Posted by HALP on Friday, November 30, 2012 at 5:07pm.
M=Torque about hinge = 12.7 * .75 = 9.525
I about hinge = (1/3) m l^2 = (.68/3)2.25
angular acceleration alpha = M/I = 9.525/.51 = 18.7 radians/s^2
resulting linear acceleration of center East = .75 alpha = 14 m/s^2 (part a)
we better get the same acceleration East from the sum of forces on the stick
12.7east + force from hinge F = .68 (14)
12.7 + F = 9.52
F = -3.18 or 3.18 N west
Now the sweet point:
M = 12.7 x
alpha = 12.7 x/.51 = 24.9 x
a of center = .75 alpha = 18.7 x meters/s^2
F = m a
18.7 x = F/m but F is just 12.7 because the hinge force is zero so
18.7 x = 12.7/.68
x = 1 meter, the end of the stick
Try this with a mass distribution like a baseball bat or tennis racquet and the result will make more sense :)
Oh, one meter is not the end of the stick. It is 2/3 of the way out.
Which is about how far out on a bat you want to hit the ball without stinging your hand.
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