Answer to Question #120978 in Mechanics | Relativity for Mamart Sanchez

Question #120978
A thin rod of lengh L lies on the +x-axis with its left end at the origin. A string pulls on the rod with a force f directed toward P point a distance is above the rod should you attach the string to det the greatest torque about the origin if point P is above the right end of the rod.
Expert's answer

Explanations & Calculations

  • Assume the force being applied is located as shown in the picture.
  • Tension in the string is equal to the magnitude of the applied force.

  • Torque around a pivotal point is defined as the force "\\times" perpendicular distance to it from the pivot. "\\tau = f \\times d"

  • Therefore, torque due to the applied force f can be written as "f\\cos\\theta \\times l"
  • Now, maximize the product, "\\cos\\theta" should be maximum. "-1 \\eqslantless \\cos\\theta \\eqslantless1"
  • "\\cos\\theta_{maximum} = 1"

  • Therefore, "\\tau_{max} = f \\times l"

  • Maximum torque is obtained when the force is applied on the far end from the pivotal & perpendicular to the rod.

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