Principle of Work and Energy for Particles in a Plane                

 

 

Example:  A weightless, inextensional  string connects block A to block B around a weightless

frictionless pulley, P.  The blocks are released from rest.  The coefficient of friction, μ, between the horizontal plane and block A equals 0.2.  Block  A weighs 32.2 lb and block B weighs

16.1 lb.  First show that the blocks slide after being released from rest.  Then determine the

speed of the blocks after block B has fallen 2 ft.

 

                                                            

 

            

Strategy:  The first step is to draw a free body diagram to identify forces acting on each block and on

the pulley then apply Euler’s first and 2nd  laws and determine if sliding actually occurs.

 

                                                            

 

 

Sum moments about the center of the pulley.   Σ Mcenter = 0       TA = TB   =  T      

 

Sum forces in x-direction for block A.    Σ Fx  =  mA aA       T  -  F  =   mA aA                  (1)

 

Sum forces in y-direction for block A.    Σ Fy  =  0            WA - N  =   0  so  N  =  WA    (2)

 

Sum forces in y-direction for block B.    Σ Fy  =  mB aB      WB - T  =   mB aB                  (3)

 

Now the maximum friction force  F  =  μ N  =  μ WA                                                       (4)

 

From kinematics (for inextensional cord)    aA   =  aB   =  a                                              (5)                    

                                        

Put  (4) into (1) and add to (3) gives     WB – μ WA =  (mA + mB) a

 

So    a  =  ( WB – μ WA ) / (mA + mB) =  ( 16.1 – 6.44 ) / ( 2 + 1 ) >  0  So sliding occurs.

 

 

Click here to continue with this example.

 

 

 

 

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