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Problem 13.10: Calculate reaction forces and torques on a stuck lever

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An emergency lever (the red, sideways, L-shaped object) is designed to rotate clockwise about an axle in a hinge (the gray half circle) as shown in the animation. Assume the lever is rigid, is made of uniform material, and has a mass of 0.20 kg. The axle (the black circle) exerts a frictional force on the lever (position is given in meters). Restart.

  1. What are the magnitude and direction of the torque on the lever due to friction between the lever and axle?
  2. What are the magnitude and direction of the net force of the axle on the lever?
  3. In trying to turn the lever, you apply a force of magnitude 5.0 N in the direction shown in the following animation. Show Animation with Applied Force Vector. But the lever remains in equilibrium. What is the torque on the lever due to friction between the lever and axle, and what are the magnitude and direction of the net force of the axle on the lever?
  4. Suppose you keep the magnitude of the applied force the same (5.0 N) but wish to apply a greater torque to the lever. What could you do differently?
  5. Suppose the maximum torque on the lever due to friction at the axle is 10.0 N·m. You decide to apply a force straight downward at the left end of the lever. What is the minimum value of the magnitude of the force in order to just barely turn the lever?

Problem authored by Aaron Titus.

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