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DYNAMICS - CASE STUDY SOLUTION

    Velocity


General Motion

 


Velocity Motion
 

The velocity of the truck can be determined using velocity equation in polar coordinates,

     
where
     

     v = 0.0889t er + 14(0.0500) eθ

However, this is still a function of t. To find the time time t required for the truck to travel from r = 4 to r = 14 meters, integrate the radial component of the velocity, giving

     

     (0.0889 t2)/2 = 14 - 4

     t = 15 s

Now, substitute t into the equation to calculate the final velocity, v,

     

     
    Acceleration


Acceleration Motion

 

Similarly, the acceleration equation can be used to calculate the acceleration of the truck when it is 14 meters from the center of the carousel. Since the time has already be determined previously, no integration is required.

     
where
     

     a = [0.0889 - 14(0.0500)2]er
                           + [2(0.0889)(15)(0.0500) - 0]eθ

     a = 0.5390er + 0.1334eθ

     
   
 
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