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Question
A 4⋅0 kg block is suspended from the ceiling of an elevator through a string having a linear mass density of \[19 \cdot 2 \times {10}^{- 3} kg m^{- 1}\] . Find the speed (with respect to the string) with which a wave pulse can proceed on the string if the elevator accelerates up at the rate of 2⋅0 m s−2. Take g = 10 m s−2.
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Solution
Given,
Mass of the block = 4.0 kg
Linear mass density,
\[m = 19 . 2 \times {10}^{- 3} kg/m\]
From the free body diagram,
\[T - 4g - 4a = 0\]
\[ \Rightarrow T = 4\left( a + g \right)\]
\[ = 4\left( 2 + 10 \right) = 48 \text{ N }\] 
\[Wave speed, \nu = \sqrt{\left( \frac{T}{m} \right)}\]
\[ = \sqrt{\frac{48}{19 . 2 \times {10}^3}}\]
\[ = \sqrt{\left( 2 . 5 \times {10}^{- 3} \right)} = 50 m/s\]
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