A tennis ball is attached by a thread to the rim of a rotating bicycle wheel (ra

Question

A tennis ball is attached by a thread to the rim
of a rotating bicycle wheel (radius = 0.5 meter) that rotates
once per second. The axle of the wheel is horizontal. A
very sharp blade cuts the thread (thereby detaching the
ball from the wheel) when the ball and the axle are in the
same horizontal plane (at the moment shown on the
diagram to the right).
a. Describe the trajectory of the tennis ball after the thread
is cut.
b. After the thread is cut, what maximum vertical height
(above where the thread is cut) does the ball reach?

Explanation / Answer

I would choose the body as the container+liquid+ball+thread (taken as weightless, probably); in that case the only downward force is the weight of all three and the only upward force is the scale, so the scale reads the total weight with no reference to whether the thread is connected to the ball or not. You can make this problem difficult by focusing on a different body, maybe the container, but if you draw all your free-body diagrams correctly and apply Newton's third law, you still get the same answer that the the scale reads the total weight. To the left I have shown all the forces on each of the bodies: red is the tension in the string which is also the force the string exerts on the sphere and the on the container; light blue is the force the container and fluid exert on each other; black represents the weight of each; green is the buoyant force which is the force of the fluid on the sphere and the force of the sphere on the fluid; purple is the force the scale exerts on the container.

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