A puck of mass m 1 is tied to a string and allowed to revolve in a circle of rad

Question

A puck of mass m1 is tied to a string and allowed to revolve in a circle of radius R on a frictionless, horizontal table. The other end of the string passes through a small hole in the center of the table, and an object of mass m2 is tied to it (see figure below). The suspended object remains in equilibrium while the puck on the tabletop revolves.

(a) What is the tension in the string? (Use any variable or symbol stated above along with the following as necessary: g.)
T =

(b) What is the radial force acting on the puck? (Use any variable or symbol stated above along with the following as necessary: g.)
F =

(c) What is the speed of the puck? (Use any variable or symbol stated above along with the following as necessary: g.)
v =

Explanation / Answer

(a) Since the suspended object is in equilibrium, it must have no net force on it. Therefore: T = m2g (b) Since we have no specific information about the string, we can assume that the tension is constant throughout the string, therefore we can use the answer from part (a) for part (b) F = T = m2g (c) The force acting on the puck on the table is providing centripetal acceleration. We know the equation for centripetal force is: F = mv^2/r Now plug in the values that are given: T = m1v^2/R m2g = m1v^2/R v^2 = (m2/m1)gR v = sqrt((m2/m1)gR)

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