Mechanics problem -- a mass on a table that can freely move on wheels

[Clara Chung]

Homework Statement

A point like body with mass m₁ is placed on top of a table, that can freely move on wheels with respect to the ground. There is a static friction coefficient of u=0.3 between the body and the table. If the body is subject to the gravitational acceleration g, what is the maximal horizontal acceleration that the table can have, before the body start moving with respect to it?

Consider now the case of where the body is attached to a horizontal massless and frictionless rope. This rope turns around a frictionless pulley placed at the side of the table, and below it hangs another body with mass m₂. Calculate the forces acting on the system in the reference frame of the table. Calculate the maximum acceleration (in the direction opposite to m₂) that the table can stand before the masses start to move, neglecting the change in the angle of the string supporting m₂.

Homework Equations

The answer of the first part is um₁. The answer of the second part is a=(m₂-um₁)/(m₁+m₂).

The Attempt at a Solution

I have no idea how to do both parts of the questions. I want to solve the first part first. I attempted to solve the question by equating um₁g = m_table a_table, because the friction force is equal to the force m₁ acting on the table. Without the mass of the table, how can I know its acceleration?

 

[.Scott]

The mass of the table does not matter. When the table accelerates, you are applying whatever force is needed.
If you still think the mass of the table matters, take it to be zero.

 

[Orodruin]

You do not need to know the mass of the table. However, you do need that the acceleration of the mass is the same as that of the table and you need to compare that with the maximal possible force that can be provided by the friction.

 

[Clara Chung]

I see your points, but why is the answer um₁ ?
Shouldn't it be um₁g=m₁a
so a=ug?

 

[PeroK]

I see your points, but why is the answer um₁ ?
Shouldn't it be um₁g=m₁a
so a=ug?

Where did you get the answer $a_{max} = um_1$?

PS The dimensions are wrong, for one thing.

PPS Same for part b). The dimensions are wrong there too.