Question

A$4.0kg$ block is suspended from the ceiling of an elevator through a string having a linear mass density of $19.2\times {10}^{-3}kg{m}^{-1}$. 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 $2.0m{s}^{-2}$. Take $g=10m{s}^{-2}$.

Answer 1

Step 1.Given data

The mass of the block, $m=4.0kg$

The linear mass density of the block, $\rho =19.2\times {10}^{-3}kg{m}^{-1}$

The acceleration of the block, $a=2.0m{s}^{-2}$

Step 2. Find the ${\mathit{g}}_{\mathbf{e}\mathbf{f}\mathbf{f}}$

Due to accelerated motion in the upward, $g_{eff}=\left(10+2\right)m{s}^{-2}$

Step 2. Find the tension in the string

Tension in the string,

$T=m{g}_{eff}=4kg\times 12m{s}^{-2}=48N$

Step 3. Find the of the pulse

Speed of the pulse,

$v=\sqrt{T}/\sqrt{\rho }=\sqrt{48/19.2\times {10}^{-3}}=\sqrt{2500}=50m{s}^{-1}$

Hence. the speed is $50m{s}^{-1}$.