_AQA_Edexcel A_Level_Physics_Gravitational_Fields_Answers_2

1. ThegraphbelowshowsthevariationoftheorbitalperiodsquaredwiththeradiuscubedforJupiter’smoons. TotalforQuestion1:10 (a) Define a gravitational field. (b) Byequatingthecentripetalforceandthegravitationalforceonaplanet,showthatT2= 4π2 r3. [1] [4] (c) UsetheresultfromthepreviouspartandthegraphabovetocalculateJupiter’smass. [3] (d) Kepler’s second law states that a line segment joining a planet and the sun sweeps out equal areasduring equal intervals of time. Use this to explain why we rarely see great comets, whose orbits arehighlyelliptical. [2] 2. Satellites can also be analysed using the various laws of gravitation and circular motion. For this question,assumethatEarth’smassis6.0×1024kgandthatithasaradiusof6400km. TotalforQuestion2:10 (a) Byequatinggravitationalandcentripetalforces,showthatthemassofasatelliteinorbitdoesnotaffectitsspeed. [2] (b) Calculatethespeedatwhichasatellitemustbereleasedintoorbitifitistomaintainaheightof100kmaboveEarth’ssurface. [2] (c) Defineageostationaryorbit. [3] (d) Calculatethealtitudeofageostationaryorbit. [3] 3. Allvectorfieldshaveanassociatedscalarpotential.Forthisquestion,assumeEarthhasaradiusof6400kmandamassof6.0×1024kg. (a) Define,inwords,thegravitationalpotential. TotalforQuestion3:10 [1] (b) Giventhatthegravitationalpotential,Vg,is63MJkg−1atEarth’ssurface,calculatethefollowing: i. Vgatinfinity. [1] ii. VgatanaltitudeequaltoEarth’sradius. [1] (c) Calculatethegravitationalpotentialenergyofa10kgballatanaltitudeequaltothreetimesEarth’sradius. [2] (d) Sketch a graph to show how the magnitude of the gravitational force varies with the distance fromthecentreofthesphericalobjectcreatingthefield.Whatisrepresentedbytheareaunderneaththegraph? [1] (e) TheaveragekineticenergyofanH2moleculeisgivenbytheequation1mc¯2=3kT,wheremisthe [4] 2 2 massofthemolecule,,kistheBoltzmannconstantandTistemperature.By andtheescapevelocity,determinewhetherornotaheliummoleculeat300KcanescapeEarth’satmosphere.Themassofoneatomofheliu