A simple sling can be built by placing a projectile in a tube and then spinning

Question

A simple sling can be built by placing a projectile in a tube and then spinning it. Consider a simple model on which the tube is pinned as shown and is rotated about the pin in the horizontal plane at a constant angular velocity omega. Assume that there is no friction between the projectile and the inside of the tube and that the projectile is initially kept fixed at a distance d from the open end of the tube.

Letting d= 3ft and L= 7ft, determine the value of the tube's angular velocity omega if, after release, the projectile exists the tube with a speed 90 ft/s.

Please show FBD if it's easy to, as well as all steps and operations. Please also define any new variables.

For EML 3217.

Explanation / Answer

writing eqns along the length of the tube

a=-2rcos-gsin

=>vdv/dr=-2rcos-gsin

=>v2/2-u2/2=(-2L2/2*cos-gsin*L)-(-2d2/2*cos-gsin*d)

v=90ft/s; u=0; L=7 ft; d=3ft; needs to be given

putting the above values we get

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