Question

In the figure below, m1 = 10.0 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?
m/s²

(b) If the system is set in motion with m₂ moving downward, what will be the acceleration of the system?
m/s²

Answer 1

(a) Check first if the system would even move. To check, get the static friction.
static friction = μmg = (0.60)(10kg)(9.8m/s2) = 58.8N

Then compare it with the gravitational force on m2, which is the force that would move the system.

F = m₂g = 4.5kg(9.8m/s2) = 44.1N

Since 58.8N > 44.1N, the system won't move. The gravitational force is not enough to overcome the static friction of mass 1.

acceleration = 0 m/s²

(b) When it is moving downward already, the kinetic friction takes action, not static friction.

net force on system = gravitational force on m2 - kinetic friction on m1

(m1 + m2)a = m2 g - μm1 g

(10 + 4.5)a = (4.5)(9.8) - (0.30)(10)(9.8)

a = 1.01m/s²