50 lb Package Sliding Down Chute


A package chute has been installed at a distribution center to quickly move packages from the second floor to the first floor. The center's manager would like to know where a person should stand so that a relatively heavy 50 lb package will stop within reach after bounding off the spring stop.

What is known:

  • chute height, 10 ft
  • chute angle, 26.6°
  • horizontal chute length, 7 ft
  • spring constant, k, 50 lb/ft
  • package weight, 50 lb
  • initial velocity, 0.0 ft/s
  • coefficient of friction, μ, 0.30
  • package width, 2 ft

Package Chute Diagram

If the package is released from rest, where will the package stop? Does the package weight matter?


  • Assume the package is a particle and all forces act at its center.
  • Assume smooth transition between the sloped and horizontal sections of the chute.
  • Use the Principle of Work and Energy:
        T1 + ΣU1-2 = T2
  • Include friction forces between the chute and package.
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