Ball bounces several times on an inclined plane

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Homework Help Overview

The problem involves a ball falling onto an inclined plane at an angle theta, making a perfectly elastic collision, and subsequently determining where it will hit the plane again. The scenario is analyzed under two conditions: one with a coefficient of restitution of e=0.75 and the other as perfectly elastic, with specific values provided for theta and height.

Discussion Character

  • Mixed

Approaches and Questions Raised

  • Participants discuss the nature of the collision, questioning whether it is perfectly elastic given the coefficient of restitution. There is also exploration of the angle of reflection and its relationship to the angle of incidence, particularly in the context of differing values from a textbook.

Discussion Status

The discussion has seen participants explore the implications of the coefficient of restitution on the collision dynamics. Some have provided calculations and comparisons to textbook values, while others have clarified the conditions under which the collision is considered elastic or inelastic. There is acknowledgment of differing results, but no explicit consensus has been reached regarding the correct angle of reflection.

Contextual Notes

Participants are working under the constraints of specific values for theta, e, and height, and are navigating the implications of these values on their calculations and interpretations of the problem.

carlyn medona

Homework Statement



A ball falls on an inclined plane of inclination theta from a
height h above the point of impact and makes a perfectly
elastic collision. Where will it hit the plane again ?
Solve the previous problem if the coefficient of restitution
is e. Use theta = 45°, e = .75 and h = 5 m.

Homework Equations

The Attempt at a Solution


I was able to solve first part of the problem and got the distance along the incline to be =8hsinθ. For second part I am getting angle of reflection of ball with normal to be 53 degree but the value in my text is 37degree. but I don't think the angle should be less than theta
 
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perfectly elastic collision
coefficient of restitution is e.
e = 0.75
So is it perfectly elastic or not?
 
yrjosmiel said:
So is it perfectly elastic or not?
They want it solved twice. Once perfectly elastic then again with e=0.75.
 
that's right. In second case it is not elatic
 
carlyn medona said:
angle of reflection of ball with normal to be 53 degree but the value in my text is 37degree. but I don't think the angle should be less than theta
You are correct. If e < 1 then the angle to the normal of the reflection will be greater than the incident angle to the normal.
I assume you noticed that 37=90-53.
 
yes.
 
okay i finally solved it and got a value of 18.5 m along the incline, thanks for the help.
 
carlyn medona said:
okay i finally solved it and got a value of 18.5 m along the incline, thanks for the help.
Good. (I get 18.56.)
 
Thank you for your help.
 

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