Search
 
 

DYNAMICS - CASE STUDY

    Introduction


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
     
    Questions


Package Chute Diagram
 

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

   
  Approach

 
  • 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.
     
   
 
Practice Homework and Test problems now available in the 'Eng Dynamics' mobile app
Includes over 400 problems with complete detailed solutions.
Available now at the Google Play Store and Apple App Store.