LVang+-+L7+-+Air+Resistance+Lab

Lue Vang Mr. Kellogg AP Physics - Pd. 7 22 October 2011 Performed On: 10 October 2011 Lab Partners: Scott Smith, Brent Keath **Measurements Lab **
 * Purpose: **
 * The purpose of this lab is to observe the effects of air resistance, specifically on falling coffee filters. The lab will also analyze the terminal velocity of falling objects and how it is affected by air resistance. Finally, the lab will practice the art of choosing between two competing force models for air resistance. **


 * Background: **
 * Prior to the lab, it is known that air resistance may cause objects to fall without constant acceleration. If the falling object is prone to the effects of air resistance, the object will reach terminal velocity sooner because the force of air pushing up reduces acceleration gained from the force of gravity pulling down. **


 * Resistance, also known as drag force, is proportional to the velocity and sometimes square of the velocity of objects falling in air. Of course, drag force is opposite of the direction of motion. **

**Air Resistance (Drag Force) = ** **//Fdrag = -bv … … or … … Fdrag = -cv2 //** **//*b //**** and //c// are drag coefficients that depend on the size and shape of the object **

**//mg = -bv //** **//mg = -cv2 //**
 * At terminal velocity, downward force is equal to upward force. Upward force is //mg// while air resistance is //–bv// or //–cv2//. Therefore, **

**VT ∞ m ** **VT2 ∞ m **
 * Since //g//, //b//, and, //c// are constants, terminal velocity is only affected my mass, so **


 * <span style="font-family: 'Calibri','sans-serif';">Hypothesis: **
 * <span style="font-family: 'Calibri','sans-serif';">According to the two above formulas for drag force, mass is the only factor that will change the amount of drag force on an object. The formula for downward force also shows that mass is multiplied with the force of gravity (-9.8m/s), so a larger mass should result in a greater downward force at terminal velocity. Therefore, if the falling object is greater in mass, the downward force will be greater, thus resulting in greater terminal velocity. For example, a set of two coffee filters will have a greater terminal velocity when dropped than just one coffee filter. **


 * <span style="font-family: 'Calibri','sans-serif';">Greater air resistance will cause an object to reach terminal velocity sooner, thus make them “slower” because the lighter objects will have less time to accelerate. **


 * <span style="font-family: 'Calibri','sans-serif';">Apparatus: **
 * <span style="font-family: 'Calibri','sans-serif';">Computer **
 * //<span style="font-family: 'Calibri','sans-serif';">Logger Pro //**
 * <span style="font-family: 'Calibri','sans-serif';">Vernier Motion Detector **
 * <span style="font-family: 'Calibri','sans-serif';">Vernier Computer Interface **
 * <span style="font-family: 'Calibri','sans-serif';">5 Basket-style Coffee Filters **


 * <span style="font-family: 'Calibri','sans-serif';">Procedure: **
 * 1) **<span style="font-family: 'Calibri','sans-serif';">Connect the Motion Detector to your computer and set it to person/ball. **
 * 2) **<span style="font-family: 'Calibri','sans-serif';">Suspend the detector in the ceiling so that it points towards the floor. **
 * 3) **<span style="font-family: 'Calibri','sans-serif';">Open the custom-made //Logger Pro// file made by your teacher. **
 * 4) **<span style="font-family: 'Calibri','sans-serif';">Place a coffee filter 0.5m from the detector’s sensor beam. **
 * 5) **<span style="font-family: 'Calibri','sans-serif';">Activate the “Collect” command in //Logger Pro// and release the coffee filter so that it falls directly downward. *Be sure to move your hand out of the radar beam. **
 * 6) **<span style="font-family: 'Calibri','sans-serif';">Repeat the following steps for until a smooth graph is created. **
 * 7) **<span style="font-family: 'Calibri','sans-serif';">The velocity of the coffee filter can be determined by finding the slope of the position vs. time graph. *Do this with the “Linear Fit” option in //Logger Pro//. **
 * 8) **<span style="font-family: 'Calibri','sans-serif';">Record the data. **
 * 9) **<span style="font-family: 'Calibri','sans-serif';">Repeat steps 4-8 for two, three, four, and five coffee filters. **


