DO PHYSICS ONLINE SPACE QUESTIONS AND PROBLEMS Under development – early phase only – could be numerous typographical errors until proof read more carefully VIEW ANSWERS How to answer a question: problem solving (t0_372.pdf) View periodic table (cited Aug 2012) Numerical values for constants and useful physical quantities) Review: Displacement, velocity, acceleration (t5_dva) Review: Rectilinear motion with a uniform acceleration (t5_aconst.pdf) Review: Forces and Newton’s laws of motion (t5_force.pdf) Review: Forces, momentum and energy (t5_fme.pdf) Review: Conservation laws (t5_conservation.pdf) Gravitational fields (t5_gravity.pdf) P5117 P5293 P5023 P5086 P5542 P5345 P5489 P5487 P5891 P5738 Gravitational potential energy (t5_gpe.pdf) P5860 P5188 P5440 Projectile Motion (t5_project.pdf) P5234 P5921 P5160 P5555 P5682 Motion of rockets (t5_rockets.pdf) P5697 P5854 P5497 P5876 P5674 Motion of satellites (t5_satellites.pdf) P5378 P5593 P7777 P5461 P5661 Einstein’s theory of special relativity – frames of reference (t5_fofr.pdf) P5950 P5886 Concepts of special relativity (t5_sr.pdf) P5606 P5609 Time dilation (t5_time.pdf) P5486 P5410 Length contraction (t5_length.pdf) P5791 P5935 P5176 P5615 Mass and energy (t5_emc2.pdf) P5456 P5893 P5544 P5023 How could you find the mass of the Earth from its radius and the acceleration due to gravity at the Earth’s surface? P5086 What is the gravitational force acting a 2000 kg satellite when it is orbiting the Earth at twice the Earth’s radius? Earth’s mass ME = 5.971024 kg Earth’s radius RE = 6.38106 m P5117 A 50 kg person and a 75 kg person are sitting on a bench 500 mm apart. Estimate the gravitational force acting between the two people. P5160 A golfer strikes a ball sitting on the ground on a level golf course. The ball hits the ground 180 m north from where it was struck, 5.6 s later. Assuming air resistance is negligible find: (a) the maximum height the ball reached, (b) the initial velocity (direction and magnitude) of the ball as it left the golf club. P5176 Two clocks are synchronized and then one is sent into space at 0.45c for one hour of its time. (a) Calculate the time passed for the clock left behind in the stationary frame of reference. (b) Describe and draw the space of the moving clock as observed from the stationary clock. Assume they are circular to start. (c) What shape will the moving clock to an observer moving with the clock? (d) If the moving clock had a mass of 294 g when stationary, calculate the mass when it is moving at 0.45c. P5188 (21 22) (a) Explain the reason for the selection of infinity as the place of zero gravitational potential energy. (b) How does this selection of zero level result in any point with a gravitational field having a negative gravitational potential energy value? P5234 A ball thrown in the air traces a path as shown. What does the diagram tell you? (HSC 2005) P5293 How could you design a pendulum to have a period of 1 s, 1 min, 1 hour? P5345 Find the net force acting on the Moon from the Earth and the Sun assuming that they are at right angles to each other. MM = 7.351022 kg MS = 1.991030 kg RME = 3.84105 km RMS = 1.50108 km P5378 A remote sensing satellite has been placed in a circular orbit with a period of 1.5 h. Determine the distance above the Earth’s surface and its speed. Earth’s mass ME = 5.971024 kg Earth’s radius RE = 6.38106 m universal gravitation constant G = 6.67310-11 N.m2.kg-2 P5410 Astronaut Chris travels to Vega, the fifth brightest star in the night sky, leaving his 35 year old twin Pat behind on Earth. Chris travels at a speed of 0.990c and Vega is 25.3 light-years from Earth. (a) How long does the trip take from the point of view of Pat. How old is Pat when Chris arrives at Vega? (b) How old is Chris when he arrives at Vega (use the time dilation effect)? (c) What distance did Chris travel from his point of view and how old is he at the end of his journey. P5440 (23 24 25) (a) Determine the gravitational potential energy of a 1000 kg communications satellite orbiting the Earth at an altitude of 40 000 km. (b) Calculate the change in gravitational potential energy when the 3177 kg space shuttle is launched from the surface of the Earth into a 400 km altitude low Earth