answer = 2.5 m/s^2 i need help with d) , show me steps PLZ!! Two crates of mass

Question

answer = 2.5 m/s^2

i need help with d) , show me steps PLZ!!

Two crates of mass 5.0 kg and 9.0 kg arc connected by a rope that runs over a pulley of mass 4.0 kg as shown in Figure P8.57. (a) Make a sketch showing all the forces on both crates and the pulley, (b) Express Newton's second law for the crates (translational motion) and for the pulley (rotational motion). The linear acceleration a of the crates, the angular acceleration a of the pulley, and the tensions in the right and left portions of the rope are unknowns, (c) What is the relation between a and ai (d) Find the acceleration of the crates, (e) Find the tensions in the right and left portions of the rope.

Explanation / Answer

9g - T2 = 9a -->(1)

T1 - 5g = 5a -->(2)

(T2 - T1) .r = 4 r2/2 = 2a (as a = r )

( T2 - T1) = 2a -->(3)

Now 1+2+3 gives:

4g = 16 a

a = 4*10/16 = 2.5 m/s^2

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