Linear Impulse and Momentum   (impact)  (example continued)

 

 

                                          

 

 

The coefficient of restitution, e, relates normal velocities before and after impact.

 

i.e.  e  =  ˗  the relative velocity after impact divided by the relative before impact.

 

 

So   in this example     e  =  ˗  (vBfx  –  vPfx ) / (vo  –  vPix ) =  ˗ (vBfx  –  vPfx ) / vo

 

or               vBfx  ˗  vPfx   = ˗ e vo       (since      vPix  is zero)                                           (5)           

 

                                                   

and combine this with     M vBfx  ˗  M vo  +  m vPfx    =  0                                            (3)

 

yields 2 equations in 2 unknowns,     vBfx   and    vPfx  

 

   By (3)       vBfx  ˗  vo  +  (m/M) vPfx    =  0      or   - vBfx  + vo ˗ (m/M) vPfx    =  0    add to (5)

 

              vo   ˗   vPfx  ˗  (m/M) vPfx   =  ˗ e vo          

 

                                     

so

 

     vPfx  =  ( 1 + e ) vo / ( 1 + m/M )  =  (1 + 0.7) 5 / (1 + 0.025/0.5) =  8.095 ft/sec

 

 

Now use (5)  vBfx  =   vPfx  ˗ e vo  =  8.095 ˗ (0.7)5  =  4.595 ft/sec

 

 

   vBf  =  4.595 i  +  2.5 j  ft/sec    vPf  =  8.095 i ft/sec            (result)

 

 

Click here for another example involving impact as well as work and energy.

              

 


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