Question

A block of mass m is attached with a massless spring of force constant K. The block is placed over a rough inclined surface for which the coefficient of friction is $\mu =\frac{3}{4}$. Find the minimum value of M required to move the block up the plane. (neglect mass of string and pulley. Ignore friction in pulley).

Answer 1

$N=mg\cos {37}^{\circ }=\frac{4}{5}mg$

Now, if block have to move up

$T=mg\sin {37}^{\circ }+f$ ....................(1)

and, $T=Mg$ .....................(2)

From eq. 1 and 2;

$Mg=mg\sin {37}^{\circ }+f=\frac{3}{5}mg+\frac{4}{5}\mu mg$

$M=\frac{3}{5}m+\frac{4}{5}\times \frac{3}{4}m$

$M=\frac{6}{5}m$