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Physics 2065A/B

Helium Football Notes Intro: kicking a ball is a skill and highly variable; in experiment kicker couldn’t tell if ball did or didn’t have helium in it Results: avg helium ball went 3yds further; bc of variability btwn kicks, there is statistically no difference Helium effect on ball: weight empty, full of air, full of helium- 410g, 3.2 g at 13psi, -0.9% less than empty ball Reasoning: “helium is only half as dense as air so sound travels through it twice as fast” Speed of sound in a gas: Cs= square root of [(ϒ/p) times P] where ϒ is the constant, P is pressure and p is density; Fhe ~ 3 Fair ratio of densities Football facts: regulation NFL football 13 psi, 90kPa; circumference middle btwn 52.7 and 54, and around the ends 70.5-72.4 with the length 14-14.2 (all in cm); weight is 397-425g; shape of prolate ellipsoid Weight of gas added to football: first find volume of football, then the amount of gas added to this volume (SLIDE 12) Pressure is the force per unit area exerted by a body; when you are underwater the relevant weight is the column of water above you; atmospheric pressure results from the weight of the air in a column above you (barometer measures atmospheric pressure); units- force per area= N/m², 1 N/m²= 1 Pascal (Pa); room pressure on avg is 101 300 N/m²= 101.3 kPa (equivalents include 1kg/cm², 1.013 bar (greek baros, weight), 1 atmopshere, 14.7psi) Gauge Pressure pressure on tire pump is relative to atmospheric pressure (gauge pressure); absolute pressure of football is 13psi + 14.7psi= 27.7 psi Moles: 1 mole= same # particles as in 12g of C12 atoms which is Avogadro’s number, 6.022x10(23) particles/mole; mole of gas has a mass equal to its molecular number... so Helium which is “2” has molar mass of 4g/mol; air is 79%N (“14”, 28g/mol) and 21% O (“16”, 32g/mol) so air is 28.96g/mol Ideal Gas Law: PV=nRT (P is pressure in Pa, V is volume in m³, n is number of moles of gas, R is gas constant of 8.314m³Pa/K/mol, T is temperature in Kelvin (0degress=273.1K) SLIDE 13 Mass of gas in football: application of PV=nRT P=13psi, 90kPa, V=0.00430 m³, T=20 degrees= 293.1K, R=8.314 m³Pa/K/mol number of moles added to football n=0.14; mass air is 28.96g/mol x n=4.5g, mass helium is 4g/mol x n=0.36g Weight: Wair=411g+4.5g=416g; He football weight is ~0.9%less than empty footballs (407g); Buoyancy: He molecules are lighter than air molecules which causes upward force on balloon buoyancy; with sufficient He in balloon Fbuoyancy (greater than) Fgravity and balloon rises Archimedes’ Principle: the buoyancy force on a submerged object is equal to weight of fluid that is displaced by the object SLIDE 23 Imparting Energy: He football has more ‘spring’ to it so kicker ‘imparts more energy’ to it Coefficients of Restitution: =1 for elastic collisions, =0 for completely inelastic collisions (objects stick together), 0
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