An air puck of mass m1 is tied to a string and allowed to revolve in a circle of

Question

An air puck of mass m1 is tied to a string and allowed to revolve in a circle of radius R on a horizontal, frictionless 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). The suspended object remains in equilibrium while the puck on the tabletop revolves.
(a) Find a symbolic expression for the tension in the string in terms of m2 and g.
T = ________________


(b) Write Newton's second law for the air puck, using the variables m1, v, R, and T. (Do this on paper. Your instructor may ask you to turn in this work.)
_____________________________

(c) Eliminate the tension T from the expressions found in parts (a) and (b) and find an expression for the speed of the puck in terms of m1, m2, g, and R.
speed = _____________________

Explanation / Answer

(a) T = m2 g            

because m2 is suspended by the tension

(b)   forces = mass * acc

so

T = m1 v1^2 / R

(c)   m2 g = m1 v1^2 / R

so

    v1 = sqrt (m2 g R / m1)

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