Two blocks, of masses m1 and m2, are connected to each other and to a central po

Question

Two blocks, of masses m1 and m2, are connected to each other and to a central post by cords as shown in the figure(Figure 1) . They rotate about the post at a frequency f (revolutions per second) on a frictionless horizontal surface at distances r1 and r2 from the post.

Part A

Derive an algebraic expression for the tension in the segment of the cord from the post to the block of mass m1.

Express your answer in terms of some or all of the variables m1, m2,  f , r1, and r2.

Part B

Derive an algebraic expression for the tension in the segment of the cord from the block of mass m1 to the block of mass m2.

Express your answer in terms of some or all of the variables m1, m2,  f , r1, and r2.

Explanation / Answer

frequency f revolution per second

in rad per sec

frequency w = 2pif rad/s

T = m * centripetal acc.

centripetal acc. = w^2 R

A) T1 = m1 w^2 r1 = m1 (2pi f)^2 r1   = 4 pi^2 m1 f^2 r1

B )T2 = m2 w^2 r2^2   = m2 (2pi f)^2 r2   = 4 pi^2 m2 f^2 r2

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