William W. answered • 01/03/22
Experienced Tutor and Retired Engineer
Initial momentum (P0) = momentum after 1 collision (P1) = momentum after 2 collisions (P2) . . . = momentum after 10 collisions (P10)
Let the mass of the right ball be mR with its associated velocity as vR and the mass of the left ball be mL with its associated velocity as vL
P0 = mRvR-0 + mLvL-0
P10 = mRvR-10 + mLvL-10
So, since P0 = P10 then mRvR-0 + mLvL-0 = mRvR-10 + mLvL-10
But we know that mR = 2000mL so:
(2000mL)vR-0 + mLvL-0 = (2000mL)vR-10 + mLvL-10
we can divide both sides by mL to get:
2000vR-0 + vL-0 = 2000vR-10 + vL-10
vL-0 - vL-10 = 2000vR-10 - 2000vR-0
vL-0 - vL-10 = 2000(vR-10 - vR-0)
(vL-0 - vL-10)/2000 = (vR-10 - vR-0)
Divide both sides by vR-0 to get:
(vL-0 - vL-10)/(2000vR-0) = (vR-10 - vR-0)/vR-0
The right side of this equation, (vR-10 - vR-0)/vR-0 is the percent change in the right ball's speed after all impacts so the left side is the answer we are looking for:
(vL-0 - vL-10)/(2000vR-0)
William W.
Please be aware that since you did not show the figure, I am unaware of the context of the problem so there may be additional information that can be derived from such a figure that are not reflected here.01/04/22