Kinetics - Body Translating in a Plane

 

 

Example:  (continued)       The FBD's of each part are shown below.

 

                      

 

 

First check equilibrium.    F  =  T,  2T  =  P,  P  =  WB  =  4 WA

 

So  F = (1/2)P  =  2 WA  and  F  =  μ N  =  μ WA   For equilibrium   μ  must equal 2. 

But  μ  is only  1/4.  So starting from rest,  block  A  will accelerate to the right.

 

 

Next relate the accelerations of block  A  and block  B  using kinematics.

See the figure below.

                                 

 

 

The length, L, of the cord is:  x + (π/4)r + y + π(2r) + y + k = L   giving  ˗ dx/dt + 2 dy/dt = 0

Or for accelerations   d2x/dt2 =  2  d2y/dt2.     i.e.  aA  =  2 aB

 

 

Click here to continue with this example.

 


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