- Homework Statement
- Two elastic balls of masses m1 and m2 are placed one above the other (leaving a very small gap between them) and
are released to fall freely on a height from a height h. Assuming that the impact on the floor is elastic, calculate:
a. what must be the ratio m1/m2 of the balls so that the top ball gets the biggest part of total balls energy after impact?
b. What is the maximum height a ball of mass m1 can rise after impact?
h is much bigger than dimension the of balls.
- Relevant Equations
- Conservation of energy and momentum.
With given information in the problem I can't decide which direction balls will go after collision. I assumed they will go in opposite directions. I know that is not a full solution, but I can't come up with anything else.
From conservation of energy we have:
Conservation of momentum:
from these equations I get:
dividing by m2:
Then I replaced v2 from (3), solved quadratic and took derivative with respect to ##m1/m2## , but that gives me absolutely nothing.
I suppose I am making mistake in (2).
I also do not understand derivation of equation of balls speeds in perfectly elastic collision. There is equation:
And I do not understand how can we take them all positive if we don't know which direction after collision will they go.
If I take all momentum terms positive in equation (2), I get ##v_1=v_2##, which can't be true.
Please explain it to me.