Contents Page SECTION 1 - SIGNALS FROM SPACE 2 Distances in Space 2 Ray Diagrams 3 SECTION 2 - SPACE TRAVEL 5 Weight 5 Weight, Thrust and Acceleration 8 Projectiles 12 Re - Entry 16 SPACE PHYSICS REVISION QUESTIONS 19 General Level 19 Credit Level 20 APPENDIX (I) DATA SHEET 24 APPENDIX (II) ANSWERS TO NUMERICAL PROBLEMS 25 GMV Science. Photocopiable only by the purchasing institution. 1
Section 1 - Signals from Space Distances in Space In this section you can use the following equation: where: v = average speed in meters per second (m/s) d = distance travelled in metres (m) t = time taken in seconds (s). Helpful Hint Because distances in space are so large, astronomers use light years to measure distance. One light year is the distance light will travel in one year. Light travels at 3 x10 8 m/s. 1. How far is a light year? v = d t 2. The star Vega is 27 light years from earth. How far away is Vega in metres? 3. The star Pollux is 3 78 x10 17 m from earth. How far is this in light years? 4. The star Beta Centauri is 300 light years from earth. How long does it take light to travel from this star to the earth? 5. An astronomer on Earth views the planet Pluto through a telescope. Pluto is 5 763 x 10 6 km from earth. How long did it take for the light from Pluto to reach the telescope? 6. Our galaxy, the Milky Way, is approximately 100 000 light years in diameter. How wide is our galaxy in kilometres? 7. The nearest star to our solar system is Proxima Centuri which is 3 99 x10 16 m away. How far is this in light years? 8. Andromeda (M31) is the nearest galaxy to the Milky Way and can just be seen with the naked eye. Andromeda is 2 1 x 10 22 m away from the Milky Way. How long does it take for light from Andromeda to reach our galaxy? 9. The Sun is the nearest star to the planet Earth. It takes light 8 3 minutes to reach us from the Sun. Use this information to find out the distance from the Earth to the Sun in kilometres? 10. Sir William Herschel, an amateur astronomer, discovered the planet Uranus in March 1781. Uranus is 2 871 x 10 6 km away from the sun. How long does it take for sunlight to reach Uranus? GMV Science. Photocopiable only by the purchasing institution. 2
Ray Diagrams Helpful Hint You may have noticed that all the images produced by convex lenses in Health Physics were on the opposite side of the lens from the object. These images are called real images. Sometimes, however, an image cannot be formed in this way because the rays spread out after passing through the lens. In this case we must extend the ray lines backwards until they meet. Example image f object f lens This type of image, which is formed on the same side of the lens as the object is called a virtual image. Remember the rules for drawing ray diagrams: 1. a ray from the tip of the object parallel to the axis passes through the focal point of the lens. 2. a ray from the tip of the object to middle of the lens continues through the lens in the same direction. 1. An object is placed 3 cm from a lens which has a focal length of 2 cm. The object is 1 cm high. Using a suitable scale, copy and complete the ray diagram below. (You may find it useful to use graph paper!) 1 cm high lens 3 cm 2 cm (a) How far from the lens is the image produced? (b) Is the image inverted or upright? (c) Is the image real or virtual? GMV Science. Photocopiable only by the purchasing institution. 3
2. A magnifying glass produces an image which is described as virtual, magnified and upright. A 1 cm high object is placed 2 cm from a magnifying lens whose focal length is 3 cm. (a) Copy and complete the ray diagram below to show how the image is formed. 1 cm high lens 2 cm 3 cm (b) Explain why the image is described as virtual, magnified and upright. 