orbit. (c) How much work must be done to increase the altitude of a 1000 kg satellite by 5000 m (assuming its mass is unchanged)? P5456 An electron with a rest mass of 9.1110-31 kg is travelling at 0.999c. Determine the relativistic mass of the electron. P5461 Why would a satellite in low orbit around Earth eventually fall to Earth? (HSC 2005). P5486 A spacecraft is travelling at 0.99c. An astronaut inside the craft records a time of 1 hour for a certain event to occur. How long would an observer stationary relative to the craft record for this event? P5487 Describe an experiment where a ball is dropped from different heights in a vacuum to determine the value of the acceleration due to gravity at the surface of the Earth. You need to describe the equipment used and how it was set up, the results you collected, how you analyzed them and the conclusion(s) you drew from them. You should use scientific diagrams where possible to aid your description. P5489 What is the value of g on the top of Mount Everest, h = 8848 m P5497 Discuss the effects of the motion of the Earth on the launch of a rocket. P5542 If an astronaut with all his gear on weights 240 N on the Moon, what is their mass on the surface of the Earth? Gravitational field strength on the Moon is (1/6)th of that on Earth. P5544 A particular radioactive isotope loses 5102 J of energy. Calculate its resultant loss of mass. P5555 A cannon fires a shot with a horizontal velocity of 200 m.s-1 from the top of a cliff 30.0 m above the level of the sea. Calculate (a) the time taken for the shot to travel from the cannon to the sea, (b) the range of the cannon ball hitting the water. (HSC School Exam 2008). P5593 A spy satellite of mass 1000 kg is orbiting the Earth (RE = 6380 km) at an altitude of 300 km. (a) What is its period? (b) What is its orbital speed? High resolution photographs on film are sent back to Earth in a special container which can withstand a maximum acceleration of 8g. The container and contents have a mass of 50 kg. (c) Calculate the kinetic energy of the container as it traveling with the satellite. (d) The gravitational potential energy of the container relative to the surface of the Earth is the difference between the gravitational potential energy of the container in the satellite and the gravitational potential energy at the Earth’s surface. Calculate this value. (e) Determine the shortest time the container’s velocity can be brought to zero. (f) If the total orbital energy = kinetic energy + gravitational potential energy relative to the surface, determine the rate energy must be lost to remove the orbital energy of the container by the time it reaches the Earth’s surface. P5606 A new EFT (extremely fast train) is travelling along the tracks at the speed of light relative to the Earth’s surface. A passenger is walking towards the front of the train at 5 m/s relative to the floor of the train. Clearly, relative to the Earth’s surface, the passenger is moving faster than the speed of light. Analyse this situation from the point of view of Special Relativity. P5609 Einstein’s 1905 theory of special relativity made several predictions that could not be verified for many years. (a 1) State ONE such prediction. (b 2) Describe an experiment to test this prediction. (c 3) Explain how technological advances since 1905 have made it possible to carry out this experiment. (HSC 2005) P5615 The radius of our galaxy is 31020 m, or about 3104 light years. Assume the speed of a spacecraft is 0.99c. (a) (b) (c) (d) (d) From the point of view of an observer on Earth, calculate the time to travel to the edge of our galaxy? Use the length contraction formula to calculate the time for a person to travel from the centre to the edge of our galaxy. Use the time dilation effect to calculate the time for a person to travel from the centre to the edge of our galaxy. How fast would a spaceship have to travel to go from the centre to the edge of our galaxy in 30 yrs as measured from within the spaceship? How much time would elapse on Earth during this journey? What does this tell us about the future of traveling to edge of our galaxy? P5661 From nearest to furthest, the four satellite moons of Jupiter first observed by Galileo in the year 