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DYNAMICS - EXAMPLE


Box Slide with Sprint
  Example

 

An 8 lb box slides down slope (kinetic coefficient of friction, μk = 0.1) and compresses a spring. How far is the spring compress before the box is pushed back up the slope?

 

   
    Solution


FBD and Spring Compression

 

The problem involves both energy and forces. The friction force needs to be determined before energy methods can be applied.

Find the normal and friction forces,
     ΣFy = 0
     N = 8 cos55 = 4.589 lb

     f = μN = 0.3 (4.589) = 1.377 lb

Energy balance
     T1 +  U1-2 = T2
     0 + (mgh - fd) = 0.5 k s2
     8 (8 + s) sin55 - 1.377 (8 + s) = 0.5 (100) s2
     52.43 + 6.553s - 11.01 - 1.377 s = 50 s2
     50s2 - 5.176s - 41.42 = 0

Solving the quadratic equation
     

  s = 0.05176 +/- 0.9116     (use positive answer)

s = 0.9634 ft

     
   
 
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