Each action there is a responsive reaction

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Discussion Overview

The discussion revolves around the concept of action and reaction forces, particularly in the context of a falling ball and its interaction with the ground upon impact. Participants explore the dynamics of the ball's motion, the forces involved, and the implications of these forces on the time the ball spends in contact with the ground, while considering various simplifying assumptions.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant describes the scenario of a falling ball and questions the logic behind the time it takes for the ball to reaccelerate after hitting the ground, suggesting that the reaction force should equal the weight of the ball.
  • Another participant challenges the assumption that the force equals the weight, arguing that the force during impact is greater than the weight when hitting a hard surface.
  • A different participant acknowledges the distinction between hardness and mass, noting that harder surfaces typically result in less energy loss during the bounce.
  • One participant proposes a formula for the time the ball stays on the ground, but seeks confirmation of its validity, indicating uncertainty about the relationship between force and time.
  • Another participant points out that the time spent on the ground is influenced by the deformation of both the ball and the ground, suggesting that in an ideal case with no deformation, the time would be zero.
  • A later reply introduces an integral expression related to force and motion, indicating a more complex relationship than initially considered.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the forces involved during the impact of the ball with the ground, with no consensus reached on the validity of the proposed equations or the assumptions made regarding force and time.

Contextual Notes

Limitations include assumptions about the ideal behavior of the ball and ground, the neglect of factors such as deformation, and the potential variability of forces during impact.

Werg22
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We all know that to each action there is a responsive reaction. Let's take the case of a falling ball. Ignoring factors such as friction, elasticity and thermal energy, the ball is dropped from a certain distance perpendicularly above the ground with an inexistent initial velocity. At the instant the ball hits the ground with a certain a certain force, the ground applies an equal force on the ball. The ball is then reflected in the opposite direction. But to get from a direction to one that is opposite, the ball has to, at a certain point drop to a velocity of zero. My thoughts were, naturally, that the reaction force reaccelerates the ball until a certain velocity is reached (witch is equivalent to the final velocity of the falling motion). And here is my problem; if really this is the case, then the force needs a certain time to reaccelerate the ball. Since the force is equivalent to the one of gm, so the time needed would be the same as the time the ball was in the air… this is obviously wrong, but by what logic?
 
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Werg22 said:
Since the force is equivalent to the one of gm, so the time needed would be the same as the time the ball was in the air… this is obviously wrong, but by what logic?
What makes you think the force equals the weight? It's much greater than that (at least for ball hitting a hard surface).
 
Okay, so the acceleration would be relative to the mass of the floor... thank you for teaching me!
 
That is not what Doc Al ment. Hardness [itex]\neq[/itex] Mass. Typical harder the surface the less energy lost from the ball and its return bounce.
 
This i know, but I am talking about the force, and ignoring such factors... Wouldnt the time the ball stays on the ground (then again ignoring all other factors) would be:
T= 2vm/F? Correct me if I am still wrong...
 
The time the ball spends on the ground depends on how the ground and ball deform.

In the ideal case where the ball and the ground do not deform then the ball spends zero time on the ground.

Your equation only works if the force provided by deformation is a constant this will not typically be true.
[tex] \int_{t_o}^{t_f}\vec{F}dt = 2\vec{v} m[/tex]
 
Hummm I would be lying if I said I completely understand... thanks for helping, Ill investigate this.
 

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