Work Energy And Power Question 252
Question: Two blocks of masses m and M are joined with an ideal spring of spring constant k and kept on a rough surface as shown. The spring is initially unstretched and the coefficient of friction between the blocks and the horizontal surface is u. What should be the maximum speed of the block of mass M such that the smaller block does not move?
Options:
A) $ \mu g\sqrt{\frac{Mm}{( M+m )k}} $
B) $ \mu g\sqrt{\frac{( M+m )k}{Mm}} $
C) $ \mu g\sqrt{\frac{( 2M+m )m}{kM}} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
[c] For the smaller block to move $ kx_0=\mu mg $ and
from work energy theorem $ -\mu Mgx_0-\frac{1}{2}kx_0^{2}=-\frac{1}{2}Mv^2_0 $ $ +\mu Mg( \frac{\mu mg}{k} )+\frac{1}{2}k{{( \frac{\mu mg}{k} )}^{2}}=\frac{1}{2}Mv^{2} $
$ v=\mu m\sqrt{\frac{( 2M+m )m}{kM}} $