3. A 1 cm high object is placed 5 cm from a lens which has a focal length of 2 cm. (a) Use a ray diagram to find out what kind of image is formed (i.e. real or virtual? magnified, diminished or same size? inverted or upright?) (b) The same object is moved to a distance of 4 cm from the lens. Describe the image which is now formed. (You will need to draw a new ray diagram!) (c) The object is again moved - this time to a distance of 1 5 cm from the lens. Describe what happens to the image now. 4. A magnifying glass, which has a focal length of 1 cm, is used to examine some small objects. Each object is placed 0 5 cm from the lens. By drawing ray diagrams, to an appropriate scale, find out the size of the image produced by each of the following objects. (a) A printed letter which is 4 mm high. (b) A 2 mm grain of rice. (c) A 5 mm pearl. 5. A man creates an image of a fuse using an 8 cm lens. The fuse is 2 cm high and is positioned at a distance of 4 8 cm from the lens. (a) Draw a ray diagram in order to find out the height of the image produced. (b) How far was this image from the lens? GMV Science. Photocopiable only by the purchasing institution. 4
Section 2 - Space Travel Weight In this section you can use the equation: weight = mass x gravitational field strength also written as W = mg where W = weight in Newtons (N) m = mass in kilograms (kg) g = gravitational field strength in Newtons per kilogram (N/kg) Helpful Hint On Earth g = 10 N/kg but it varies from planet to planet. In questions about weight on other planets you must use these values by referring to the data sheet on page 24 1. Find the missing values in the following table. Mass (kg) Gravitational field strength (N/kg) Weight (N) (a) 12 10 (b) 279 4 (c) 0 56 5 6 (d) 7 89 78 9 (e) 12 700 (f) 10 58 2. Calculate the weight of a 70 kg man on Earth. 3. If a moon rock has a weight of 4 6 N, what is its mass? 4. An objects weight depends on the strength of the gravitational field around it. A scientist records the weight of a 3 kg rock on each planet and records the information GMV Science. Photocopiable only by the purchasing institution. 5
in the table overleaf. GMV Science. Photocopiable only by the purchasing institution. 6
Planet Weight(N) Earth 30 Jupiter 78 Mars 12 Mercury 12 Neptune 36 Saturn 33 Venus 27 Uranus 35 1 Pluto 12 6 Use the results from the table to work out the value of the gravitational field strength on each planet ( you can check your answers against the data sheet on page 24). 5. Using your results to question 4, state which planet(s) have: (a) the strongest gravitational field strength (b) the weakest gravitational field strength (c) a gravitational field strength nearest to that on Earth (d) a gravitational field strength three times as strong as that on Mercury. 6. Which is heavier, a 2 kg stone on Neptune or a 0 9 kg rock on Jupiter? 7. How much lighter does a 65 kg woman seem on the moon, where g = 1 6 N/kg, than on Earth? 8. Find the weight of a satellite booster on Mars if it weighs 24 N on the moon. 9. What is the difference in mass between a 40 N weight on Venus and a 104 N weight on Jupiter? 10. A rock weighs approximately two and a half times its weight on Earth somewhere in our solar system. Where is it likely to be? GMV Science. Photocopiable only by the purchasing institution. 7
Weight, Thrust and Acceleration In this section you can use the equation: unbalanced force = mass x acceleration also written as F = ma where F = unbalanced force in newtons (N) m = mass in kilograms (kg) a = acceleration in metres per second per second (m/s 2 ). Helpful Hint When a spacecraft is in space the only force acting on it is its engine thrust. engine thrust (F) 1. Find the missing values in the table. Force (N) Mass (kg) Acceleration (m/s 2 ) (a) 700 000 2 0 (b) 45 000 0 9 (c) 1 000 0 05 (d) 3 600 000 0 01 (e) 10 000 80 000 (f) 2 600 000 2 000 000 2. The engine of a space shuttle can produce a thrust of 600 000 N. The mass of the shuttle is 8 x 10 5 kg. Calculate the acceleration of the shuttle in space. GMV Science. Photocopiable only by the purchasing institution. 8
