Question

In the attached figure, m1 = 9.5 kg and m2 = 4.5 kg. The coefficient of static friction between m1 and the horizontal surface is 0.60 while the coefficient of kinetic friction is 0.30.

(a) If the system is released from rest, what will its acceleration be?
(b) If the system is set in motion with m2 moving downward, what will be the acceleration of the system?

Answer 1

And here is the picture. Thank you someone for helping!

Answer 2

tension in string = m_2 g
for m_1: friction force= friction coeff. * normal force
if system left in static and since static friction on m_1 is 0.6*9.5g>4.5g
that's why there won't be any motion in m_1 and hence in m_2
i.e accn.= 0
in 2nd condition:
objects are already in motion, and hence kinetic friction(<static friction) is acting over m_1.
let accn.of system be a. then
for m_2: m_2 g - T = m_2 a
for m_1: T- F = m_1a
=> T- 0.3m_1g = m_1a
combining the two eqn.:
a={(m_2 - 0.3m_1)g}/(m_1 + m_2)