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DYNAMICS - CASE STUDY

    Introduction


Problem Diagram

 

At the ACME factory, crates containing precious goods are carried through the plant on conveyor belts. When a conveyor belt stops, the boxes must not slide or the goods may be damaged.

What is known:

  • The conveyor belts move at a constant speed of 10 ft/s.
  • The crates first travel on a horizontal belt, then down a belt with a 15° decline.
  • The static, μs, and kinetic (dynamic), μk, coefficient of friction, μs, between the belt and the crates are = 0.5 and 0.3, respectively.
   
  Questions

 

What is the shortest distance in which the horizontal belt can be brought to a stop without causing the crates to slide?

What is the shortest distance for the inclined belt?

     
  Approach

 
  • Using Newton's Second Law, relate the forces acting on the crate with its acceleration.
  • Analyze the problem in terms of rectangular coordinates.
  • Since no sliding actually occurs, use the static coefficient of friction.
  • Derive an equation for the position by integrating the acceleration equation a = d2x/dt2.