Multiple Concepts EXAMPLE 12 deals with a situation thathas similities to this o

Question

Multiple Concepts EXAMPLE 12 deals with a situation thathas similities to this one and uses some of the same concepts thatare needed here. By means of a rope whose mass is negligible, twoblocks are suspended over a pulley, as the drawing shows. Thepulley can be treated as a uniform solid cylindrical disk. Thedownward acceleration of the 44.0 kg block is observed to beexactly one-half the acceleration due to gravity. Nothing that thetension in the rope is not the same on each side of the pulley,find the mass of the pulley.
Block 1 = 11 kg block 2 = 40 kg

Explanation / Answer

     the sum of forces on each box, andthe sum of torques for the pulley:      T1 - m1 g = m1 a                T1 = m1 a - m1 g = m1 (a + g) You are told that a is one half g so    a= 4.9 and    T1 =  11 (4.9 + 9.8 ) =161.7 N      m2 g - T2 = m2 a               T2 = m2 (g - a )    T2 = 40 * (9.8 - 4.9) =  196N Pulley:    T2 r - T1 r = I Now in the pulley equation, we replace with    a / r   and   T2 r - T1 r = I a /r       r2 ( T2 - T1 ) = Ia           now replace T2 and T1 with the above values    r2 ( 196 - 161.7 ) = I * 4.9      I =   7  r2   the pulley is a disk, so    I =(1/2) M r2    so (1/2) M r2 =  7  r2 M = 14 kg   mass of thepulley

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