Impact and the Coefficient of Restitution

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Homework Help Overview

The discussion revolves around the coefficient of restitution and its application to the normal velocity component during a collision, specifically in the context of a ball bouncing off a wall. Participants are exploring the implications of this concept and how it relates to the velocities involved in the collision.

Discussion Character

  • Conceptual clarification, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants are questioning why the coefficient of restitution applies only to the normal velocity component and how to calculate the resulting velocities. There are discussions about resolving initial velocities into components and the effects of friction on the collision dynamics.

Discussion Status

The conversation is actively exploring different interpretations of the coefficient of restitution and its application. Some participants have provided insights into the mechanics of the collision, while others are seeking clarification on the assumptions regarding friction and velocity components.

Contextual Notes

There are assumptions being made about the absence of friction between the ball and the wall, which influences the analysis of the collision. The complexity of oblique bouncing with friction is also noted, indicating that the discussion is considering various scenarios that could affect the outcome.

Vladimir_Kitanov
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Homework Statement
V1=50 ft/m
e = 0,75
Relevant Equations
e=(relative velocity after collision)/(relative velocity before collision)
Last post with picture, after this i will use Latex.

She say that correct answer is 41 ft/m.

Capture.PNG

IMG_20220730_194136.jpg

Is this correct?
 
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I get answer b). ##41 \ ft/m##
 
The coefficient of restitution applies only to the normal velocity component.

PS effectively you just multiplied 50 by 0.75.
 
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PeroK said:
The coefficient of restitution applies only to the normal velocity component.
Why only to normal velocity?
And how to calculate x then?
 
Vladimir_Kitanov said:
Why only to normal velocity?
Because the energy lost is in the compression and subsequent expansion of the object, and the extent of the compression depends on the velocity component normal to the contact surface.
Vladimir_Kitanov said:
And how to calculate x then?
Resolve the initial velocity into components.
 
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Normal component is in x direction, and ball bounce of wall just in x direction.That is why we can use coefficient of restitution in that direction?
And speed in y is same because we need to calculate speed right after collision?
Is that correct?
 
I guess one has to assume that there is no friction between the ball and the wall so that the compression is only in the horizontal direction.
 
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malawi_glenn said:
I guess one has to assume that there is no friction between the ball and the wall so that the compression is only in the horizontal direction.
Yes, and that.
 
malawi_glenn said:
I guess one has to assume that there is no friction between the ball and the wall so that the compression is only in the horizontal direction.
Oblique bouncing with friction is quite complicated. Assuming no slipping, as the ball compresses, the frictional component of the reaction force exerts a torque about the ball's centre, causing it to start rotating. So now we have rolling resistance as a new part of the ball starts to compress and a corresponding part starts to decompress.
Superballs (https://en.wikipedia.org/wiki/Super_Ball), popular in the late '60s, could acquire so much spin that at the next bounce they would reverse direction, bouncing back and forth between two points on the floor.
 
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