Help me find the distance traveled using COR

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SUMMARY

The discussion focuses on calculating the distance traveled by a ceramic ball that falls from a height and bounces on a surface with a coefficient of restitution (COR) that halves after each bounce. The COR is defined as the ratio of the speed of separation to the speed of approach. The problem requires determining the total distance the ball travels by the time it hits the surface for the third time, taking into account the diminishing height of each bounce due to the halving of the COR.

PREREQUISITES
  • Understanding of the coefficient of restitution (COR) in physics.
  • Basic principles of kinematics, particularly free fall and bounce dynamics.
  • Knowledge of energy conservation in elastic and inelastic collisions.
  • Familiarity with mathematical series and summation techniques.
NEXT STEPS
  • Study the mathematical derivation of the distance traveled in a series of bounces.
  • Learn about the implications of the coefficient of restitution on energy loss during collisions.
  • Explore kinematic equations for vertical motion under gravity.
  • Investigate real-world applications of COR in material science and engineering.
USEFUL FOR

Physics students, educators, and anyone interested in understanding the dynamics of bouncing objects and energy loss in collisions.

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Homework Statement



A ceramic ball of mass m falls form rest a distance h[0] above a horizontal ceramic surface. The subsequent motion of the ball is purely vertical, bouncing ONLY on one spot on the surface. If the coefficient of restitution between the ball and surface halves after every bounce, find the distance traveled by the ball when the ball hits the surface for the third time.

Homework Equations



COR= speed of separation/speed of approach


The Attempt at a Solution



If the coefficient of restitution between the ball and surface halves after every bounce, find the distance traveled by the ball when the ball hits the surface for the third time.
 
Last edited:
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corpuzdawn said:

Homework Statement



A ceramic ball of mass m falls form rest a distance h[0] above a horizontal ceramic surface. The subsequent motion of the ball is purely vertical, bouncing ONLY on one spot on the surface. If the coefficient of restitution between the ball and surface halves after every bounce, find the distance traveled by the ball when the ball hits the surface for the third time.

Homework Equations



COR= speed of separation/speed of approach


The Attempt at a Solution



If the coefficient of restitution between the ball and surface halves after every bounce, find the distance traveled by the ball when the ball hits the surface for the third time.
Your attempt is just a restatement of the problem, so not really an attempt :frown:

What are your thoughts on how you might approach this problem? For example, how does the height of a bounce depend upon the velocity?
 

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