You pull downward with a force of 29N on a rope that passes over a disk-shaped p

Question

You pull downward with a force of 29N on a rope that passes over a disk-shaped pulley of mass 1.2 kgand radius 0.075 m. The other end of the rope is attached to a0.69-kg mass. Find the tension in the ropeon both sides of the pulley. I tried to solve this problem by separating the components inthree systems considering that the positive direction iscounterclockwise for the pulley, so on the mass side positivedirection is up and on the hand side positive direction isdown. the mass side: Fmass= T2-Mg = Ma the pulley: = T1 - T2 = I, whereI=(mr2)/2 and =a/r I used a combination of these sums to find a=15.605, and thenT1=18.233, T2=17.52, but these numbers are not correct. I need somehelp. Thank you, Ani You pull downward with a force of 29N on a rope that passes over a disk-shaped pulley of mass 1.2 kgand radius 0.075 m. The other end of the rope is attached to a0.69-kg mass. Find the tension in the ropeon both sides of the pulley. I tried to solve this problem by separating the components inthree systems considering that the positive direction iscounterclockwise for the pulley, so on the mass side positivedirection is up and on the hand side positive direction isdown. the hand pulling:Sigma Fpulling= F - T1 = Ma the mass side: Sigma Fmass= T2-Mg = Ma the pulley: Sigma t= T1 - T2 = I?, whereI=(mr2)/2 and alpha=a/r I used a combination of these sums to find a=15.605, and thenT1=18.233, T2=17.52, but these numbers are not correct. I need somehelp. Thank you, Ani

Explanation / Answer

T1 = 29N To findT2 Let M = hanging mass , m = pulleymass , r = pulley radius Moment of inertia I =    1/2 mr2 Upward force on hanging mass   Ma =T2 - Mg Net torque on pulley is     r(T1 ) - r ( T2 ) = ( 1/2mr2 ) Mass or pulley relationship a = r                                                             T1 - T2 = 1/2 ma                                                       a = 2/m ( T1 - T2 )                                                      2M /m  ( T1 - T2 ) = T2- mg    solvingfor T2                                               T2   = Mmg + 2 M  T1   / 2 M +m                                                 = 0.69 * 1.2 *9.8 + 2 *0.69 ( 29 ) / 2 * 0.69 + 1.2                     calculate the above to get solution           

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