Any help would be greatly appreciated. 2. A on mass m 0.20 kg is attached to a s

Question

Any help would be greatly appreciated.

2. A on mass m 0.20 kg is attached to a string and placed into circular motion the a horizontal frictionless surface, at a radial distance of ru 0.4 m from center, with an angular velocity of o 6.0 rad/s and moment of inertia of I mri 0.2 kg 0.032 kg m The other end of the string passes through a hole in the center of the horizontal surface. 0.4 m a. What constant force F must exerted at the end of the string in be order to maintain this angular velocity and radius r? 15 points] b. The string is pulled by increasing the force F and the radius is reduced to rz 0.2 m. What is the new angular velocity ar2 at the reduced radius r? [10 pointsl c. How much work was done in reducing the radius from rl 0.4 m to rz 0.2 m? [10 points]

Explanation / Answer

T = mw^2 .r  

F = T = 0.20 x 6^2 x 0.4 = 2.88 N

b) angular momentum about point hole will be constant (Iw)

I1w1 = I2w2

0.032 x 6   = 0.2 x 0.2^2 x w2

w2 = 24 rad/s

c) work done = change in K.E.

W = I2w2^2 /2 - I1w1^2 /2

    = 0.2 x 0.2^2 x 24^2 /2 - 0.032 x 6^2 /2      = 1.728 J

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