A small heavy object of mass m is attached to a thin string to make a simple pendulum whose length is L. When the object is pulled aside by a horizontal force F it is in static equilibrium and the string makes a constant angle from the vertical.
(a) The tension in the string should be (1) the same as, (2) greater than, or (3) less than the object’s weight, mg.
(b) Use the force condition for static equilibrium (along with a free-body diagram of the object) to prove that the string tension is T = mg/cos θ > mg. Use the same procedure to show that F = mg tan θ.
(c) Prove the same result for F as in part
(b) Using the torque condition, summing the torques about the string’s tied end. Explain why you cannot use this method to determine the string tension.