{"id":19,"date":"2016-05-04T13:08:06","date_gmt":"2016-05-04T13:08:06","guid":{"rendered":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/?page_id=19"},"modified":"2016-05-04T15:15:45","modified_gmt":"2016-05-04T15:15:45","slug":"tutorial-5","status":"publish","type":"page","link":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/tutorial-5\/","title":{"rendered":"Tutorial 5"},"content":{"rendered":"

Circular Motion<\/strong><\/p>\n

\u00a0<\/strong><\/p>\n

1\u00a0\u00a0 An Earth satellite is required to be in a circular orbit at a distance of 7.5 x 106<\/sup> m from the centre of the Earth.\u00a0 The central force is due to the gravitational force.\u00a0 The acceleration due to the Earth\u2019s gravity at this point\u00a0 is 7.0 ms-2<\/sup>.<\/p>\n

Find:<\/p>\n

(a)\u00a0\u00a0 the required satellite speed<\/p>\n

(b)\u00a0\u00a0 the period of revolution of the satellite.<\/p>\n

 <\/p>\n

2\u00a0\u00a0 What would be the period of rotation of the Earth about its axis if its speed of rotation increased to such an extent that an object at the equator became \u2018weightless\u2019?<\/p>\n

(Hint:\u00a0\u00a0equate\u00a0mg\u00a0to\u00a0mv\u00b2\/r).<\/p>\n

 <\/p>\n

3\u00a0\u00a0 A sphere of mass 0.20 kg is rotating in a circular path at the end of a string 0.80 m long. The other end of the string is fixed.\u00a0 The period of the motion is 0.25 s.<\/p>\n

 <\/p>\n

(a)\u00a0\u00a0 Calculate the tension in the string, which you may assume to be horizontal.<\/p>\n

(b)\u00a0\u00a0 In practice the string is not horizontal.\u00a0 Explain why this is so.<\/p>\n

(c)\u00a0\u00a0 Draw a force diagram for the sphere. From this calculate the angle the string would make with the horizontal.<\/p>\n

 <\/p>\n

4\u00a0\u00a0The moon takes 27.3 days (2.0 x 106<\/sup> s) to complete one orbit of the Earth.<\/p>\n

The distance between the centres of the Earth and Moon is 4.0 x 108<\/sup> m.<\/p>\n

Calculate the magnitude of the Moon\u2019s acceleration towards the Earth.<\/p>\n

 <\/p>\n

5\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 A ball of mass 2.0 kg is attached to a string 1.6 m long and is made to travel in a vertical circle.\u00a0 The ball passes its highest point with a speed of 5.0 ms-1<\/sup>.<\/p>\n

(a)\u00a0\u00a0\u00a0\u00a0 What is the kinetic energy of the ball at its highest point?<\/p>\n

(b)\u00a0\u00a0\u00a0\u00a0 What is its potential energy when it is at the highest point (with reference to its lowest point)?<\/p>\n

(c)\u00a0\u00a0\u00a0\u00a0 What is its kinetic energy at the lowest point?<\/p>\n

(d)\u00a0\u00a0\u00a0\u00a0 What is its speed at the lowest point?<\/p>\n

(e)\u00a0\u00a0\u00a0\u00a0 What is the tension in the string at the highest and lowest points?<\/p>\n

(f)\u00a0\u00a0\u00a0\u00a0\u00a0 What is the least<\/strong> speed the ball could have at the highest point in order to be able to complete a vertical circle at all?<\/p>\n

 <\/p>\n

6\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 An old humpback bridge has a radius of curvature of 20 m.\u00a0 What is the maximum speed at which a car can pass over this bridge if the car is not to leave the road surface?<\/p>\n

 <\/p>\n

7\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 (a)\u00a0\u00a0\u00a0\u00a0 A pail of water is swinging in a vertical circle of radius 1.2 m, so that the water does not fall out.\u00a0 What is the minimum linear speed required for the pail of water.<\/p>\n

(b)\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 Convert this speed into an angular velocity.<\/p>\n

 <\/p>\n

8\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 An object of mass 0.20 kg is connected by a string to an object of half its mass.\u00a0 The smaller mass is rotating at a radius of 0.15 m on a table which has a frictionless surface.\u00a0 The larger mass is suspended through a hole in the middle of the table.<\/p>\n

Calculate the number of revolutions per minute the smaller mass must make so that the larger mass is stationary.<\/p>\n

 <\/p>\n

 <\/p>\n

Banking of a Track<\/strong><\/p>\n

\u00a0<\/strong><\/p>\n

9\u00a0\u00a0 A circular track of radius 60 m is banked at angle.\u00a0 A car is driven round the track at 20 ms-1<\/sup>.<\/p>\n

(a) \u00a0 Draw a diagram showing the forces acting on the car.<\/p>\n

(b) \u00a0\u00a0 Calculate the angle of banking required so that the car can travel round the track without relying on frictional forces (i.e. no side thrust supplied by friction on the track surface).<\/p>\n

 <\/p>\n

 <\/p>\n

Conical Pendulum<\/strong><\/p>\n

\u00a0<\/strong><\/p>\n

10\u00a0 A small object of mass\u00a0 m\u00a0 <\/strong>revolves in a horizontal circle at constant speed at the end of a string of length 1.2 m.\u00a0 As the object revolves, the string sweeps out the surface of a right circular cone.<\/p>\n

\"Capture\"<\/a><\/p>\n

The cone has semi-angle 30\u00b0.<\/p>\n

Calculate:<\/p>\n

(a) \u00a0 the period of the motion;<\/p>\n

(b)\u00a0\u00a0 the speed of the object.<\/p>\n

 <\/p>\n

[Hint: try resolving the tension in the string into horizontal and vertical components.]<\/p>\n","protected":false},"excerpt":{"rendered":"

Circular Motion \u00a0 1\u00a0\u00a0 An Earth satellite is required to be in a circular orbit at a distance of 7.5 x 106 m from the centre of the Earth.\u00a0 The central force is due to the gravitational force.\u00a0 The acceleration due to the Earth\u2019s gravity at this point\u00a0 is 7.0 ms-2. Find: (a)\u00a0\u00a0 the required … Continue reading Tutorial 5<\/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-19","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages\/19","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=19"}],"version-history":[{"count":3,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages\/19\/revisions"}],"predecessor-version":[{"id":26,"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/pages\/19\/revisions\/26"}],"wp:attachment":[{"href":"https:\/\/blogs.glowscotland.org.uk\/gc\/advancedhigher\/wp-json\/wp\/v2\/media?parent=19"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}