The Skill of Putting

Putting at golf is a skill. You not only have to aim the ball properly, allowing for an uneven green. You have to hit the ball hard enough to reach the hole. You also have o hit it no so hard that it does not hit the far side of the hole hard enough to roll back out of the hole.
All the time the ball is rolling, it is encountering resistance due to friction which slows it down/ A simple model assumes this frictional force is equal to  
\[\mu R\]
  where  
\[R\]
  is the normal reaction force (equal to  
\[mg\]
  on level ground). Overcoming this frictional force requires the expenditure of energy, which must be supplied by the ball's kinetic energy according to the work energy principle.
\[\mu mg \times d= \frac{1}{2}mv^2\]

The initial kinetic energy is supplied by the golfer hitting the ball with their club. Suppose the golfer hit the ball with a force  
\[F\]
  for a time  
\[t\]
. The impulse  
\[Ft\]
  is equal to the momentum supplied  
\[mv\]
  so that  
\[Ft=mv \rightarrow v= \frac{Ft}{m}\]
  then  
\[\nu mg = \frac{m}{2} (\frac{Ft}{m})^2 = \frac{F^2t^2}{2m} \rightarrow F^2= \frac{2 \mu m^2g}{t^2}\]
.

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