Work Energy And Power Question 313
Question: A block of mass m moving with a velocity $ v_0 $ on a smooth horizontal floor collides with a light spring of stiffhess k that is rigidly fixed horizontally with a vertical wall. If the maximum force imparted by the spring on the block is F, then
Options:
A) $ F\propto \sqrt{m} $
B) $ F\propto \sqrt{k} $
C) $ F\propto v_0 $
D) None of these
Show Answer
Answer:
Correct Answer: D
Solution:
[d] Energy conservation between the positions A and B requires that $ \Lambda PE+KE=0 $ or
$ \frac{1}{2}kx^{2}-\frac{1}{2}mv_0^{2}=0 $
$ \therefore $ $ x=\sqrt{\frac{m}{k}}v_0 $
$ \therefore {F _{\max }}=kx=\sqrt{mk}v_0 $
or $ {F _{\max }}\propto \sqrt{k}\propto \sqrt{m}\propto v_0 $
