{"id":44,"date":"2016-05-04T16:18:30","date_gmt":"2016-05-04T16:18:30","guid":{"rendered":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/?page_id=44"},"modified":"2016-05-04T16:18:30","modified_gmt":"2016-05-04T16:18:30","slug":"tutorial-10","status":"publish","type":"page","link":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/tutorial-10\/","title":{"rendered":"Tutorial 10"},"content":{"rendered":"

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

 <\/p>\n

1\u00a0\u00a0\u00a0\u00a0 Show that the force of attraction between two large ships of mass 50000 tonnes and separated by a distance of 20 m is 417 N. (1 tonne\u00a0 =\u00a0 1000 kg)<\/p>\n

 <\/p>\n

2\u00a0\u00a0\u00a0\u00a0 Calculate the gravitational force of attraction between the proton and the electron in a hydrogen atom.\u00a0 Assume the electron is describing a circular orbit with a radius of\u00a0 5.3 x\u00a010-11<\/sup> m.<\/p>\n

(mass of proton\u00a0 =\u00a0 1.67 x\u00a010-27<\/sup> kg; mass of electron\u00a0 =\u00a0 9.11 x\u00a010-31<\/sup> kg).<\/p>\n

 <\/p>\n

3\u00a0\u00a0\u00a0\u00a0 A satellite, of mass 1500 kg, is moving at constant speed in a circular orbit 160 km above the Earth\u2019s surface.<\/p>\n

(a)\u00a0\u00a0 Calculate the period of rotation of the satellite.<\/p>\n

(b)\u00a0\u00a0 Calculate the total energy of the satellite in this orbit.<\/p>\n

(c)\u00a0\u00a0 Calculate the minimum amount of extra energy required to boost this satellite into a geostationary orbit which is at a distance of 36 000 km above the Earth\u2019s surface.<\/p>\n

 <\/p>\n

4\u00a0\u00a0\u00a0\u00a0 The planet Mars has a mean radius of 3.4 x 106<\/sup> m. The Earth\u2019s mean radius is 6.4 x 106<\/sup> m.\u00a0 The mass of Mars is 0.11 times the mass of the Earth.<\/p>\n

(a)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 How does the mean density of Mars compare with that of the Earth?<\/p>\n

(b)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Calculate the value of \u201cg\u201d on the surface of Mars.<\/p>\n

(c)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Calculate the escape velocity on Mars.<\/p>\n

 <\/p>\n

5\u00a0\u00a0\u00a0\u00a0 Determine the potential energy between the planet Saturn and its rings.<\/p>\n

The mass of Saturn is 5.72 x 1026<\/sup> kg.\u00a0 The rings have a mass of 3.5 x\u00a01018<\/sup> kg and are concentrated at an average distance of 1.1 x 108<\/sup> m from the centre of Saturn.<\/p>\n

 <\/p>\n

6\u00a0\u00a0\u00a0\u00a0 During trial firing of Pioneer Moon rockets, one rocket reached an altitude of 125 000 km.<\/p>\n

Neglecting the effect of the Moon, estimate the velocity with which this rocket struck the atmosphere of the Earth on its return.\u00a0 (Assume that the rocket\u2019s path is entirely radial and that the atmosphere extends to a height of 130 km above the Earth\u2019s surface).<\/p>\n

 <\/p>\n

7\u00a0\u00a0\u00a0\u00a0 (a)\u00a0\u00a0 Sketch the gravitational field pattern between the Earth and Moon.<\/p>\n

(b)\u00a0\u00a0 Gravity only exerts attractive forces.\u00a0 There should therefore be a position between the Earth and Moon where there is no gravitational field – a so-called \u2018null\u2019 point.<\/p>\n

By considering the forces acting on a mass m placed at this point, calculate how far this position is from the centre of the Earth.<\/p>\n

 <\/p>\n

8\u00a0\u00a0\u00a0\u00a0 Mars has two satellites named Phobos and Deimos.\u00a0 Phobos has an orbital radius of 9.4 x 106<\/sup> m and an orbital period of 2.8 x 104<\/sup> s.<\/p>\n

Using Kepler\u2019s third law ( r\u00b3\/T\u00b2 =\u00a0 constant ), calculate the orbital period of Deimos which has an orbital radius of 2.4 x 107<\/sup> m.<\/p>\n

 <\/p>\n

9\u00a0\u00a0\u00a0\u00a0 When the Apollo 11 satellite took the first men to the Moon in 1969 its trajectory was very closely monitored.<\/p>\n

The satellite had a velocity of 5374 ms-1<\/sup> when 26306 km from the centre of the Earth and this had dropped to 3560 ms-1<\/sup> when it was 54368 km from the centre of the Earth.\u00a0 The rocket motors had not<\/strong> been used during this period.<\/p>\n

Calculate the gravitational potential difference between the two points.\u00a0 Remember that the unit of gravitational potential is Jkg-1<\/sup>.<\/p>\n

 <\/p>\n

10\u00a0\u00a0\u00a0Show that an alternative expression for the escape velocity from a planet may be given by: v = \u221a(2gR),\u00a0where g = the planet\u2019s surface gravitational attraction and R = the radius of the planet.<\/p>\n

 <\/p>\n

11\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 The Escape Velocity for the Earth v\u00a0=\u00a0\u221a(2gr),\u00a0or\u00a0\u00a0v =\u00a0\u221a(2GM\/r)<\/p>\n

Using data on the Earth, show that the escape velocity equals\u00a0 1.1 x 104<\/sup> ms-1<\/sup>.<\/p>\n

 <\/p>\n

12\u00a0\u00a0 Show that a satellite orbiting the Earth at a height of 400 km has an orbital period of 93 minutes.\u00a0 Note that a height of 400 km is equal to a radius of\u00a0 R + 400 km.<\/p>\n

 <\/p>\n

13\u00a0\u00a0 (a) \u00a0 A geostationary orbit has a period of approximately 24 hours.\u00a0 Find the orbital radius for a satellite in such an orbit.<\/p>\n

(b)\u00a0\u00a0 Hence find the height of this satellite above the Earth.<\/p>\n

(c)\u00a0\u00a0 Show on a sketch of the Earth the minimum number of geostationary satellites needed for world-wide communication.<\/p>\n","protected":false},"excerpt":{"rendered":"

Gravitation   1\u00a0\u00a0\u00a0\u00a0 Show that the force of attraction between two large ships of mass 50000 tonnes and separated by a distance of 20 m is 417 N. (1 tonne\u00a0 =\u00a0 1000 kg)   2\u00a0\u00a0\u00a0\u00a0 Calculate the gravitational force of attraction between the proton and the electron in a hydrogen atom.\u00a0 Assume the electron is … Continue reading Tutorial 10<\/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-44","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages\/44","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=44"}],"version-history":[{"count":1,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages\/44\/revisions"}],"predecessor-version":[{"id":45,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages\/44\/revisions\/45"}],"wp:attachment":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/media?parent=44"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}