Answer
(a) $0.79m/s$
(b) positive
(c) $0.36J$
Work Step by Step
(a) The required speed can be determined as
$v=\sqrt{\frac{2gd(m_2+\mu_km_1)}{m_1+m_2}}$
We plug in the known values to obtain:
$v=\sqrt{\frac{2(9.81)(0.065)(1.1+(0.65)(2.4))}{2.4+1.1}}$
$v=0.79m/s$
(b) Since the rope exerts the force on $m_2$ in the same direction in which it moves, the work done by the rope on $m_2$ is positive.
(c) We can calculate the required work done as follows:
$W=m_2gd-\frac{1}{2}m_2v^2$
We plug in the known values to obtain:
$W=(1.1)(9.81)(0.065)-\frac{1}{2}(1.1)(0.79)^2$
$W=0.36J$
