===== Example: Predicting the final momentum & velocity using the Momentum Principle =====

[[http://en.wikipedia.org/wiki/Henrik_Zetterberg|Henrik Zetterberg]] is passing a hockey puck at a Red Wings practice. From video of the pass, you can determine the stick was in contact with the puck for $0.05 s$. You estimate the force with which "Zäta" passes the puck is about a tenth of his weight, so $100 N$. Determine how fast the puck leaves Zäta's stick.

=== Facts ====

  * The puck experiences several forces including
    * the gravitational force (directly downward)
    * the force of the stick
    * the force due to the ice (upward)
    * some frictional forces and air resistance

=== Lacking ===

  * The mass of an NHL regulation hockey puck is unknown but can be [[http://lmgtfy.com/?q=mass+of+a+regulation+NHL+hockey+puck|found online]] ($m_{puck}=0.17kg$).

=== Approximations & Assumptions ===

  * Over the time interval the puck is in contact with the stick, the frictional forces are negligible.
  * The puck is contact with the stick for $0.05 s$.
  * The force the stick exerts on the puck is roughly constant over the $0.05 s$ time interval.
  * The force the stick exerts is $100 N$, and can be considered to act in a single direction.
  * The puck starts from rest.

=== Representations ===

  * The free-body diagram for this situation is given by the diagram below.
  {{ 183_notes:hockeystickfbd.png }}
  * The final momentum of the puck is given by the update form of the [[183_notes:momentum_principle|Momentum Principle]]: $\vec{p}_f = \vec{p}_i + \vec{F}_{net} \Delta t$.
 
==== Solution ====

Given the approximations and assumptions above, you can write the update form of the momentum principle for this question,

$$\vec{p}_f = m_{puck}\vec{v}_f = \vec{F}_{net} \Delta t$$

because the puck starts from rest. So that,

$$\vec{v}_f = \dfrac{\vec{F}_{net}}{m_{puck}} \Delta t$$

which we can consider in one dimension,

$$v_f = \dfrac{F_{net}}{m_{puck}} \Delta t = \dfrac{100 N}{0.17 kg}(0.05 s) = 29.4 \dfrac{m}{s}$$