Physics pulley problem tension?

Question

Say you have two masses attached by a massless spring over a massless frictionless pulley. One is hanging and the other one is held on the table by the force of friction. The friction force is equal to the mass of the hanging block times gravity right? And it's represented by (hanging mass known as m) -mg because the friction force is opposite the motion? Or would the force of gravity be negative and friction positive? 

Also, if you suddenly took all the friction away so the table mass started moving, would tension increase, decrease, or stay the same? 

I am preparing for a physics exam and I don't recall these particulars.

Thanks.

Technobuff · Accepted Answer

I think you mean string, not spring?
The mass on the table multiplied by gravity is the weight (force) of the block on the table.
If the mass hanging is just enought to prevent slipping of the mass on the table, the mass hanging multiplied by gravity is the maximum force that can be applied without the other mass slipping, so the ratio between the 2 forces (weights in Newtons) is the coefficient of static friction between the mass and table, e.g. if force down on table was100N, and the force trying to pull it along was 25N., the coefficient will be (25/100) = 0.25.
Coefficients of friction (static or sliding) are always under 1. That's handy to remember when working with forces.
The force of gravity is positive on both the mass on the table and the hanging mass. Both operate vertically and in the same direction.
The force applied to try to slide the mass on the table is positive, and the frictional force negative. They operate horizontally, and are equal and oppose each other.
If you suddenly took away all friction, the string tension will remain at a steady value because the system is then accelerating.
This assumes as stated earlier, the mass on the table  is JUST being prevented from sliding by friction between it and the table.

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Physics pulley problem tension?

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