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A weight of mass m hangs on a thread. The thread is deflected by an angle alpha_0and let go. Find the tension of the thread as a function of the angle alpha . |
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Answer» `T-F_(2) = mv^(2)//L` To find the velocity apply the law of conservation of energy `mgh_(0) = mgh +mv^2//2` Hence `T = mg cos alpha +(2mg)/l (h_0 -h)` However , `h_(0) = 1 (1- cosalpha_(0)), h = l ( 1 - cos alpha) , ` therefore `h_0 -h = l (cos alpha_(0) - cosalpha_0)` Substituting into the EXPRESSION for the tension of the thread we obtain `T = mg (3 cos alpha - 2 cos alpha_0)` 
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