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Both sides previous revision Previous revision Next revision | Previous revision | ||
183_notes:examples:mit_water_balloon_fight [2014/10/10 20:29] – pwirving | 183_notes:examples:mit_water_balloon_fight [2014/10/11 06:03] (current) – pwirving | ||
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Surroundings: | Surroundings: | ||
- | {{course_planning: | + | {{course_planning: |
=== Solution === | === Solution === | ||
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And the initial and final conditions are: | And the initial and final conditions are: | ||
- | Initial | + | Initial |
- | Final = 0 \longrightarrow relaxed | + | Final = $0 \longrightarrow$ relaxed |
Sub in the force for hose into the equation for work done by a non constant force: | Sub in the force for hose into the equation for work done by a non constant force: | ||
Line 97: | Line 97: | ||
Going back a couple of steps we now have an equation for work which we can relate to our previous equation for v_{f}. | Going back a couple of steps we now have an equation for work which we can relate to our previous equation for v_{f}. | ||
- | $$V_{f} = \sqrt {\dfrac{2W}{m}}$$ | + | $$V_{f} = \sqrt {\dfrac{2W}{m}}$$ |
+ | |||
+ | $$W = \dfrac{1}{2}S_{max}^2$$ | ||
+ | |||
+ | Substitute work in the equation for $v_{f}$ | ||
$$V_{f} = \sqrt {\dfrac{2}{m}(\dfrac{1}{2}ks^2_{max})}$$ | $$V_{f} = \sqrt {\dfrac{2}{m}(\dfrac{1}{2}ks^2_{max})}$$ | ||
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$$ = \sqrt {\dfrac{k}{m}}S_{max}$$ | $$ = \sqrt {\dfrac{k}{m}}S_{max}$$ | ||
- | Sub in values for known variables and solve for v_{f} | + | Sub in values for known variables and solve for $v_{f}$ |
$$ v_{f} = \sqrt {\dfrac{100N/ | $$ v_{f} = \sqrt {\dfrac{100N/ |