Question

A 4⋅0 kg block is suspended from the ceiling of an elevator through a string having a linear mass density of 19·2×10-3 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

Wave Speed is 50 ms^-1

Explanation:

Given,

Mass of the block = 4.0 kg

Linear mass density, m = $19.2\times 10^-^3 kgmm^-^1 = 19.2\times 10^-^3 kgm^-^1$

From the free body diagram,

 T−4g−4a=0

⇒ T = 4(a+g)      

= 4(2+10) = 48 N

Wave Speed, $\nu = \sqrt(T/m)$

= $\sqrt (\frac {48}{19.2 \times 10^-^3})$

= $\sqrt (2.5 \times 10^-^3)$

= $50 ms^-1$