Frictionless, horizontal table radius and speed ?

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SUMMARY

The discussion focuses on calculating the speed required for a 0.20 kg puck to rotate in a circle of radius 0.50 m while connected to a 1.20 kg block hanging at rest. The tension in the rope must equal the gravitational force acting on the block, which is 11.76 N (1.20 kg × 9.81 m/s²). This tension also provides the necessary centripetal force for the puck, leading to the equation T = (mv²)/r. Solving for speed, the puck must rotate at approximately 3.42 m/s to maintain the system in equilibrium.

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Frictionless, horizontal table...radius and speed...?

The 0.20 kg puck on a frictionless, horizontal table is connected by a string through a hole in the table to a hanging 1.20 kg block. With what speed must the puck rotate in a cicle of radius 0.50 m if the block is to remain hanging at rest?
 
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Remember that it is the rope tension that:

1. May hold the block hanging (what must therefore the tension be equal to?)

2. Provides the centripetal acceleration of the puck.

The tension of the rope is equal in magnitude in whatever segment of the rope..
 

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