Static Equilibrium and Friction in Pulley Systems

System Description

This problem involves three objects connected by weightless, flexible strings and a frictionless pulley. One block rests on a horizontal bench, while another hangs vertically. The string pulls the block on the bench parallel to the surface. The system is observed to be at rest, indicating static equilibrium.

• Coefficient of static friction (): 0.60

• Coefficient of kinetic friction (): 0.325

• System remains at rest: Static equilibrium applies

Key Concepts

• Static Equilibrium: The sum of all forces and torques on each object is zero.

• Friction Force: The force resisting motion between the block and the bench, given by where is the normal force.

• Tension: The force transmitted by the string, assumed equal throughout due to massless, frictionless pulley.

Relevant Equations

• Force of static friction:

• Normal force on block on bench:

• Equilibrium for block on bench:

• Equilibrium for hanging mass:

Problem Breakdown

(a) Find the mass of the hanging object

Since the system is at rest, the tension in the string equals the maximum static friction force:

• For the block on the bench:

• For the hanging mass:

Setting these equal:

Example: If , :

(b) Magnitude of the friction force on the block on the bench

Since the system is at rest, the friction force equals the tension, which equals the weight of the hanging mass:

• Using from above,

Summary Table

Additional info:

• If the system were moving, kinetic friction () would be used instead of static friction.

• Static equilibrium problems often require careful identification of all forces acting on each object.