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This is how you include air resistance in projectile motion. It requires the Drag Force and Numerical Modeling (or the Euler Method). It is also very helpful to use a spreadsheet to do the calculations. I prove a statement from a previous projectile motion problem video, "Air resistance decreases the x displacement of the ball by less than 1 cm." Content Times: 0:22 The statement this video proves 1:01 The basic concept of air resistance 1:54 The Free Body Diagram 2:20 The Drag Force Equation 3:13 Information about the Lacrosse Ball 4:03 The Drag Coefficient 4:55 The Density of Air 5:18 How the Drag Force affects the motion 5:58 The basic idea of Numerical Modeling (or the Euler Method) 6:50 Solving for the acceleration in the x direction 8:53 Solving for the final velocity in the x direction 9:54 Solving for the final position in the x direction 11:41 Entering the Lacrosse Ball information into Excel 13:34 Solving for the Drag Force in x direction in Excel 14:29 Solving for the acceleration in the x direction in Excel 14:58 Solving for the final velocity and final position in the x direction in Excel 15:46 Solving for the acceleration in the y direction 17:21 Solving for all the variables in the y direction in Excel 19:13 Click and Drag Copy. Harnessing the Power of Excel! 19:43 Understanding the numbers in Excel 20:35 Solving for the decrease in the x displacement caused by the Drag Force [url="http://www.flippingphysics.com/theeulermethod.html"]Want lecture notes & the Excel File?[/url] (also contain's photo credits and links to website's shown in video) The original problem videos for this are: [url="http://www.flippingphysics.com/projectilemotionproblempart1of2.html"](part 1 of 2) An Introductory Projectile Motion Problem with an Initial Horizontal Velocity[/url] [url="http://www.flippingphysics.com/projectilemotionproblempart2of2.html"](part 2 of 2) An Introductory Projectile Motion Problem with an Initial Horizontal Velocity[/url] [url="http://www.flippingphysics.com/howmany.html"]How Many Attempts did it Really Take?[/url]  with live music from Amos Lee [url="http://www.flippingphysics.com/give.html"]1¢/minute[/url]
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Name: A Brief Look at the Force of Drag using Numerical Modeling (or The Euler Method) Category: Dynamics Date Added: 22 May 2014  05:01 PM Submitter: Flipping Physics Short Description: None Provided This is how you include air resistance in projectile motion. It requires the Drag Force and Numerical Modeling (or the Euler Method). It is also very helpful to use a spreadsheet to do the calculations. I prove a statement from a previous projectile motion problem video, "Air resistance decreases the x displacement of the ball by less than 1 cm." Content Times: 0:22 The statement this video proves 1:01 The basic concept of air resistance 1:54 The Free Body Diagram 2:20 The Drag Force Equation 3:13 Information about the Lacrosse Ball 4:03 The Drag Coefficient 4:55 The Density of Air 5:18 How the Drag Force affects the motion 5:58 The basic idea of Numerical Modeling (or the Euler Method) 6:50 Solving for the acceleration in the x direction 8:53 Solving for the final velocity in the x direction 9:54 Solving for the final position in the x direction 11:41 Entering the Lacrosse Ball information into Excel 13:34 Solving for the Drag Force in x direction in Excel 14:29 Solving for the acceleration in the x direction in Excel 14:58 Solving for the final velocity and final position in the x direction in Excel 15:46 Solving for the acceleration in the y direction 17:21 Solving for all the variables in the y direction in Excel 19:13 Click and Drag Copy. Harnessing the Power of Excel! 19:43 Understanding the numbers in Excel 20:35 Solving for the decrease in the x displacement caused by the Drag Force View Video

This past week it has gotten pretty cold up here in the (somewhat) North. With windchill, temperatures have dropped below zero, and with weather like that it can always be a struggle to stay warm. But with the proper clothing, one can still brave the harsh climate and still have a good time. We might often take it for granted, but how exactly does this insulating process work? Heat travels in three ways: conduction, convection, and radiation. Conduction is simply the transfer of heat by colliding molecules, like when a pan will get heated along its full surface instead of the bottom, and this form of energy transfer is the reason why things like microwave burritos often tell you to wait a few minutes before eating, to let the heat distribute itself evenly. In more conductive objects like metal, it is a good way of transferring heat, but in less conductive things like air (air is, in fact, a poor thermal conductor, which seems counterintuitive), it doesn't exactly do much. Radiation is simply the transfer of heat energy through electromagnetic radiation (primarily thermal, or infrared radiation), such as with sunlight or tungsten light bulbs, and for most common objects it doesn't play a big role in the transfer of heat. In fact, if you wound up stranded in space, one half of you would not freeze as the other side boils, as is popular belief. While space is technically very cold, through radiation along heat leaves your body very slowly. The real issue would be (still) your blood boiling, not due to temperature but due to the vacuum of space, and of course the lack of oxygen. But nonetheless, radiation for cooler objects doesn't transfer heat too well. The real reason why winter is cold is because of convection: the movement of air molecules in our atmosphere, the reason for our weather and the reason why open doors have "drafts". While air is a poor conductor, it convects very well, and with colder air being denser and of a higher pressure, cold air will flow into warmer areas, like when a cold front blows in, or you feel a "blast" of cold from your freezer. So in order to combat this flow of air, we bundle up, putting on layers to protect us from the wind and these currents. However, just one layer to stop the wind won't cut it  the transfer of heat itself will generate convection. The real secret to staying warm is a measure of "dead air", or the pockets of gas within our coats or mittens that are too small to give rise to convection currents but still present as to slow conduction. It's the measure of these microscopic packets of air that allow our clothes to be warm without being unnecessarily expensive. While we can certainly cut out these small pockets of air altogether (certain jackets do), the benefits of using dead air maintain warmth at a lower physical cost, and usually make a coat thicker and more resilient to tears. With that, now you know not only how to stay warm, but how staying warm works. So don't forget to bundle up.
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