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183_notes:energy_dissipation [2014/10/31 13:18] – created caballero | 183_notes:energy_dissipation [2021/06/02 23:15] (current) – [Air Resistance] stumptyl | ||
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- | ===== Dissipation of Energy ===== | + | Section 7.10 in Matter and Interactions (4th edition) |
- | You have read that [[183_notes: | + | ===== Dissipation |
+ | You have read that [[183_notes: | ||
+ | ** | ||
==== Air Resistance ==== | ==== Air Resistance ==== | ||
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Let's say you dropped a metal ball from rest. Below is a set of frames (taken at equal time intervals) from a video of a metal ball being dropped straight down. Notice the ball's displacement increases as each time step elapses. The effect of air resistance is very small. To a reasonable degree, we can [[183_notes: | Let's say you dropped a metal ball from rest. Below is a set of frames (taken at equal time intervals) from a video of a metal ball being dropped straight down. Notice the ball's displacement increases as each time step elapses. The effect of air resistance is very small. To a reasonable degree, we can [[183_notes: | ||
- | {{ 183_notes:mi3e_07-039.jpg?400 }} | + | {{ 183_notes:week10_dissipation1.png?400 }} |
If you instead dropped a coffee filter, you would observe something all together different. The frames below are taken from a video of a coffee filter dropped from rest. Notice that the displacement between each frame is roughly the same (especially near the end of the video). This latter motion could be modeled to a reasonable degree [[183_notes: | If you instead dropped a coffee filter, you would observe something all together different. The frames below are taken from a video of a coffee filter dropped from rest. Notice that the displacement between each frame is roughly the same (especially near the end of the video). This latter motion could be modeled to a reasonable degree [[183_notes: | ||
- | {{ 183_notes:mi3e_07-040.jpg?600 }} | + | {{ 183_notes:week10_dissipation2.png?600 }} |
==== Where does the energy go? ==== | ==== Where does the energy go? ==== | ||
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$$\underbrace{\Delta K_{filter}}_{0\mathrm{\: | $$\underbrace{\Delta K_{filter}}_{0\mathrm{\: | ||
+ | |||
+ | The kinetic energy of the coffee filter doesn' | ||
+ | |||
+ | $$\vec{F}_{net} = \vec{F}_{grav} + \vec{F}_{air} = 0$$ | ||
+ | $$\vec{F}_{grav} = -\vec{F}_{air} \rightarrow F_{grav} = F_{air} $$ | ||
+ | $$ mg = cv_{terminal}^2 \rightarrow v_{terminal} = \sqrt{\dfrac{mg}{c}}$$ | ||
+ | |||
+ | where $c$ is a constant that contains all the constants in the [[183_notes: | ||
$$W_{surr} = \Delta U _{grav} $$ | $$W_{surr} = \Delta U _{grav} $$ | ||
- | What can do work on the coffee filter if the Earth is in the system? The air molecules | + | // |