has travelled 0 - 10 metres)
0.5 revolutions per 10 metres of ball travel: (when the ball has travelled 10 - 20 metres)
1.0 revolutions per 10 metres of ball travel: (when the ball has travelled 20 - 30 metres)
1.5 revolutions per 10 metres of ball travel: (when the ball has travelled 30 - 40 metres)
etc. etc.

Now how many sides on average will have been hit once the ball has travelled 1000m ?


Edited by BMAD, 13 April 2013 - 03:22 AM.

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#2 bonanova

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Posted 13 April 2013 - 07:18 AM

Assumptions?

  1. Distance (1000 m) traveled is with respect to a stationary coordinate system, not that of the star?
  2. Elastic collisions with the walls, with equal angles of incidence and reflection?
  3. Since the ball is not a point, what bounce angle is assumed if the ball hits an interior point of the star?

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#3 BMAD

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Posted 13 April 2013 - 01:48 PM

 

Assumptions?

  1. Distance (1000 m) traveled is with respect to a stationary coordinate system, not that of the star?  Yes. 
  2. Elastic collisions with the walls, with equal angles of incidence and reflection? Yes, kinetics stays the same and equal angles of reflection is fine.
  3. Since the ball is not a point, what bounce angle is assumed if the ball hits an interior point of the star? perpendicular from the points from the sphere hitting the point on the line and the direction of the ball.

taken from http://www.physics.u...ross/BOUNCE.htm  to help

 

 

 

If the ball slides throughout the bounce then F/N = coefficient of sliding friction. But that happens only if the ball is incident at a glancing angle to the surface, typically about 20 degrees or less. At larger angles of incidence, the bottom of the ball will come to a stop before the ball bounces, and grip the surface, in which case static friction acts on the ball. F is then determined by elastic distortion of the ball in a direction parallel to the surface, and acts as a shear force. F can even reverse direction during the bounce.

 

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