Question

Two masses, m and M , are connected to a pulley system attached to a table, as shown in the above diagram . What is the minimum value for the coefficient of static friction between mass M and the table if the pulley system does not move?

• A. m /M
• B. M /m
• C. g (m /M )
• D. g (M /m )
• E. g (M m )

Answer 1

The correct option is A m /M

If the pulley system does not move, then the net force on both masses is zero. For mass m , that means that the force of gravity, m g , pulling it downward, is equal to the force of tension in the rope, pulling it upward. If the force of tension pulling mass m upward is $mg$ , then the force of tension pulling mass M toward the edge of the table is also $mg$ . That means that the force of static friction resisting the pull of the rope must also equal $mg$ . The force of static friction for mass M is $\mu Mg$, where $\mu$ is the coefficient of static friction. Since this force must be equal to $mg$ , we can readily solve for $\mu$:

$\mu Mg=mg$
$⟹\mu =\frac{m}{M}$