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.

Answer 1

Given,
Mass of the block = 4.0 kg
Linear mass density,
\[m = 19 . 2 \times  {10}^{- 3}   kg/m\]
From the free body diagram,

\[T - 4g - 4a = 0\] 

\[ \Rightarrow T = 4\left( a + g \right)\] 

\[ = 4\left( 2 + 10 \right) = 48  \text{ N }\] 

\[Wave  speed,   \nu = \sqrt{\left( \frac{T}{m} \right)}\] 

\[                                             = \sqrt{\frac{48}{19 . 2 \times {10}^3}}\] 

\[                                             = \sqrt{\left( 2 . 5 \times {10}^{- 3} \right)} = 50  m/s\]