How to Figure Out the Tension of a Rope Between Two Objects
The idea of tension in physics refers to the amount of pulling force being applied to a rope, cable or other similar object. Tension is measured in newtons and always indicates the degree of force parallel to the rope. Two possibilities exist in rope tension problems. The first is when the acceleration of the objects being held by the rope equals zero, in which case tension simply equals the amount of force being exerted on the rope. The other possibility is when the system of objects is accelerating and the net force must be considered. Also, the rope is considered to have no mass in these calculations.
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Instructions
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Find the masses of the two objects. Mass equals the weight of an object divided by the acceleration of gravity working on the object. For example, if Object 1 weighs 900 newtons (N), then the mass of the object equals 900 N / 9.8 (meters/second)^2 = 91.8 kilograms. If Object 2 equals 1,300 N, then the mass of this object equals 1,300 N / 9.8 m/s^2 = 132.7 kg.
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Set up the equation for Newton's Second Law of Motion, F = ma, where "F" is the net force of the objects on the rope, "m" is the combined mass of the objects and "a" is the acceleration of the objects. For example, if the rope is being accelerated in the positive direction at a rate of .5 meters per second squared, the equation becomes: F = (91.8 kg + 132.7 kg)(0.5 m/s^2) = 112.25 kg*m/s^2.
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Add the forces (weight) of the objects to the result of Newton's Second Law equation. For example, if the net force of two objects equals 112.25 and the combined force of the two objects applying the force is (1,300 + 900) = 2,200 N, then the tension "T" of the rope becomes: T = 112.25 kg*m/s^2 + 2,200 N = 2,211.25 N.
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