mass of full bucket= 12kg Figure gives no information. You accidentally knock a

Question

mass of full bucket= 12kg

Figure gives no information.

You accidentally knock a full bucket of water off the side of the well shown in Figure P11.65. The bucket plunges 15 m to the bottom of the well. Attached to the bucket is a light rope that is wrapped around the crank cylinder. The cylinder has a radius of 0.080 m and inertia of 4.0 kg. How fast is the handle turning when the bucket hits bottom? How fast is the bucket moving as it hits the bottom? For comparison, how fast would the bucket have been moving when it hit the bottom as it weren't attached to the rope?

Explanation / Answer

here Tension in rope = T,

acceleration of bucket is given by: ma = mg -T or 12a = 12*9.8 - T

for cylinder, 0.5*4*0.08^2* a/0.08 = T*0.08 or T = 2a

14 a = 12*9.8

a = 12*9.8/14 = 8.4 m/s^2

a) using third equation of motion,

v = sqrt(2*8.4*15) = 15.87 m/s

w = v/r = 15.87/0.08 = 198.4 rad/s answer

b) v= 15.87 m/s as found above

c) v = sqrt(2*9.8*15) = 17.15 m/s

  

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