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183_notes:examples:two_students_colliding [2014/09/25 16:57] – pwirving | 183_notes:examples:two_students_colliding [2014/10/02 15:50] (current) – caballero | ||
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- | ===== Example: | + | ===== Example: |
Two students are running to make it to class. They turn a corner and collide; coming to a complete stop. What force did they exert on each other. | Two students are running to make it to class. They turn a corner and collide; coming to a complete stop. What force did they exert on each other. | ||
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=== Solution === | === Solution === | ||
+ | |||
+ | We use the momentum principle to relate the momentum of the students to the force applied. We have chosen student 1 as our system. | ||
${p}_{fx} = {p}_{ix} + {F}_{x, | ${p}_{fx} = {p}_{ix} + {F}_{x, | ||
+ | |||
+ | We are told that the students come to a complete stop and so ${p}_{fx}$ = 0. | ||
$0 = M{V}_{ix} + {F}_{x, | $0 = M{V}_{ix} + {F}_{x, | ||
+ | |||
+ | Rearranging the equation we relate ${F}_{x, | ||
$ {F}_{x, | $ {F}_{x, | ||
- | negative means $-\hat{x}$ direction | + | The negative |
- | Need to find collision time ${\Delta t}$ | + | Now that we have the above relationship we must find the missing variables in order to solve for $ {F}_{x, |
$\vec{v}_{avg} = \dfrac{\vec{v}_{f} + \vec{v}_{i}}{2} = \dfrac{\Delta \vec{r}}{\Delta t}$ | $\vec{v}_{avg} = \dfrac{\vec{v}_{f} + \vec{v}_{i}}{2} = \dfrac{\Delta \vec{r}}{\Delta t}$ | ||
- | In 1D: $\vec{v}_{avg} = \dfrac{\Delta x}{\Delta t} = \dfrac{\vec{v}_{f} + \vec{v}_{i}}{2}$ | + | |
+ | |||
+ | In 1D this looks like: $\vec{v}_{avg} = \dfrac{\Delta x}{\Delta t} = \dfrac{\vec{v}_{f} + \vec{v}_{i}}{2}$ | ||
+ | |||
+ | Relate these 3 equations together to solve for ${\Delta t}$ | ||
$ {\Delta t} = \dfrac{\Delta x}{{V}_{avg}} = \dfrac{\Delta x}{\dfrac{\vec{v}_{f} + \vec{v}_{i}}{2}} $ | $ {\Delta t} = \dfrac{\Delta x}{{V}_{avg}} = \dfrac{\Delta x}{\dfrac{\vec{v}_{f} + \vec{v}_{i}}{2}} $ | ||
+ | |||
+ | Fill in the values for the variables from the assumptions and approximations you made previous. | ||
$ \dfrac{0.025}{\dfrac{5m/ | $ \dfrac{0.025}{\dfrac{5m/ | ||
+ | |||
+ | Having solved for $ {\Delta t}$ fill this value and the known value for mass and the approximated value for velocity into the equation that we arranged earlier to find $ {F}_{x, | ||
$ {F}_{x, | $ {F}_{x, |