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A 2.85-kg bucket is attached to a disk-shaped pulley of
Chapter 11, Problem 46P(choose chapter or problem)
A \(2.85-\mathrm{kg}\) bucket is attached to a disk-shaped pulley of radius \(0.121 \mathrm{~m}\) and mass \(0.742 \mathrm{~kg}\). If the bucket is allowed to fall, (a) what is its linear acceleration? (b) What is the angular acceleration of the pulley? (c) How far does the bucket drop in \(1.50 \mathrm{~s}\) ?
Questions & Answers
QUESTION:
A \(2.85-\mathrm{kg}\) bucket is attached to a disk-shaped pulley of radius \(0.121 \mathrm{~m}\) and mass \(0.742 \mathrm{~kg}\). If the bucket is allowed to fall, (a) what is its linear acceleration? (b) What is the angular acceleration of the pulley? (c) How far does the bucket drop in \(1.50 \mathrm{~s}\) ?
ANSWER:Step 1 of 5
a.)
We have to find the linear acceleration of the falling bucket.
The linear acceleration can be found by using the expression for net force acting in the \(y\) direction.
\(\sum F_{y}=m a_{y}\)
\(\Rightarrow-T+m g=a \text { (downward direction is taken as positive) }\)
where,
\(m=\text { mass of the bucket }=2.85 \mathrm{~kg}\)
\(a=\text { linear acceleration of the bucket in } \mathrm{m} / \mathrm{s}^{2}\)
\(T=\text { Tension in the rope in } \mathrm{N}\)