3. What engine thrust must be produced by a rocket of mass 3 x 10 6 kg in order to produce an acceleration of 1 4 m/s 2 in space? 4. The maximum engine thrust of a spacecraft is 2 4 x 10 7 N and this produces an acceleration of 12 m/s 2 in space. What is the mass of the spacecraft? 5. An engine force of 160 kn is used to slow down a shuttle in space. If the mass of the shuttle is 120 000 kg what is its rate of deceleration? Helpful Hint To find the acceleration, a, of an object during a vertical take-off you will need to calculate the unbalanced force acting on the object first. Example thrust 1st. Unbalanced force = thrust - weight 2nd. a = F m (where F = unbalanced force) weight 6. Use the three stages outlined in the example above to find the missing values in the following table. Assume that each mass is in the Earth s gravitational field. Mass (kg) Weight (N) Thrust (N) Unbalanced force (N) Acceleration (m/s 2 ) (a) 3 30 60 (b) 2 000 2 000 21 000 (c) 1 500 20 000 (d) 50 000 550 000 (e) 70 000 840 000 (f) 76 000 896 800 GMV Science. Photocopiable only by the purchasing institution. 9
7. A water rocket has a mass of 0 8 kg and is launched in a school playground with an initial upwards thrust of 12 N. (a) What is the weight of the water rocket in the playground? (b) What is the initial acceleration of the rocket in the playground? (c) If this water rocket were launched from the moon, what would be its initial acceleration? (Remember to find the new weight first!) 8. A rocket is launched from Earth with an initial acceleration of 2 5 m/s 2. The mass of the rocket is 1 600 000 kg. (a) Calculate the unbalanced force acting on the rocket during its launch. (b) What is the weight of the rocket? (c) Calculate the engine thrust of the rocket. (d) What engine thrust would be required to launch this rocket from the moon with the same acceleration? 9. Calculate the acceleration of the following objects. (a) A model rocket of mass 30 kg being launched from Earth with an engine thrust of 800 N. (b) A satellite in space whose mass is 1 800 kg and whose engine force is 4 68 kn. (c) A 100 000 kg shuttle travelling at 50 m/s in space. (d) A toy rocket of mass 1 5 kg whose engine stopped while the rocket was in mid air. (e) A spaceship of mass 4 x 10 7 kg lifting off from Saturn with an engine thrust of 9 x 10 8 N. GMV Science. Photocopiable only by the purchasing institution. 10
(f) A rocket of mass 2 2 x 10 6 kg being launched from Neptune with an engine thrust of 4 4 x 10 7 N. 10. A space shuttle has a weight of 1 8 x 10 7 N on Earth. Its engines produce a thrust of 2 7 x 10 6 N during part of its journey through space. (You will need to refer to the data sheet on page 24 for parts of this question.) (a) Calculate the mass of the shuttle. (b) What is the acceleration of the shuttle in space while its engine thrust is 2 7 x 10 6 N? (c) Could the shuttle have been launched from Earth with this engine thrust of 2 7 x10 6 N? Explain your answer. (d) The engine thrust was 2 7 x 10 7 N during the launch from Earth. What was the acceleration of the shuttle during its launch? (e) If a similar shuttle was launched from Venus with an engine thrust of 2 7 x 10 7 N, what would be the acceleration of this shuttle during lift off? (f) What engine thrust would be required in order to launch this shuttle from Jupiter with an acceleration of 5 m/s 2? GMV Science. Photocopiable only by the purchasing institution. 11
Projectiles Helpful Hint In this section you can make use of the fact that any projectile path can be split into separate parts - horizontal and vertical. To solve any projectile problem it is necessary to use the formula which applies to each of these directions. Horizontally Velocity is constant ( a = 0 m/s 2 ) v = d t where v = average horizontal velocity in metres per second (m/s) d = horizontal distance travelled in metres (m) t = time taken in seconds (s). Vertically Acceleration due to gravity a = v - u t where a = acceleration due to gravity in metres per second per second (m/s 2 ) u = initial vertical velocity in metres per second (m/s) v = final vertical velocity in metres per second (m/s) t = time taken in seconds (s). To calculate the vertical distance travelled during any projectile journey you must draw a speed time graph for the journey and use: distance travelled = area under speed time graph. 1. A stone is kicked horizontally at 20 m/s from a cliff top and lands in the water below 2 seconds later. 20 m/s Calculate : (a) the horizontal distance travelled by the stone (b) the final vertical velocity (c) the vertical height through which the stone drops. GMV Science. Photocopiable only by the purchasing institution. 12
