When tightening a bolt, you push perpendicularly on a wrench with a force of 165 N at a distance of 0.140 m from the center of the bolt. (a) How much torque are you exerting in newton × meters (relative to the center of the bolt)? (b) Convert this torque to footpounds.
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Final Answer
  1. 23.1 Nm23.1 \textrm{ N}\cdot\textrm{m}
  2. 17.0 ftlbs17.0 \textrm{ ft}\cdot\textrm{lbs}

Solution video

OpenStax College Physics for AP® Courses, Chapter 9, Problem 2 (Problems & Exercises)

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Video Transcript
This is College Physics Answers with Shaun Dychko. A force of 165 Newtons is exerted on a wrench and it's directed perpendicular to the lever arm of the wrench and the lever arm is this distance from where the force is applied and the bolt. So this is r perpendicular and we are told it's 0.140 meters and here is the force perpendicular to that lever arm, which is 165 Newtons. Okay! So what is the torque is the question? So the torque is the product of the force and the perpendicular component of the lever arm and since the force and lever arm are perpendicular, there's no need for any trigonometry here we just multiply 165 Newtons by 0.140 meters and that is 23.1 Newton-meters. Part (b) asks us to convert that into foot-pounds so we multiply by 0.73756 foot-pounds per Newton-meter and we are left with 17.0 foot-pounds. I found this conversion factor just through an internet search.