Question #188055

Mike kicks soccer ball at a speed of 2.5m/s his friend Jake kicks it back at a speed of 5.5 m/s (Mass of ball is 0.5kg) a.What was the change in momentum? b. If the ball was in contact with Jakes foot for 0.07 seconds, what force did Jake apply?


1
Expert's answer
2021-05-04T06:34:07-0400

The information given is

  • The initial velocity is Vi=+2.5  m/s\vec{V_{i}}=+2.5\;\text{m}/\text{s}
  • The final velocity Vf=5.5  m/s\vec{V_{f}}=-5.5\;\text{m}/\text{s} city is
  • The mass is m=0.5  kgm=0.5\;\text{kg}
  • The interaction time is t=0.07  st=0.07\;\text{s}

Part A


The change in momentum is given by


ΔP=Vf  mVi  m\Delta \vec{P}=\vec{V}_{f}\;m-\vec{V}_{i}\;m


Where.

ViV_{i} is the initial velocity

VfV_{f} is the final velocity.

mm is the mass.


Evaluating numerically.


ΔP=Vf  mVi  m\Delta \vec{P}=\vec{V}_{f}\;m-\vec{V}_{i}\;m\\

ΔP=5.5  m/sf×0.5  Kg2.5  m/sf×0.5  Kg  m\Delta \vec{P}=-5.5\;\text{m}/\text{s}_{f}\times 0.5\;\text{Kg}-2.5\;\text{m}/\text{s}_{f}\times 0.5\;\text{Kg}\;m\\

ΔP=4.0  Kg  m/s\Delta \vec{P}=-4.0\;\text{Kg}\;\text{m}/\text{s}


Answer A

The change in momentum is ΔP=4.0  Kg  m/s\displaystyle \color{red}{\boxed{\Delta P=-4.0\;\text{Kg}\;\text{m}/\text{s}}}


Part B


The average force is


Favg=ΔPt\vec{F}_{avg}=\dfrac{\Delta \vec{P}}{t}


Where.

ΔP\Delta \vec{P} is the change of momentum.

tt is the interaction time.


Evaluating numerically.


Favg=ΔPtFavg=4.0  Kg  m/s0.07  sFavg=57  N\vec{F}_{avg}=\dfrac{\Delta \vec{P}}{t}\\ \vec{F}_{avg}=\dfrac{-4.0\;\text{Kg}\;\text{m}/\text{s} }{0.07\;\text{s}}\\ \vec{F}_{avg}=-57\;\text{N}


Answer B

The average force is Favg=57  N\displaystyle \color{red}{\boxed{\vec{F}_{avg}=-57\;\text{N}}}


The negative sign indicates that the force and the change in momentum (impulse) points in the opposite direction to the initial movement, that is, when it goes back towards Mike


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