|Nov16-08, 03:50 PM||#1|
Finding Velocity of a ball hitting a ball hanging from a string
1. The problem statement, all variables and given/known data
A 20.0 ball is fired horizontally with initial speed Vi toward a 110 g ball that is hanging motionless from a 1.10 m -long string. The balls undergo a head-on, perfectly elastic collision, after which the 110 g ball swings out to a maximum angle theta = 50.0.
What was Vi?
2. Relevant equations
call ball mass .02 kg = A
call ball .11 kg = B
Avai + Bvbi = Avaf + Bvbf
Ki = Kf
(1/2)Avai^2 + (1/2)Bvbi^2 = (1/2)Avaf^2 + (1/2)Bvbf^2
vaf = (A - B)/(A + B) * vai
3. The attempt at a solution
vbi = 0 m/s
Bvbi = 0
Avai = -Avaf + Bvbf
vai = (A + B)/(A - B) * vaf
my problem is finding vaf, the final velocity of block A.
the final height y = L(1 - cos(theta)) = 1.1(1 - cos(50)) = .393 m
|Nov16-08, 04:32 PM||#2|
You know the height the ball on the string went up to, so you know from conservation of energy and the m*g*h what the KE of the ball on the string was from the collision.
mv2/2 = m*g*h
|Nov16-08, 04:51 PM||#3|
So, I find vbf = sqrt((2*g*h)), masses cancel out.
that gets me about 2.775 m/s
Vai = Vbf*(A + B)/2*A
which equals about 9.02 m/s.
and algebraically plugging it back in to find vbf, I find that my answer is correct (at least for the previous work that I did).
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