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

Question

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

let the tension in the chord be T

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)= 0.5899 m/s^2

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

upward acceleration = 0.5866 m/s^2

P.S:: please confirm the answer then i'll give you the hing reaction

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