## The Skill of Putting

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 \[\nu mg = \frac{m}{2} (\frac{Ft}{m})^2 = \frac{F^2t^2}{2m} \rightarrow F^2= \frac{2 \mu m^2g}{t^2}\]

.