{"id":42,"date":"2016-05-04T16:01:59","date_gmt":"2016-05-04T16:01:59","guid":{"rendered":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/?page_id=42"},"modified":"2016-05-04T16:01:59","modified_gmt":"2016-05-04T16:01:59","slug":"tutorial-9","status":"publish","type":"page","link":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/tutorial-9\/","title":{"rendered":"Tutorial 9"},"content":{"rendered":"

Gravitation<\/strong><\/p>\n

 <\/p>\n

    \n
  1. State the inverse square law of gravitation.<\/li>\n<\/ol>\n

     <\/p>\n

      \n
    1. Calculate the gravitational force between two cars parked 0.50 m apart. The mass of each car is 1000 kg.<\/li>\n<\/ol>\n

       <\/p>\n

        \n
      1. Calculate the gravitational force between the Earth and the Sun.<\/li>\n<\/ol>\n

         <\/p>\n

          \n
        1. (a) By considering the force on a mass, at the surface of the Earth, state the expression for the gravitational field strength, g, in terms of the mass and radius of the Earth.<\/li>\n<\/ol>\n

          (b)\u00a0\u00a0 (i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 The gravitational field strength is 9.8 N kg-1 <\/sup>at the surface of the Earth. Calculate<\/em> a value for the mass of the Earth.<\/p>\n

          \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em>(ii)\u00a0\u00a0\u00a0\u00a0\u00a0 Calculate the gravitational field strength at the top of Ben Nevis, 1344 m above the surface of the Earth.<\/p>\n

          (iii)\u00a0\u00a0\u00a0\u00a0 Calculate the gravitational field strength at 200 km above the surface of the Earth.<\/p>\n

           <\/p>\n

            \n
          1. (a) What is meant by the gravitational potential at a point?<\/li>\n<\/ol>\n

            (b)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 State the expression for the gravitational potential at a point.<\/p>\n

            (c)\u00a0\u00a0 Calculate the gravitational potential:<\/p>\n

            (i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 at the surface of the Earth<\/p>\n

            (ii)\u00a0\u00a0\u00a0\u00a0\u00a0 800 km above the surface of the Earth.<\/p>\n

             <\/p>\n

              \n
            1. \u2018A gravitational field is a conservative field.\u2019 Explain what is meant by this statement.<\/li>\n<\/ol>\n

               <\/p>\n

                \n
              1. Calculate the energy required to place a satellite of mass 200 000 kg into an orbit at a height of 350 km above the surface of the Earth.<\/li>\n<\/ol>\n

                 <\/p>\n

                  \n
                1. Which of the following are vector quantities: gravitational field strength, gravitational potential, escape velocity, universal constant of gravitation, gravitational potential energy, period of an orbit?<\/li>\n<\/ol>\n

                   <\/p>\n

                    \n
                  1. A mass of 8.0 kg is moved from a point in a gravitational field where the potential is \u201315 J kg-1<\/sup> to a point where the potential is \u201310 J kg-1<\/sup>.<\/li>\n<\/ol>\n

                    (a)\u00a0\u00a0 What is the potential difference between the two points?<\/p>\n

                    (b)\u00a0\u00a0 Calculate the change in potential energy of the mass.<\/p>\n

                    (c)\u00a0\u00a0 How much work would have to be done against gravity to move the mass between these two points?<\/p>\n

                     <\/p>\n

                      \n
                    1. (a) Explain what is meant by the term \u2018escape velocity\u2019.<\/li>\n<\/ol>\n

                      (b)\u00a0\u00a0 Derive an expression for the escape velocity in terms of the mass and radius of a planet.<\/p>\n

                      (c)\u00a0\u00a0 (i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Calculate the escape velocity from both the Earth and from the Moon.<\/p>\n

                      (ii)\u00a0\u00a0\u00a0\u00a0\u00a0 Using your answers to (i) comment on the atmosphere of the Earth and the Moon.<\/p>\n

                       <\/p>\n

                        \n
                      1. Calculate the gravitational potential energy and the kinetic energy of a 2000 kg satellite in geostationary orbit above the Earth.<\/li>\n<\/ol>\n

                         <\/p>\n

                          \n
                        1. (a) A central force required to keep a satellite in orbit.\u00a0 Derive the expression for the orbital period in terms of the orbital radius.<\/li>\n<\/ol>\n

                          (b)\u00a0\u00a0 A satellite is placed in a parking orbit above the equator of the Earth.<\/p>\n

                          (i)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 State the period of the orbit.<\/p>\n

                          (ii)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Calculate the height of the satellite above the equator.<\/p>\n

                          (iii)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Determine the linear speed of the satellite.<\/p>\n

                          (iv)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Find the central acceleration of the satellite.<\/p>\n

                           <\/p>\n

                            \n
                          1. A white dwarf star has a radius of 8000 km and a mass of 1.2 solar masses.<\/li>\n<\/ol>\n

                            (a)\u00a0\u00a0 Calculate the density of the star in kgm-3<\/sup>.<\/p>\n

                            (b)\u00a0\u00a0 Find the gravitational potential at a point on the surface.<\/p>\n

                            (c)\u00a0\u00a0 Calculate the acceleration due to gravity at a point on the surface.<\/p>\n

                            (d)\u00a0\u00a0 Estimate<\/em> the potential energy required to raise your centre of gravity from a sitting position to a standing position on this star.<\/p>\n

                            \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 <\/em>(e)\u00a0\u00a0 A 2 kg mass is dropped from a height of 100 m on this star. How long does it take to reach the surface of the star?<\/p>\n

                              \n
                            1. (a) How are photons affected by a massive object such as the Sun?<\/li>\n<\/ol>\n

                              (b)\u00a0\u00a0 Explain, using a sketch, why light from a distant star passing close to the Sun may suggest that the star is at a different position from its \u2018true\u2019 position.<\/p>\n

                              (c)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Explain what is meant by the term \u2018black hole\u2019.<\/p>\n","protected":false},"excerpt":{"rendered":"

                              Gravitation   State the inverse square law of gravitation.   Calculate the gravitational force between two cars parked 0.50 m apart. The mass of each car is 1000 kg.   Calculate the gravitational force between the Earth and the Sun.   (a) By considering the force on a mass, at the surface of the Earth, … Continue reading Tutorial 9<\/span> →<\/span><\/a><\/p>\n","protected":false},"author":6460,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-42","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages\/42","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/users\/6460"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/comments?post=42"}],"version-history":[{"count":1,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages\/42\/revisions"}],"predecessor-version":[{"id":43,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages\/42\/revisions\/43"}],"wp:attachment":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/media?parent=42"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}