1610 are called Io, Europa, Ganymede and Callisto. For the first three moons, the orbital period T of each is exactly twice the period of the one orbiting immediately inside it. That is TEuropa 2 TIo TGanymede 2 TEuropa The mass of Jupiter is 1.901027 kg, and the orbital radius of Io is 421 600 km. (a) Use Kepler’s Law of Periods to calculate Ganymede’s orbital radius. (b) Calculate Ganymede’s orbital speed. (HSC 2005) P5674 The initial velocity required by a space probe to just escape the gravitational pull of a planet is called escape velocity. What quantities affect the magnitude of the escape velocity? P5682 Two projectiles are fired at the same initial speed on level ground. Prove that that if one projectile was launched at an angle of w.r.t. the ground and the other at an angle such that ( + ) = 90o that they have the same range. For the case when = 60o and = 30o, which projectile takes the longest time to hit the ground? Sketch for the two projectiles (a) the trajectory and (b) the vertical displacement against time. P5697 A rocket takes off from the launch pad with constant thrust. Which choice shows how the acceleration and velocity changes as it rises? v a A v v B a a a v C D Explain your answer. P5738 Given the radius of the Earth is 6400 km, a rocket places a satellite into a stable orbit of altitude 4020 km. Calculate the period of the satellite, P5777 A space probe P is in a stable orbit around small, distant planet. Sketch the orbit of the space probe. The probe fires a forward-facing rocket that reduces its orbital speed by half. Sketch the subsequent motion of the planet. (HSC 2005). P5791 A missile travelling at 90% of the speed of light has a rest length of 10 m. Calculate the length of the moving missile as measured by a stationary observer directly under the flight path of the missile. P5854 (a) Give two reasons to explain why the concept of g-force is useful. (b) Explain why the space shuttle is apparently “weightless” while in orbit. P5860 Two astronauts landed on a very small asteroid orbiting the Sun between Mars and Jupiter. They experienced almost negligible weight force. Explain. P5876 Calculate the escape velocity from the Earth’s surface (m.s-1 and km.h-1). Earth’s mass ME = 5.971024 kg Earth’s radius RE = 6.38106 m universal gravitation constant G = 6.67310-11 N.m2.kg-2 P5886 The idea of a universal aether was first proposed to explain the transmission of light through space. Michelson and Morley attempted to measure the speed of Earth through the aether. Evaluate the impact of the result of the Michelson and Morley experiment on scientific thinking. P5891 In 1970 NASA launched Apollo 13, their third mission planned to land humans on the Moon. Half-way to the Moon a huge explosion crippled the spacecraft. The only way home for the astronauts was to fly around the back of the Moon and then fire the rocket engine to take the craft out of lunar orbit and put it into an Earth-bound trajectory. At the completion of the rocket engine burn, mission leader Jim Lovell was heard to say, ‘We just put Isaac Newton in the driver’s seat’. Given that the spacecraft returned safely to Earth, justify Jim Lovell’s statement. P5893 Energy is radiated by the Sun at the rate of about 3.921026 W. Find the corresponding decrease in the Sun’s mass for every second that it radiates. P5899 Compare the orbital radius of a geostationary satellite above Mars with that above the Earth. mass of Mars = 6.421023 kg period of rotation of Mars = 24 h 47 min radius of Mars = 0.53 radius of Earth ME = 5.971024 kg Earth’s radius RE = 6.38106 m P5921 A cannon ball was observed by Isaac Newton to be fired at a velocity of 300 m.s-1 and at an angle of 30o from the horizontal. Determine: (a) the horizontal and vertical components of its initial velocity, (b) time taken to reach its maximum height, (c) the maximum height of the cannon ball, (d) the range of the cannon ball. (HSC School Exam 2008). P5935 A spacecraft in the shape of a square box with sides 300 mm long moves away from the Earth at a velocity of 0.5c. Find the volume of the box as measured from Earth. P5950 Describe an experiment that you could perform in a reference frame to determine whether or not the frame was non-inertial.