2. A parcel is dropped from a plane and follows a projectile path as shown below. The horizontal velocity of the plane is 100 m/s and the parcel takes 12 seconds to reach the ground. 100 m/s Calculate : (a) the horizontal distance travelled by the parcel (b) the final vertical velocity of the parcel as it hits the ground (c) the height from which the parcel was dropped. 3. Sand bags are released from an air balloon while it is at a fixed height. The bags follow a projectile path because of strong winds. 30 m/s The bags have an initial horizontal velocity of 30 m/s and land on the ground 10 seconds later. Calculate: (a) the horizontal distance travelled by the sand bags (b) their final vertical velocity. 4. A satellite is launched during a practice simulation. The satellite is given a horizontal velocity of 400 km/s and crashes 200 seconds later. practise launch pad Calculate : (a) the horizontal distance travelled by the satellite (b) the final vertical velocity of the satellite (c) the height from which the satellite was launched. 400 km/s GMV Science. Photocopiable only by the purchasing institution. 13
5. An archer fires an arrow and aims to hit a target 50 metres away. The arrow is launched with a horizontal velocity of 100 m/s. 100 m/s (a) What is the time of flight of the arrow? (b) Calculate the final vertical velocity of the arrow. (c) By how much does the arrow miss the target? 6. A golfer strikes a golf ball and it follows a projectile path as shown below. (a) What is the vertical velocity of the ball at its maximum height? (b) What is the horizontal component of the velocity if the ball takes 4 seconds to travel 400 metres? 7. While on the moon an astronaut throws a rock upwards and at an angle. The path of the rock is shown below. (a) What is the vertical velocity of the rock at its maximum height? (b) How long does the rock take to reach its maximum height if it has an initial vertical velocity of 20 m/s? (Remember! On the moon a = 1 6 m/s 2 ) GMV Science. Photocopiable only by the purchasing institution. 14
8. Part of the space flight of a shuttle is represented in the velocity time graphs below. (a) Horizontal motion (b) Vertical motion 90 speed 40 speed in m/s in m/s 30 time in seconds 30 time in seconds Use the graphs to find out how far the shuttle travels both horizontally and vertically in the 30 second journey. 9. During take off from Mars one of the boosters on a rocket fails causing the rocket to follow a projectile path rather than a vertical one. The speed time graphs for a 20 second interval immediately after the booster failed are shown below. (a) Horizontal motion (b) Vertical motion speed speed in m/s in m/s 10 15 20 time in seconds 20 time in seconds Use the graphs to calculate: (a) the horizontal distance travelled during take off (b) the deceleration in the vertical direction during the first 20 seconds (c) the vertical distance travelled. 10. A stunt motor cyclist tries to beat the record for riding over double decker buses. He leaves the start position with a horizontal velocity of 35 m/s and lands 2 4 seconds later. Calculate : (a) the horizontal distance travelled by the cyclist (b) the final vertical velocity of the motor cycle as it touches the ground (c) the height of the platform. GMV Science. Photocopiable only by the purchasing institution. 15
