tension in moving string

[MrLobster]

I understand that if a string is holding up a hanging mass then the magnitude of the tension in the string is mass * gravity.

The other end of the string is tied to an object on a flat surface (after being redirected by a frictionless pully). If the tension force is great enough to overcome static friction then the object, string, and mass will move. If I know all the relevant weights and coefficients of friction is there a way to calculate the magnitude of the tension in the string?

It must be less than mass * gravity because the mass is being pulled down.
It can't be the same as the frictional force slowing the object because the object is moving too.

[Doc Al]

I understand that if a string is holding up a hanging mass then the magnitude of the tension in the string is mass * gravity.
If the hanging mass is in equilibrium, then you are correct.

The other end of the string is tied to an object on a flat surface (after being redirected by a frictionless pully). If the tension force is great enough to overcome static friction then the object, string, and mass will move. If I know all the relevant weights and coefficients of friction is there a way to calculate the magnitude of the tension in the string?
Sure. Apply Newton's 2nd law to both masses.

It must be less than mass * gravity because the mass is being pulled down.
If the hanging mass is accelerating, then you are correct: the upward force of the string must be less than the weight of the mass.
It can't be the same as the frictional force slowing the object because the object is moving too.
Again, if the system is accelerating you are correct. There must be a net force on each accelerating mass.

[MrLobster]

Sure. Apply Newton's 2nd law to both masses.

Do I need to know the tension in the string or the accelerations of the objects to do this? I was going to use the tension of the string to figure out the accelerations on the objects which should be equal since they are connected by a string.

Hmmm. Can you verify if I'm on the right track if I say:

The magnitude of the force on the mass: mass * gravity - magnitude of the frictional force on the object?

The accelerations for *both* the object and mass would be the force on the mass / mass?

Then I can calculate the force on the object and tension in the rope based on that start...

[Doc Al]

Do I need to know the tension in the string or the accelerations of the objects to do this? I was going to use the tension of the string to figure out the accelerations on the objects which should be equal since they are connected by a string.
Generally the tension and the acceleration is what you are trying to find. By setting up Newton's 2nd law for the object and the hanging mass you'll get two equations with two unknowns: the tension and the acceleration.

Hmmm. Can you verify if I'm on the right track if I say:

The magnitude of the force on the mass: mass * gravity - magnitude of the frictional force on the object?
No. The net force on the hanging mass is mg (downward) - tension force (upward). (Don't take shortcuts.)

The accelerations for *both* the object and mass would be the force on the mass / mass?
The acceleration of any mass equals the net force on it divided by its mass. This is just Newton's 2nd law and its the key to solving these kinds of problems.

Do this. Identify all the forces acting on each mass. Then write down Newton's 2nd law for each mass:
\vec{F}_{net} = \Sigma \vec{F} = m \vec{a}

If you do it right, you'll get two equations with two unknowns. Solve!

[MrLobster]

Thank you, this problem is clear to me now.