1.1.1 gravitational fields

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Teaching Notes for Unit 9.2 Space Topic of NSW HSC Physics Course

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<ul><li> 1. Topic 9.21.1.1 Gravitational Fields</li></ul> <p> 2. Mass, Weight and Gravity Remember that mass is a measureof the amount of substance in anobject. Weight is the force of gravity pullingdown on the object's mass. This is expressed as the formula: W=mg What are the units of each term in thisequation? 3. The Simple Pendulum A simple pendulum consists of amass (called a bob) on a light (nomass) string. The weight of the object causes itto try to return to the lowestposition when it is disturbed. The time taken to make onecomplete swing (Left to right toLeft) is called the TIME PERIOD, T. 4. Investigating the Simple Pendulum Set up a simple pendulum asshown. Investigate the effect of the massof the bob, m, on the time period,T, of the pendulum. Identify what variables need to becontrolled. How can you make your timemeasurement as precise as possible? Remember keep the angle of swingsmall for the best results! What does a graph of T against mshow?mgl 5. Investigating the Simple Pendulum Now investigate the effect of thependulum length, l, on the period,T. Identify what variables need to becontrolled. How should you measure the lengthof the pendulum? What does a graph of T against lshow? What does a graph of T2 against lshow? 6. Measuring gThe time period of a simple pendulum isgiven by the equation:T = 2p lgThis can be written as:22 = 4plgTCalculate g from the gradient of your T2versus l graph. 7. Gravitational Fields Gravity can act over large distances,even through space. To explain this we use the idea of a field. All objects with mass create their owngravitational field. This field extends to infinity and causesother objects to be attracted towards themass. This is similar to the electromagnetic fields. The gravitational field is much weaker thanthe other fields. 8. Gravitational Fields 9. Uniform Gravitational Fields Very close to an object thegravitational field can beconsidered to be uniform. g has a constant value Further away the gravitational fieldbecomes weaker. g decreases with distance. 10. Gravitational Potential Energy Close to Earth, where g is constant, we knowthat the energy gained by an object when it islifted equals the work done on it. EG = Work Done = Force x DistanceEG = Wh = mgh How much GPE is gained when a 65kg objectis raised through 7.0m close to the Earth'ssurface? 11. Gravitational Potential Energy Normally, the Earth's surface is definedto have a GPE of 0J. In space, a new zero must be definedwhich is the same for everyone. A point an infinite distance from Earth isdefined as having zero GPE. Gravitational Potential Energy is ameasure of the work done to move anobject from infinity to a point within thegravitational field 12. Gravitational Potential Energy If a point an infinite distance fromEarth has zero GPE AND lifting anobject away from the Earthincreases its GPE then GPE MUSTALWAYS BE NEGATIVE!! i.e. lifting an object makes its GPEless negative! 13. Gravitational Potential Energy GPE is given by the formula:EG=G MmR Where G is the Universal Gravitational Constant=6.67x10-11 m3kg-1s-2 What do the other symbols mean? 14. Gravitational Potential Energy Calculate the GPE of a 200kgsatellite when in low Earth orbit125km above the Earth's surface. What is the GPE of a 400kgsatellite in a geostationary orbit36,000km above the Earth'ssurface? mEarth=5.98x1024 kg rEarth=6.38x106 m 15. Gravitational Field Strength Equating our universal equation for GPEand our close to Earth equation gives onthe Earth's surface (radius R):mg h= G MmrD -mg R = G Mm( )- -g = G M20RR- The acceleration due to gravity is notconstant! It falls off with r2. Notice that g is a vector and that the sign indicates attraction. 16. Gravitational Field Strength 17. Gravitational Field Strength Visit www.nineplanets.org Record values for the mass anddiameter of each of the 8 majorplanets. Create a table or use aspreadsheet to calculate values ofg for each planet. g=6.67E-11*mass/(radius^2) 18. Homework Read pages 3-4 of Keep It SimpleScience Complete worksheet on page 5. </p>

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