The tension in a cable is an example of a force. Scientists and engineers measure force in newtons. (According to Newton's second law of motion, the net force on an object equals the object's mass times its acceleration. The tension in a cable holding up a crate for example is just one force on the object. Another is the weight of the crate which points down. Forces that point up, like tension, are positive, while downward forces are negative.
Multiply the mass of the object attached to the cable by its acceleration. A downward acceleration is negative while an upward acceleration is positive. Call this quantity "x." Assuming a mass of 10kg and an acceleration of 2 meters per second squared upward, "x" has the value 20kg times meter per second squared, or 20 newtons. A newton equals one kilogram times one meter per second squared.
Subtract all the downward forces on the object from the upward forces. Call this quantity "y." Assume you get a result of 10 newtons.
Subtract "y" from "x" to obtain the tension in the cable in newtons. Completing the exercise you have 20 newtons minus 10 newtons, resulting in a tension of 10 newtons.
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