To find tension (T) in a rope or string using a formula, consider the forces acting on an object connected by the rope. The tension is essentially the force transmitted through the rope.
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If an object is subject to vertical forces, such as gravity (mg), the formula for tension (T) is:
T = mg
where m is the mass of the object and \(g\) is the acceleration due to gravity.
In scenarios involving horizontal forces, the formula for tension can be more complex.
For instance, if an object is accelerating horizontally and the only horizontal force is the applied force
, the tension (T) can be found using Newton's second law (F = ma):
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These formulas are fundamental in physics and are applied depending on the specific forces acting on the object in question, providing a quantitative measure of the tension in the rope or string.