Re - Entry In this section you can use all of the following equations: E k = 1mv 2 2 E h = cm T E w = F x d where E k = kinetic energy (J) E h = heat energy (J) E w = work done (J) m = mass (kg) v = speed (m/s) c = specific heat capacity (J / kg o C) T = change in temperature ( o C) F = force (N) d = distance (m). Helpful Hint Energy can not be created or destroyed. It can be changed from one form into another. When an object re-enters the Earth s atmosphere it heats up. Some or all of its kinetic energy changes to heat energy as work is done against friction. The shuttle has heat resistant tiles covering its body to stop it burning up as it re-enters the atmosphere. heat resistant tiles In order to stop the shuttle when it touches down, work must be done by friction forces in the brakes to change all its kinetic energy into heat energy. 1. A small piece of metal of mass 2 kg falls from a satellite and re-enters the Earth s atmosphere at a speed of 4 000 m/s. If all its kinetic energy changes to heat calculate how much heat is produced. 2. How much work must be done by the brakes on a shuttle of mass 2 x10 6 kg to bring it to rest if it lands with a touch down speed of 90 m/s? GMV Science. Photocopiable only by the purchasing institution. 16
3. The space shuttle Columbia re-entered the Earth s atmosphere at a speed of 8 000 m/s and was slowed down by friction to a speed of 200 m/s. The shuttle has a mass of 2 x10 6 kg. (a) How much kinetic energy did the shuttle lose? (b) How much heat energy was produced during this process? 4. A shooting star is a meteoroid that enters the Earth s atmosphere and is heated by the force of friction which causes it to glow. A certain meteoroid has a mass of 30 kg and enters the atmosphere at a speed of 4 000 m/s. Its specific heat capacity is 600 J /kg o C. (a) Calculate the heat energy produced when all the meteoroids kinetic energy is converted to heat. (b) Calculate the rise in temperature of the meteoroid as it re-enters the atmosphere. 5. A small spy satellite of mass 70 kg is constructed from a metal alloy of specific heat capacity 320 J /kg o C. The satellite has a short lifetime of two weeks before it re-enters the Earth s atmosphere at a speed of 5 000 m/s. (a) Calculate how much heat energy is produced when all the satellites kinetic energy changes to heat energy. (b) Calculate the theoretical rise in temperature of the satellite. 6. The nose section of the shuttle is covered with 250 kg of heat resistant tiles which experience a rise in temperature of 1 400 o C during the shuttle s journey back through the Earth s atmosphere. The shuttle is slowed from 10 000 m/s to 100 m/s during this part of the journey. United Sta tes shuttle enters Earth s atmosphere v = 10 000 m/s United St ate s v = 100 m/s (a) How much kinetic energy does the nose of the shuttle lose? (b) How much heat energy is produced at the nose during re-entry? GMV Science. Photocopiable only by the purchasing institution. 17
(c) Calculate the specific heat capacity of the material used to make the nose tiles. 7. A multistage rocket jettisons its third stage fuel tank when it is empty. The fuel tank is made of aluminium and has a mass of 4 000 kg. ( specific heat capacity of aluminium is 900 J/kg o C) (a) Calculate the kinetic energy lost by the fuel tank as it slows down from 5 000 m/s to 1 000 m/s during its journey through the atmosphere. (b) How much heat energy is produced? (c) Calculate the rise in temperature of the fuel tank. 8. The command module of an Apollo rocket returns to Earth at a speed of 30 km/h. During its journey through the atmosphere it is slowed to a speed of 10 km/h. The mass of the module is 2 000 kg. (a) Calculate the loss in kinetic energy of the command module. (b) How much work is done by the frictional forces which slowed it down? 9. Re-entry for a certain shuttle begins 75 miles above the Earth s surface at a speed of 10 km/s. It is slowed to a speed of 100 m/s by frictional forces during which time it has covered a distance of 4 x10 7 m. The mass of the shuttle and its payload is 2 4 x 10 6 kg. (a) Calculate the loss in kinetic energy of the shuttle. (b) How much work is done by friction? (c) Calculate the average size of the frictional forces exerted by the atmosphere on the shuttle as it slows down. 10. At touch down a shuttle is travelling at 90 m/s. The brakes apply an average force of 4 x 10 6 N in total to bring the shuttle to a stand still. The mass of the shuttle is 2 x 10 6 kg. (a) How much kinetic energy does the shuttle have at touch down? (b) How much work must be done by the brakes to stop the shuttle? (c) Calculate the length of runway required to stop the shuttle. GMV Science. Photocopiable only by the purchasing institution. 18
