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Space

HSC Core Topic 9.2. Space. Part 1. Syllabus - Space 9.2 1. The Earth’s Gravitational Field. 1. The Earth has a gravitational field that exerts a force on objects both on it and around it. Students learn to : define weight as the force on an

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Space

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  1. HSC Core Topic 9.2 Space Part 1

  2. Syllabus- Space 9.2 1. The Earth’s Gravitational Field 1. The Earth has a gravitational field that exerts a force on objects both on it and around it • Students learn to: • define weight as the force on an object due to a gravitational field • explain that a change in • gravitational potential energy is • related to work done • define gravitational potential energy as the work done to move an object from a very large distance away to a point in a gravitational field • Students: •  perform an investigation and gather • information to determine a value for • acceleration due to gravity using • pendulum motion or computer assisted • technology and identify reason for • possible variations from the value 9.8ms-2 •  gather secondary information to predict • the value of acceleration due to gravity • on other planets •  analyse information using the expression • F =mgto determine the weight force for • a body on other planets

  3. HSC Core Topic 9.2 • Quiz • What is a force? Name the SI unit used to measure force. • What are the possible effects of a force on an object? • What is mass? Name the SI unit used to measure mass. • What is weight? Name the SI unit used to measure weight.

  4. Defining (Mass and) Weight Mass is a measure of the amount of matter in an object • The mass of an object • The mass of an object • The standard kilogram kept in Paris is the only standard not based on a reproducible phenomenon. Properties does not change is measured in kilograms (kg) • define weight as the force on an object due to a gravitational field

  5. Defining (Mass and) Weight A field is a region where something experiences a force The direction of the field is always towards the centre Field lines show the direction of force A mass within a gravitational field experiences a force called weight gravity This force is produced by the effect of on the object • define weight as the force on an object due to a gravitational field

  6. Defining (Mass and) Weight What is the difference between mass and weight? The weight of an object is the force produced by the effect of gravity on the object while mass is the amount of matter

  7. Data - Comparing the Earth and the Moon

  8. Weight and Force What is the weight of a person with a mass 65.0 kg a) on Earth b) on the moon

  9. Weight and Force The gravitational field of the Earth is not uniform... … unless just a small region of the total field is considered uniform field Force of gravity In studying projectile motion near the Earth we assume the Earth is flat! mass Force of gravity mass

  10. Gravity Both graphs show the same force of gravity on the Earth’s surface. However over large distances the force of gravity reduces

  11. Weight and Force All masses fall at the same rate within a gravitational field. Galileo demonstrated this by dropping different objects from the tower of Pisa. However this is a difficult thing to prove because:

  12. Gravity g

  13. Gravitational Force Observing an apple falling inspired Sir Isaac Newton to develop the law of universal Gravitational attraction

  14. Gravitational Force Newton's Law of Universal Gravitational describes the force that exists between all objects. G = 6.67  10-11 Nm2kg-2 M, m = masses (kg) r = distance between centres of objects (m) FG = GMm r2

  15. Gravitational Force Derivation of the value of Gravity

  16. Gravitational Force Eg.1 The moon’s mass is 7.35  1022 kg. Its diameter is 3467 km. Calculate its gravitational acceleration .

  17. Gravitational Force Data - Comparing the Earth and the Moon

  18. Work and energy are measured in joules (J) • Work is done by a force acting on an object causing it tomove Work and Gravitational Potential Energy • Work is done in raising an object • against the force of gravity • Work = force x distance • W = Fh • = mgh (joules) • The energy used to lift an object against the force of gravity increases the gravitational potential energy of the object • explain that a change in gravitational potential energy is related to work done • explain that a change in gravitational potential energy is related to work done

  19. The Law of Conservation of Energy “Energy cannot be created or destroyed but only changed from one form to another.” Keep this law in mind throughout the physics course. It is fundamental and an understanding of its significance will help to make sense of much physics.

  20. Gravitational Potential Energy • The GPE of an object relative to the Earth’s surface is calculated using the expression • W = F s • Ep =  mgh • In which Ep is the GPE in joules (J) • m is the mass in kilograms (kg) • h is the height above the Earth’s surface in • metres (m)

  21. Gravitational Potential Energy Estimate the energy you gain by walking up the steps at Wollongong station. Ep = mgh = 65 x 9.8 x 9 = 6000 joules = 6 kJ

  22. Gravitational Potential Energy On the Earth we choose ground level as our zero point i.e. where EP = 0 Point X Work done = F s = mgh On a larger planetary scale the force of attraction between a planet and an object will drop to zero only at infinity. (or some distance very far away) There is a strange side effect then on our choice of zero level

  23. Gravitational Potential Energy Work must be done to move a mass against a gravitational field Point X EP at surface < EP at X < E at ∞ = 0 by our definition Therefore EP at infinity > EP at point X but EP at infinity = 0 so that EP at point X < 0 that means E at point X must have a NEGATIVE VALUE !

