How Do You Calculate Tension in a String with Mass and Acceleration?

[rchenkl]

Homework Statement

A string is attached to a mass and a pulley at the top end and the mass is free to move and descends with a constant acceleration, a.
By applying Newton's Laws to mass m, find an expression for the tension in the string, in terms of m, a and the acceleration due to gravity, g.

Homework Equations

F=ma

The Attempt at a Solution

I was thinking the net force downwards is mg-Tension force. And the net force results acceleration. So ma=mg-tension. is that correct?

 

[dx]

That's correct.

 

[nlightner]

Yes, your approach is correct. By applying Newton's Second Law (F=ma) to the mass, we can set up the following equation:

ma = mg - T

Where m is the mass, a is the acceleration, g is the acceleration due to gravity, and T is the tension in the string. We can rearrange this equation to solve for T:

T = mg - ma

Therefore, the tension in the string is equal to the weight of the mass (mg) minus the force needed to accelerate the mass (ma). This equation can also be written as:

T = m(g-a)

This expression for tension in terms of mass, acceleration, and gravity is useful in analyzing systems where a mass is attached to a string and is experiencing a constant acceleration, such as in the example given in the homework statement.