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datdo
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Homework Statement
A board of mass m and length L is hinged to the ground. Attached to the board is a cup of negligible mass and is positioned Rc away from the hinge. Also on the edge of the board a ball rests. When the board is dropped from an angle of theta the ball is meant to be caught in the cup.
A) What is the minimum angle required for the ball to lag behind the board? I think cos(theta) > 1/2
B) Where must the cup be placed in order to catch the ball in terms of theta and L? I think the answer to this one was L/2cos(theta)
Homework Equations
F=ma
[tex]\tau=Frsin\theta[/tex]
[tex]\tau=I\alpha[/tex]
[tex]\alpha r=a[/tex]
The Attempt at a Solution
I'm really lost.
I guess for the cup to catch the ball both objects must be in the same spot in time so if I find their positions with respect to time and find their intersection...
board:
[tex]\tau=.5mgLsin\theta[/tex]
[tex]\alpha=\frac{3\tau}{mL^2}[/tex]
cup:
[tex]a_c=\alpha R_c[/tex]
ball:
[tex]a_b=g[/tex]
I don't know where to go from here...
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