# How Do You Calculate Tension?

First of all, there is no single formula to calculate tension that will encompass any given situation. So, that being said, it depends on what the variables given in the question are. W(eight) = m(ass) * g(ravity) or W = m * g Newton's Law states that F(orce) = m(ass) * a(cceleration), in the last example the acceleration is gravity itself.Say you had an elevator hanging from a single cable with a mass of 350kg. What is the tension in the cable if (a) the elevator is moving at a constant velocity? (b) with an upward acceleration of 1.4 m/s²? (c) with a downward acceleration of 1.6m/s²?Assuming that the cable and any pulleys it may be attached to have no mass of their own:In all three examples the downward force is that of gravity. Thus, W = m * g or W = (350kg) * (9.8m/s²) = 3430NNote this as the magnitude, the direction is always downward.Newton's equation states that m * a = F = T - W, where T is the tension in the cable.In case (a) the velocity is constant, therefore there is no acceleration. So, T = W = 3430NIn case (b) the acceleration is positive. Using the equation from above we can assume:T = W + m * a = m * (g + a) = (350kg) * (9.8m/s² + 1.4m/s²) = 3920NIn the case (c) the acceleration is negative, so using the same equation again: T = W + m * a = m * (g + a) = (350kg) * (9.8m/s² + (-1.6m/s²)) = 2870NThe tension increases if you are accelerating an object upwards, it decreases if you let if fall downwards. The key thing to remember in this example, (as long as the rope and pulleys are massless) is that all the rope or cable does is change the direction of the force.
How to Calculate Tension
Tension is the force that a line or string exerts on a load. By Newton's third law of motion, it is also the force the load exerts on the line. The main strategy to such problems is often to look at the bodies in isolation of the others and assess all... More »
Difficulty: Moderate
Source: www.ehow.com
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