  24. Gravitational Potential Energy Gravitational potential at any point a radial distance r from a mass is defined as the work done in moving a unit mass (1 kg in the SI system) from that point to a point an infinite distance away. The value of the gravitational potential energy of a mass m2 can be calculated from the equation Ep is the GPE in joules (J) G is the Universal Gravitational Constant (G = 6.67 x 10–11 Nm2kg–2) m1 is the mass of the Earth (5.98 x 1024 kg) m2 is the mass in kilograms (kg) r is the distance from the Earth’s centre in metres (6.373 x 106 m)

  25. Gravitational Potential Energy Energy transformations occur when an object’s position changes in a gravitational field. Explain how a change in gravitational energy is related to the work done: This energy is called ‘gravitational potential energy’ symbol E and units joules (J). It is the energy of a mass due to its position within a gravitational field. If an object increases its gravitational energy it must be provided by an external force that is lifting it. The work done by this force equals its gain in energy.

  26. Gravitational Potential Energy Practice Question The space shuttle, in orbit at 500 km, is to release a satellite of 600 kg to be put in a geostationary orbit (35 850 km). Compare the change in potential energy of the satellite in the two orbits.

  27. Gravitational Potential Energy Using the equation A satellite with a mass of 600 kg is to be put into geostationary orbit after release from the cargo bay of the space shuttle. Essentially this means the satellite has to be lifted from an altitude of 500 km to one of 35850 km, above the equator. This process requires energy, which is supplied by small rocket motors attached to the satellite. Question What does the equation above tell us about the energy of the satellite in the two orbits?

  28. Gravitational Potential Energy Using the above equation to calculate the potential energy of the satellite in the two orbits... At 500 km: Ep = = – 3.475 x 1010 J At 35 850 km E p = = – 5.66x 109 J

  29. Ep = –3.475 x 1010 J Ep = –5.66 x 109 J Gravitational Potential Energy Using the above equation to calculate the potential energy of the satellite in the two orbits... At 500 km: Ep = –3.475 x 1010 J At 35850 km: Ep = –5.66 x 109 J The equation produces the result that the magnitude of the potential energy at 500 km is greater than the magnitude of the potential energy at 35850 km. This is contradictory to the result obtained from using the equation Ep = mgh for the calculation. What is the source of this apparent contradiction?

  30. Gravitational Potential Energy Important considerations… • Potential energy is not an absolute quantity. • Potential energy is always calculated relative to some reference point. • For objects near the surface of the Earth, the Earth’s surface is usually that point. • The equation Ep = mgh is an approximation of the difference in potential of an object at two positions separated by a vertical distance ‘h’. • It is an approximation because the equation is derived based on the assumption that the gravitational field is uniform, which would only really be the case if the Earth was flat. • Since in applying the formula Ep = mgh, one of the positions is usually the Earth’s surface, ‘h’ is simply the height above the Earth’s surface. • When applying this equation, it must be remembered that ‘h’ is the really the difference between the radius of the Earth and the distance of the object from the centre of the Earth.

  31. Gravitational Potential Energy Using the equation… Question What does the equation above tell us about the energy of the satellite in the two orbits? The change in potential energy is the final Ep-initial Ep ∆Ep = Ep final – Ep initial = (–5.66 x 109) – (–3.475 x 1010 J) = 2.909 x 1010 J Conclusion The equation tells us that it takes 29 gigajoules of energy to lift a 600 kg satellite from low earth orbit to its geostationary orbit!

  32. BOS Syllabus KEY TERMS • first-hand • secondary information • initial / final velocity • height • range • time of flight • data loggers • computer analysis • perform a first-hand investigation, gather secondary information and analyse data to describe factors, such as initial and final velocity, maximum height reached, range, time of flight of a projectile, and quantitatively calculate each for a range of situations by using simulations, data loggers and computer analysis  perform a first-hand investigation, gather secondary information and analyse data to describe factors, such as initial and final velocity, maximum height reached, range, time of flight of a projectile, and quantitatively calculate each for a range of situations by using simulations, data loggers and computer analysis

  33. Motion of a Simple Pendulum Compare the period of a simple pendulum with a length of 1.0 m on the Earth and on the Moon Substitution into the equation Animation IP model: Pendulum2m.ip

  34. Determining ‘g’ Using a Simple Pendulum The acceleration due to gravity can be calculated using the equation for the period of a simple pendulum. The equation can be rearranged ===>

