How Do You Calculate Velocities in a Three-Ball Elastic Collision?

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Homework Help Overview

The discussion revolves around calculating the velocities of three balls involved in a perfectly elastic collision. The original poster describes a scenario where ball A, with a mass of 0.5 kg, rolls towards ball B at a velocity of 3.5 m/s, which then impacts ball C.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need to consider momentum conservation and relative velocities in elastic collisions. There are questions regarding the presence of friction and the nature of the motion (rolling vs. sliding). Some participants suggest using initial and final velocities in equations to solve for the unknowns.

Discussion Status

Some participants have provided equations and methodologies for calculating the velocities after the collisions. The original poster expresses uncertainty about their understanding of the physics involved, indicating a lack of prior experience in the subject. There is no explicit consensus on the final outcomes, but attempts to guide the original poster are evident.

Contextual Notes

Participants note that there is no friction involved in the scenario and clarify the masses of the balls. The original poster's lack of experience in physics is acknowledged, which may affect their ability to follow the discussion.

Emily-x
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Homework Statement



The first ball (A), of mass 0.5 Kg is rolled towards the second (B) at a velocity of 3.5 ms. Ball B then impacts ball C.

Assume this collision is perfectly elastic.

Calculate:
a. The velocity at which ball A recoils after impacting with ball B.
b. The velocity with which ball B collides with ball C
c. The velocity with which ball B recoils from ball C
d. The velocity at which ball C is moving after ball B has collided with i

I don't know how to work this out! :/
 
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is there friction? as in is it actually rolling or sliding?
 
Mass;

Ball A = 0.5 kg
Ball B = 0.782 kg
Ball C = 0.386 kg

No friction just that ball A is moving at 3.5ms on a flat surface
 
do the collision between a and b first. total momentum before the impact equals the total momentum after, and the relative velocity after impact equals (-e)time relative velocity before impact. call initial velocities u1 and u2 and after collision v1 and v2

so,
m1u1+ m2u2 = m1v1 + m2v2

and

v2-v1 = -e(u2-u1)

you know u1 and u2 as 3.5 and 0 and you also know m1 and m2 as 0.5 and 0.782

just plug in the values and solve simultaneously
 
Thanks, I'll try.. I've never done Physics before!
 
The velocity at which ball A recoils after impacting with ball B

-0.7698907956318254

The velocity at which ball B collides with ball C

2.7301092043681745

The velocity at which ball B recoils from ball C

0.9256192165494838

The velocity at which ball C is moving after ball B has collided with it

3.6557284209176584
 

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