Thank you! The system shown below is in equilibrium, when the extension x is equ

Question

Thank you!

The system shown below is in equilibrium, when the extension x is equal L. Then object B is pulled down a distance 3L and released. The system will start to oscillate (assume that the surface is frictionless). a) Write the expressions for initial and final total energies of the system Ignore the energy of the pulley. b) Write an expression for x(t), assuming that the surface is frictionless. Express the result in terms of given quantities. c) If you had to take into account the mass of the pulley M and it's radius R, what would be the velocity of the object B as the object A is going through 2L point in the case of no friction? m2,

Explanation / Answer

M1 and M2 will have the same acceleration ( since the cord stays taught )
The cord will have two different tensions. The difference in the tension will create a torque that turns the pulley.

For M1

5 . 9.8 – Ti = 5 . 3.5

Ti = 31.5 N

For M2

Tii = 4 . 3.5 = 14 N

For the pulley

(Ti – Tii) . r = MI . (a/r)

(31.5 – 14) . 0.2^2 / 3.5 = MI = 0.20 kgm^2

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