Basic physics forces problem (f=ma)

[victoration1]

Homework Statement

A 28.0-kg block is connected to an empty 1.00-kg bucket by a cord running over a frictionless pulley. The coefficient of static friction between the table and the block is 0.450 while the coefficient of kinetic friction is 0.320. Sand is gradually added to the bucket until the system just begins to move. What is the mass of the sand added to the bucket and the acceleration of the system?

Homework Equations

F=ma

The Attempt at a Solution

The major assumption that the problem demands---and with which I have trouble understanding---is that static friction is overcomed the moment that tension force (pulling on the block) equals the static friction force (acting in the opposite direction as tension force). There should be zero net-force at this point, and knowing Newton's first law, the block shouldn't move at all.

Does kinetic friction take over the moment that static friction equals the tension force? (thus making this problem possible)

 

[SammyS]

Suppose that the applied force is exactly equal to the maximum static friction force.

How much would the applied force have to be increased so that it would produce a non-zero acceleration?

 

[NascentOxygen]

Does kinetic friction take over the moment that static friction equals the tension force? (thus making this problem possible)

The difference between not-yet-moving and starting to move is one grain of sand.

 

[victoration1]

The mass of the sand---the magnitude of the applied force---can be increased by a infinitesimally small amount to cause acceleration; thus allowing for the approximation of the mass that the question requires?

 

[SammyS]

Yes.