Space Physics Revision Questions General Level Clues down 1. Jupiter--- Mars are planets. 2. ------- Centauri is the nearest star outwith our Solar System. 3. The closest star to Earth. 4. A useful object for star gazing. 5. We see these because of the different frequencies in white light. 7. The moon is a natural satellite of this planet. 8. This keeps our feet on the ground! 10. This large lens in a telescope creates the image of a star. 14. This quantity is measured in kilograms and does not change from planet to planet. 15. 700 nm is the wavelength of this light. 16. The Universe is the name given to --- matter and space. Clues across 2. This object can separate white light into its various colours. 4. We could describe ourselves as this compared to the Universe. 6. The number of stars in our Solar System. 8. A cluster of stars. 9. The sun will not keep burning for ----. 11. Paths for planets around the Sun. 12. Here the gravitational field strength is virtually zero. 13. This fictional character was not from Earth.! 17. Obtained by mixing red, green and blue. 18. The Sun and its nine planets. GMV Science. Photocopiable only by the purchasing institution. 19
Credit Level 1. Stars and galaxies emit radiation at many different frequencies in the electromagnetic spectrum. By collecting these signals astronomers can learn a lot about our universe. (a) Copy and complete the diagram of the electromagnetic spectrum shown below. Gamma rays UV IR TV waves (b) Which waves have the longest wavelength? (c) It takes radio waves from the galaxy Andromeda 2 2 million years to reach us. How far away is Andromeda in kilometres? (one year = 365 days) (d) Name a detector for each type of electromagnetic radiation in the spectrum. Light gathered from the stars can be split into spectra using a prism or a diffraction grating. This allows astronomers to gather a great deal of information about the stars. (e) What is the name given to the type of spectrum shown below? (f) Identify two elements present in this spectrum using the information below. GMV Science. Photocopiable only by the purchasing institution. 20
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2. A magnifying glass, of focal length 5 cm, produces an image of an object. The object is 3 cm high and is placed 2 cm from the magnifying glass. (a) Draw a ray diagram to illustrate how the image is formed by the magnifying glass. (b) What size is the image produced by the lens? (c) Is the image real or virtual? (d) Magnifying glasses are used in the eyepieces of refracting telescopes. One such telescope used to observe stars is shown below. eyepiece X Y light from star (i) What names are given to the telescope parts labelled X and Y on the diagram? (ii) Explain why part Y should have a large diameter. (iii) What is the purpose of the eyepiece in this telescope? 3. The Chinese first used rockets in the thirteenth century. These rockets used a type of gunpowder to fuel them. Most modern rockets are liquid fuelled but work on the same principle as the early rockets. (a) Explain using Newton s third law how a rocket engine propels a rocket forward. (b) A multistage rocket of mass 1 6 x 10 5 kg is preparing for lift off from Earth. The rocket engines provide a constant thrust of 2 2 x 10 6 N. U S A GMV Science. Photocopiable only by the purchasing institution. 22
