1)A solid, frictionless cylinder reel of mass M = 2.99 kg and radius R = 0.403 m
ID: 2241567 • Letter: 1
Question
1)A solid, frictionless cylinder reel of mass M = 2.99 kg and radius R = 0.403 m is used to draw water from a well. A bucket of mass m = 2.07 kg is attached to a cord that is wrapped around the cylinder. (Indicate the direction with the sign of your answer.)
a)Find the tension T in the cord and acceleration a of the bucket.
b)If the bucket starts from rest at the top of the well and falls for 3.02 s before hitting the water, how far does it fall?
2)A hollow cylinder of mass 0.143 kg and radius 3.50 cm has a string wrapped several times around it. A string is attached to a rigid support and the cylinder allowed to drop from rest. (Indicate the direction with the sign of your answer.)
a) find the acceleration of the cylinder
b)Find the speed of the cylinder when a meter of string has unwound off of it.
T = N a = m/s2Explanation / Answer
1) torque = I x alpha
r x T = (Mr^2 /2 ) (a/r)
T = Ma / 2
and on bucket :
mg - T = ma
add them
mg - Ma/2 = ma
2.07 x 9.8 = (2.07 + (2.99/2))a
a = - 5.69 m/s2 ( downwards )
T =2.99 x 5.69 /2 =8.51 N
b) H = ut + at^2 /2 = 0 + 5.69 x 3.02^2 /2 = - 25.95 m ( downwards)
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