Class Notes 20 October Turn in FBDs / Pick up HW Today: Do NOT rotate your FBDs!!! #5: Use SFy=0, SFx=max twice? Start with FBD, SFy=0, SFx=max. Today: Midterm grades… Banking a turn. Universal Gravitational Force.

This graph proves Newton’s second law, showing that acceleration and mass are directly related. Yes No Partially correct Who is this Newton of whom you speak? 2016 Vote: 6, 3, 6, 0 First off the word “proves” is incorrect. The mass on the abscissa refers to the hanging mass, which directly affected the tension. This graph shows that acceleration is directly related to force.

Examples How fast may a car travel when negotiating a turn if the radius of curvature is 150. ft and s=0.600? Use N2 to find v = 36.7 mph If no friction is present, what must be done? Bank the turn at an angle of q = 31.0º

http://www.locsource.com/library/cat/83/01.html

Universal Gravitational Force Proposed by Newton in the Principia Force is proportional to what? |Fgrav|=Gm1m2/r2 Newton couldn’t determine G 1/r2 is need to give planets elliptical orbits. For “point” masses, but…

Universal Gravitational Force Force is always attractive FAB = –FBA (N3) Universal effect Spherical objects are treated Worked for our solar system, except Mercury… We can use this law to find g Responsible for stars, … Attractive: Force between you and your physics book

1 light year (6 trillion miles) http://antwrp.gsfc.nasa.gov/apod/ap011125.html 1 light year (6 trillion miles) Star formation Eggs: (Evaporating Gaseous Globules). Hydrogen gas is gathered together by gravitational force. Sharp points are where stars are formed. Scale is about 1 light-year (6 trillion miles) top to bottom. Notice picture on “Star Birth” poster above board; picture taken by the Hubble space telescope.

Universal Grav. Constant Henry Cavendish Universal! 1798, Used torsion balance to calculate the Earth’s density G = 6.67  10–11 Nm2/kg2 Apparent Weight Often FN but opposite direction Satellites… “Weightless”  Only Fgrav acts Satellites, such as the moon

Three quarters are placed on the rotational platform at different radii. Which will slip first? inside middle outside All at the same time 2016 Vote: 4, 0 ,11, 0 The outside one slips first. The centripetal force holding it on is friction, which is the same for all quarters. The one on the outside is moving faster, and the radial acceleration depends on v *squared*.

Three coins are placed on the rotational platform, all at the same radius. Which will slip first? penny dime quarter All at the same time 2016 Vote: 3, 9, 1, 2 All coins slip at the same time. Setting the frictional force equal to maR, we find the mass divides out. The frictional coefficient of all coins is approximately the same.

Homework For Monday: Lab next Thursday Test next Frisday Finish reading Chapter 5 Do problems on worksheet 23: Lab next Thursday Derivations for experiment 10 Test next Frisday Physics is cumulative Test 3: Chapters 4 and 5