Calculate the initial acceleration of the rocket. (c) The acceleration of the rocket increases as it burns up fuel even though the thrust provided by the engine remains constant. Explain why. (d) Once in space the rocket engines are switched off. Describe the motion of the rocket now and explain its motion in terms of Newton s laws. The graph below shows how the speed of a different rocket varied with time after lift off. (e) Calculate the initial acceleration of the rocket. (f) How far did the rocket travel in the 500 seconds shown? 4. In the future travel to other planets may be possible. During a virtual reality flight, Spacekid observes the following : A B C D Walking on the moon seemed effortless but on Jupiter his boots felt as though they were being held down. Take off from Earth needed less engine thrust than take off from Neptune. Rocket motors could be switched off during interplanetary flight. When a 1 2 kg hammer was dropped on Saturn its time and vertical velocity were recorded as: Time (s) 0 5 1 0 1 5 2 0 2 5 Velocity (m/s) 5 5 11 16 5 22 27 5 (a) Explain observation A. GMV Science. Photocopiable only by the purchasing institution. 23
(b) Draw a diagram showing the forces acting on a rocket during take off. Use the values of g from the data sheet on page 24 to explain, in terms of the forces acting on the rocket, why take off requires more engine thrust on Neptune. (c) If the rocket has a mass of 3 x 10 7 kg and the engine thrust is 3 9 x 10 8 N, calculate the acceleration of the rocket at take off from Earth. (d) Explain observation C (e) Use the results from D to plot a speed time graph of the hammer falling on Saturn. (f) From the graph: (i) How far did the hammer fall? (ii) Calculate the gravitational field strength on Saturn. (g) Spacekid has a mass of 40 kg. On which planet, Earth or Saturn, is he heavier? Justify your answer. 5. A space shuttle of mass 2 x 10 6 kg was travelling with a speed of 9 000 m/s as it entered the Earth s atmosphere. The speed of the shuttle dropped to 100 m/s at touch down, at which point the brakes were applied, bringing the shuttle to rest. (a) Explain why the speed of the shuttle decreased from 9 000 m/s to 100 m/s before the brakes were applied. (b) How much kinetic energy did the shuttle lose before the brakes were applied? (c) How much heat energy was created as the shuttle speed dropped from 9000 m/s to 100 m/s? (d) The shuttle was covered with special heat-resistant tiles. Why was this necessary? (e) The specific heat capacity of the heat-resistant material used in the tiles is 35 700 J/kg 0 C. The temperature of the tiles should increase by no more than 1 300 0 C during re-entry. What mass of tiles would be required to absorb all of the heat energy produced? GMV Science. Photocopiable only by the purchasing institution. 24
(f) Explain why in practice the mass of the tiles was less than calculated in part (e). (g) How much work was done by the brakes to bring the shuttle to rest? 6. Use the information on the data sheet to answer the following: (a) On which planet would a 3 kg rock fall fastest. Explain your answer. (b) On which planets would the same rock fall most slowly. Explain your answer. A rock is projected on Saturn as shown. 20 m/s (c) Use your knowledge of how the gravitational field strength affects falling objects to copy and complete the following table of vertical velocity and time for the rock falling on Saturn.. Time (s) 0 1 2 3 4 5 Vertical velocity (m/s) 0 (d) Draw a speed time graph for both the horizontal and vertical motion of the rock within five seconds of being thrown. (e) Use the graphs to calculate both the horizontal and vertical distance travelled by the rock in the first three seconds. (f) How long will the rock take to reach a vertical speed of 132 m/s. GMV Science. Photocopiable only by the purchasing institution. 25
