A constant F = 1200 N is applied on a cord wrapped around drum A, which, in turn

Question

A constant F = 1200 N is applied on a cord wrapped around drum A, which, in turn, rotates drum B,  elevating the weight C, as shown. Both drums are fastened together and turn as one. The two drums have a combined mass of 250 kg. Model the drums as a solid cylinder. Determine the upward acceleration of the weight C and the components of reaction at O.

A constant F = 1200 N is applied on a cord wrapped around drum A, which, in turn, rotates drum B, elevating the weight C, as shown. Both drums are fastened together and turn as one. The two drums have a combined mass of 250 kg. Model the drums as a solid cylinder. Determine the upward acceleration of the weight C and the components of reaction at O.

Explanation / Answer

Net torque = 1200*0.5-T*0.24


moment of inertia = 0.5*mR^2= 0.5*250*0.5^2= 31.25 Kg-m^3


let the acceleration of block be a


so alpha=a/0.25


==> T-200g=200*a


and 1200*0.5-T*0.25=31.25*a/0.25


now solving these two eqations

a= (1200*0.5-0.25*200*9.8)/(31.25/0.25 + 250*0.25)= 0.5866 m/s^2

==> T= 200*(9.8+0.5866) =2077.32 N

upward acceleration = 0.5866 m/s^2

reaction forces at hing

Fy = 250*9.8 + 1200*sin(30) + 2077.32 N= 3341.68 N

Fx = 1200*cos(30) = 1039.23 N

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