  35. 9.2 Space: 2. A successful rocket launch 2. Many factors have to be taken into account to achieve a successful rocket launch, maintain a stable orbit and return to Earth Students learn to: • describe the trajectory of an object undergoing projectile motion within the Earth’s gravitational field in terms of horizontal and vertical components • describe Galileo’s analysis of projectile motion • explain the concept of escape velocity in terms of the: • gravitational constant • mass and radius of the planet • outline Newton‘s concept of escape velocity • identify why the term ‘g forces’ is used to explain the forces acting on an astronaut during launch • discuss the effect of the Earth‘s orbital motion and its rotational motion on the launch of a rocket • analyse the changing acceleration of a rocket during launch in terms of the: • Law of Conservation of Momentum • forces experienced by astronauts • Students: • solve problems and analyse information to calculate the actual velocity of a projectile from its horizontal and vertical components using: • perform a first-hand investigation, gather information and analyse data to calculate initial and final velocity, maximum height reached, range, time of flight of a projectile, for a range of situations by using simulations, data loggers and computer analysis

  36. 9.2 Space: 2. A successful rocket launch • Students: • identify data sources, gather analyse and present information on the contribution of one of the following to the development of space exploration: Tsiolkovsky, Oberth, Goddard, Esnault-Pelterie, O‘Neill or von Braun • solve problems and analyse information to calculate centripetal force acting on a satellite undergoing uniform circular motion about the Earth using: • solve problems and analyse information using: Students learn to: • analyse the forces involved in uniform circular motion for a range of objects, including satellites orbiting the Earth • compare qualitatively low Earth and geo-stationary orbits • define the term orbital velocity and the quantitative and qualitative relationship between orbital velocity, the gravitational constant, mass of the central body, mass of the satellite and the radius of the orbit using Kepler's Law of Periods • account for the orbital decay of satellites in low Earth orbit • discuss issues associated with safe re-entry into the Earth’s atmosphere and landing on the Earth’s surface • identify that there is an optimum angle for re-entry for a manned spacecraft into the Earth’s atmosphere and the consequences of failing to achieve this angle

  37. A Successful Rocket Launch v = u + at s = ut + ½at2 v2 = u2 + 2as Equations of Motion u = initial speed (ms–1 ) v = final velocity (ms–1 ) t = time (seconds) a = acceleration ms– 2 s = displacement (m)

  38. Equations of Motion Eg. A car accelerates from a standing start to 60 kmh–1 in 15.0 s. Find a) its acceleration b) the distance travelled after 15.0 s v = u + at s = ut + ½at2 v2 = u2 + 2as v = u + at s = ut + ½at2 v2 = u2 + 2as

  39. Equations of Motion Eg. 2 A rocket decelerates constantly from a landing speed of 1200 kmh–1 to rest using 800 m of runway. Find the time taken to come to rest. v = u + at s = ut + ½at2 v2 = u2 + 2as

  40. Equations of Motion Eg. 1 Mitchell drops his Physics book from the top of a building and it hits the ground 5 seconds later. Find: a) the height of the building b) the speed of the book on impact

  41. Equations of Motion Eg. 2 A ball is thrown upwards and travels to a height of 20 metres. Find: a) its initial speed b) the time to reach there c) the total time of flight d) its speed on impact v = u + at s = ut + ½at2 v2 = u2 + 2as v = u + at s = ut + ½at2 v2 = u2 + 2as

  42. Equations of Motion Problems 1. A top sprinter has a velocity of 11.13 ms– 1 within 3.15 s of the start. Assuming the acceleration is uniform find its magnitude. 2. A car has a uniform acceleration of 2.30 ms– 2 . What distance will he need to travel in order to attain a velocity of 21 ms– 1 if he started from rest. 3. A car covers 400 m from a standing start in 20 s. Find its acceleration. 4. Sam drops a coin into a well and hears it plop after 2.50 s. Calculate: a) the depth of the well b) the speed of the coin before just before impact.

  43. Equations of Motion 5. A stone is thrown upwards. It is in the air for 10.0 s. a) Calculate the velocity with which it starts. b) Calculate its maximum height. c) Calculate its final velocity, just before it hits the ground. 6. A space shuttle is flying parallel to the ground, with a velocity of 750 kmh– 1, and at an altitude of 4.90 km. A lump of lead drops off from the shuttle. a) How long before it reaches the ground? b) What is the speed of the lump just before impact? 7. A balloon is ascending with a constant speed of 4.9 ms– 1. and drops a sand bag at an elevation of 98 m. a) How long will it take the sand bag to hit the ground? b) What will be the speed of the sand bag on impact?

  44. Projectile Motion

  45. Projectile Motion Its shape is parabolic trajectory

  46. Projectile Motion KEY TERMS time Initial velocity u height range

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