 * <span style="font-family: 'Calibri','sans-serif';">Data: **
 * <span style="font-family: 'Calibri','sans-serif';">Air Resistance Graphs 2 - 5 **

<span style="font-family: 'Calibri','sans-serif';"> <span style="font-family: 'Calibri','sans-serif';"> <span style="font-family: 'Calibri','sans-serif';"> <span style="font-family: 'Calibri','sans-serif';">


 * <span style="font-family: 'Calibri','sans-serif';">Table-1: **
 * ** Terminal Velocity of Falling Coffee Filters ** ||
 * ** Number of Filters ** || ** Terminal Velocity ** || ** (Terminal Velocity)2 ** ||
 * || VT (m/s) || VT2 (m2/V2) ||
 * 1 || 1.155 || 1.334 ||
 * 2 || 1.81 || 3.276 ||
 * 3 || 1.911 || 3.652 ||
 * 4 || 2.331 || 5.434 ||

<span style="font-family: 'Calibri','sans-serif';">
 * <span style="font-family: 'Calibri','sans-serif';">Graph-1: **


 * <span style="font-family: 'Calibri','sans-serif';">Analysis: **
 * <span style="font-family: 'Calibri','sans-serif';">1.) ****<span style="font-family: 'Calibri','sans-serif';">See Terminal Velocity of Falling Coffee Filters (Graph-1) above. **
 * <span style="font-family: 'Calibri','sans-serif';">2.) ****<span style="font-family: 'Calibri','sans-serif';">As seen in Graph-1 above, proportionality one (Terminal Velocity) creates a more linear curve. **
 * <span style="font-family: 'Calibri','sans-serif';">3.) ****<span style="font-family: 'Calibri','sans-serif';">Proportionality one (Terminal Velocity), -bv, creates a better model of the real data, because the second one (Terminal Velocity2), -cv2, is squaring the data, thus making the coffee filter seem to be falling faster. **
 * <span style="font-family: 'Calibri','sans-serif';">4.) ****<span style="font-family: 'Calibri','sans-serif';">The time of fall decreases as weight increases, because a larger weight results in a faster velocity as the object falls. This is because a smaller weight means there is a smaller amount of drag force, opposing force, to go against the force of gravity pulling the object. With less opposing force, it takes longer to reach terminal velocity, thus the falling object gets more time to speed up, which then results in a faster terminal velocity at the end. **


 * <span style="font-family: 'Calibri','sans-serif';"> In the perfect world, if one filter falls in time //t//, then four filters will fall in ¼//t// if the filters are always falling in terminal velocity. This is because VT ∞ m, so 4m ∞ 4VT meaning having 4 filters will fall 4 times as fast in terminal velocity, thus it’ll reach the floor in ¼ of the time the trail with only 1 filter. **


 * <span style="font-family: 'Calibri','sans-serif';">Conclusion: **
 * <span style="font-family: 'Calibri','sans-serif';">According to the experiment, the hypothesis is supported. The Table-1 shows that having more coffee filters (more mass) results in a faster terminal velocity. For example, 1 filter resulted in 1.155m/s as the terminal velocity while 4 filters ended up with 2.331m/s. **


 * <span style="font-family: 'Calibri','sans-serif';">In correlation to the background information, this means having greater mass reduces air resistance (drag force). It also means falling objects with larger mass will fall faster and hit the floor sooner if the objects are allowed to hit terminal velocity and use their terminal velocity to affect the results. If the two objects are not able to reach their terminal velocities, it’s very likely that they hit the floor at the same time, because both are accelerating at the same rate downwards. It’s the air resistance that determines how long they’ll stay accelerating, and of course, a larger mass will result in a larger “exposure time” to acceleration. **


 * <span style="font-family: 'Calibri','sans-serif';">The overall experiment conduct well, and the only possible change is to have the release of the coffee filter be more controlled. The release for this particular experiment is done with human hands, thus leaving room for human error. The release distances from the sensor varied a bit, and at times the movement of the releasing hand causes the coffee filter to float away from the sensor’s field of vision. For improvement, have a release mechanism that releases the filter at the same exact height for each trial and have it release the filter so that the filter is able to fall straight down. **