question_answer

Suppose the ceiling in the previous problem is that of an elevator which is going up with an acceleration of 2.0 m/s. Find the elongations, [\[\text{g}=\text{1}0\text{m}/{{\text{s}}^{\text{2}}}\]]

Answer:

Given \[a=2m/{{s}^{2}},\,\,\,m=2kg\] when the elevator moves upwards \[kx-mg=ma\Rightarrow kx=mg+ma=m(g+a)\] \[=2(10+2)=100x\therefore x=\frac{24}{100}=0.24m\] when 1 kg is added, total mass = 3 kg Now, \[Kx|-mg=ma\Rightarrow Kx|=mg+ma\] \[=m\times (g+a)=3(10+2)=36\] \[\Rightarrow x'=\frac{36}{100}=0.36m\] \[\therefore \]Further elongation \[=0.36-0.24\]                                                 \[=0.12m\]