Two buckets of mass m1 = 20.9 kg and m2 = 11.7 kg are attached to the ends of a

Question

Two buckets of mass m1 = 20.9 kg and m2 = 11.7 kg are attached to the ends of a massless rope, which passes over a pulley with a mass of mp = 8.33 kg and a radius of rp = 0.250 m. Assume that the rope does not slip on the pulley, and that the pulley rotates without friction. The buckets are released from rest, and begin to move. If the larger bucket is a distance d0 = 1.75 m above the ground when it is released, with what speed v will it hit the ground?

10/27/2017 06:00 PM A 87.5/10010/24/2017 04:03 PM Gradebook Print Calculator Periodic Table Question 11 of 17 Mapoob Sapling Learning Two buckets of mass m120.9 kg and m2 11.7 kg are attached to the ends of a massless rope, which passes over a pulley with a mass of mp-833 kg and a radius of rp = 0.250 m. Assume that the rope does not slip on the pulley, and that the pulley rotates without friction The buckets are released from rest, and begin to move. If the larger bucket is a distance dh1.75 m above the ground when it is released, with what speed v will it hit the ground? Number v = 12.45 m/s 20.9 kg 11.7 kg There is a hint available! View the hint by clicking on the bottom divider bar. Click on the divider bar again to hide the hint Close Previous O Check Answer Next Exit Hint

Explanation / Answer

on 20.9 kg :

20.9g - T1 = 20.9 a .... (i)

on 11.7kg :

T2 - 11.7g = 11.7a ..... (ii)

on puley,

torque = I alpha

R T = (mp R^2 / 2) (a / R)

T = 8.33 a / 2 = 4.16 a ...... (iii)

(i) + (ii) + (iii) =>

20.9g - 11.7g = (20.9 + 11.7 + 4.16) a

a = 2.46 m/s^2

Applying vf^2 - v0^2 = 2 a d

v^2 - 0 = 2 x 2.46 x 1.75

v = 2.93 m/s ......Ans

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