Appendix (i) Data Sheet Speed of light in materials Speed of sound in materials Material Speed in m/s Material Speed in m/s Air 3 x 10 8 Aluminium 5 200 Carbon dioxide 3 x 10 8 Air 340 Diamond 1 2 x 10 8 Bone 4 100 Glass 2 0 x 10 8 Carbon dioxide 270 Glycerol 2.1 x 10 8 Glycerol 1 900 Water 2 3 x 10 8 Muscle 1 600 Steel 5 200 Gravitational field strengths Tissue 1 500 Gravitational field strength on the surface in N/kg Water 1 500 Earth 10 Specific heat capacity of materials Jupiter 26 Material Specific heat Mars 4 capacity in J/kg o C Mercury 4 Alcohol 2 350 Moon 1 6 Aluminium 902 Neptune 12 Copper 386 Saturn 11 Glass 500 Sun 270 Glycerol 2 400 Venus 9 Ice 2 100 Uranus 11 7 Lead 128 Pluto 4 2 Silica 1 033 Water 4 180 Steel 500 Specific latent heat of fusion of materials Material Specific latent heat of Melting and boiling points of materials fusion in J/kg Material Melting Boiling Alcohol 0 99 x 10 5 point in o C point in o C Aluminium 3 95 x 10 5 Alcohol -98 65 Carbon dioxide 1 80 x 10 5 Aluminium 660 2470 Copper 2 05 x 10 5 Copper 1 077 2 567 Glycerol 1 81 x 10 5 Glycerol 18 290 Lead 0 25 x 10 5 Lead 328 1 737 Water 3 34 x 10 5 Turpentine -10 156 SI Prefixes and Multiplication Factors Specific latent heat of vaporisation of materials Prefix Symbol Factor Material Sp.l.ht vap(j/kg) giga G 1 000 000 000=10 9 Alcohol 11 2 x 10 5 mega M 1 000 000 =10 6 Carbon dioxide 3 77 x 10 5 kilo k 1 000 =10 3 Glycerol 8 30 x 10 5 milli m 0 001 =10-3 Turpentine 2 90 x 10 5 micro 0 000 001 =10-6 GMV Science. Photocopiable only by the purchasing institution. 26
Water 22 6 x 10 5 nano n 0 000 000 001=10-9 Appendix (ii) Answers to Numerical Problems Section 1 5.(c) Saturn & Venus (b) 1.5 m/s 2 6.(c) 35 714 J/kg o C Signals from Space (d) Neptune (c) no; thrust is less than weight 7 (a) 4.8 x 10 10 J Distances in Space(p2) 6. 2 kg stone on (d) 5 m/s 2 (b) 4.8 x 10 10 J 1. 9.46 x 10 15 m Neptune (e) 6 m/s 2 (c) 13 333 o C 2. 2.55 x 10 17 m 7. 546 N (f) 5.58 x 10 7 N 8.(a) 61 660.5 J 3. 40 light years 8. 60 N (b) 61 660.5 J 4. 300 years 9. 0.44 kg Projectiles (p11) 9.(a) 1.2 x 10 14 J 5. 19 210 s 10. Jupiter 1.(a) 40 m (b) 1.2 x 10 14 J 6. 9.46 x 10 17 km Weight,Thrust& (b) 20 m/s (c)3 x 10 6 N 7. 4.2 light years Acceleration(p7) (c) 20 m 10.(a) 8.1 x 10 9 J 8. 7 x 10 13 s 1.(a) 1.4 x 10 6 N 2.(a) 1 200 m (b) 8.1 x 10 9 J ( 2.2 million years) (b) 40 500 N (b) 120 m/s (c) 2 025 m 9. 1.49 x 10 8 km (c) 20 000 kg (c) 720 m Revision Questions 10. 9 570 s (d) 3.6 x 10 8 kg 3.(a) 300 m Credit Level(p19) (e) 0.125 m/s 2 (b) 100 m/s 1.(c) 2.08 x 10 19 km Ray Diagrams (p3) (f) 1.33 m/s 2 4.(a) 8 x 10 7 m 2.(b)5 cm 1.(a) 6cm 2. 0.75 m/s 2 (b) 2 000 m/s 3.(b) 3.75 m/s 2 (b) inverted 3. 4.2 x 10 6 N (c) 20 000 m (e) 8.5 m/s 2 (c) real 4. 2 x 10 6 kg 5.(a) 0.5 s (f) 1.02 x 10 6 m 2.(a) image height= 3cm 5. 1.33 m/s 2 (b) 5 m/s 4.(c) 3 m/s 2 image distance=6cm 6.(a) 30 ; 10 (c) 1.25 m (e) (i) 34.38 m 3.(a) real, diminished (b)19 000 ; 9.5 6.(a) 0 m/s (ii) 11 N/kg inverted (c)15 000 ; 5 000 ; (b) 100 m/s (f) Saturn (b)real,samesize, inverted 3.33 7.(a) 0 m/s 5.(b) 8.1 x 10 13 J (c) virtual, magnified, (d) 500 000; (b) 12.5 s (c) 8.1 x 10 13 J upright 50 000; 1 8. h. dist. = 1 200 m (e) 1.75 x 10 6 kg 4.(a) 8 mm (e)700 000; v. dist = 1 350 m (g) 1 x10 10 J (b) 4 mm 140 000; 2 9.(a) 200 m 6.(a) Jupiter (c) 10 mm (f) 760 000; (b) 0.75 m/s 2 (b) Mars & Mercury 5.(a) 5 cm 136 800; 1.8 (c) 150 m (c) velocities (m/s): (b) 12 cm 7.(a) 8 N 10.(a) 84 m (0), 11, 22, Section 2 (b) 5 m/s 2 (b) 24 m/s 33,44,55. Space Travel (c) 13.4 m/s 2 (c) 28.8 m (e) h.dist.: 60 m Weight (p5) 8.(a) 4 x 10 6 N Re-Entry(p15) v. dist.: 49.5 m 1.(a) 120 N (b) 1.6 x 10 7 N 1. 1.6 x 10 7 J (f) 12 s (b) 1 116 N (c) 2 x 10 7 N 2. 8.1 x 10 9 (c) 10 N/kg (d) 6.56 x 10 6 N 3.(a) 6.4 x 10 13 J (d) 10 N/kg 9.(a) 16.67 m/s 2 (b) 6.4 x 10 13 J (e) 58.33kg (b) 2.6 m/s 2 4.(a) 2.4 x 10 8 J (f) 5.8 kg (c) 0 m/s 2 (b) 13 333 o C 2. 700 N (d) 10 m/s 2 5.(a) 8.75 x 10 8 J 3. 2.88 kg (e) 11.5 m/s 2 (b) 39 062.5 o C 5.(a) Jupiter (f) 8 m/s 2 6.(a) 1.25 x 10 10 J GMV Science. Photocopiable only by the purchasing institution. 27
(b) Mars & Mercury 10.(a) 1.8 x 10 6 kg (b) 1.25 x 10 10 J GMV Science. Photocopiable only by the purchasing institution. 28