9.2 Worksheet #3 - Circular and Satellite Motion

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1 9.2 Worksheet #3 - Circular and Satellite Motion 1. A car just becomes airborne as it comes off the crest of a bridge that has circular cross section of radius 78.0 m. What is the speed of the car? 2. A satellite has a circular path of radius 4.87 x 105 km about a planet that rotates once in 16.5 hours. To an observer on the planet's surface, the satellite always appears to be stationary. a. What is the speed of the satellite in its orbit? b. Calculate the centripetal acceleration of the satellite. c. What is the local acceleration due to gravity "g" at the altitude of the satellite above the planet? 3. Sputnik I, Earth s first artificial satellite, had an orbital period of s. What was the average orbital radius of Sputnik s orbit? (Hint: Mass of earth, Me = 5.98 x 1024 kg) 4. During an Apollo lunar landing mission, the command module continued to orbit the Moon in a near circular orbit of height 100 km above the lunar surface. How long did it take the command module to orbit the Moon? [Mass of moon = 7.4 x 1022 kg ; Radius of Moon = x 106 m] 5. A satellite in GEO (Geosynchronous Earth Orbit) is placed at such a height so that its period of orbit equals 1 day. If it moves in the same direction that the earth rotates, it will always appear at the same location in the sky. Use the earth-moon distance (3.84 x 108 m, measured centre to centre) along with the lunar period (27.3 days) to calculate: a. the fraction of its distance to the moon from the earth's centre b. the number of earth radii above the ground c. the height above the ground for such a satellite if it moves in a geostationary orbit above the earth's equator.

2 6. A 150-g ball at the end of a string is revolving uniformly in a horizontal circle of radius m. The ball makes 2 revolutions in one second. a. What is its centripetal acceleration? b. Draw a free body diagram showing the forces acting on the ball. c. Calculate the tension in the string 7. A device used for training astronauts and jet fighter pilots is designed to rotate the trainee in a horizontal circle of radius 10.0 m. If the force felt by the trainee is 7.5 times their own weight (7.5 W), how fast is he/she rotating? Give your answer in both ms-1 and r.p.m. 8. The rings of Saturn are composed of chunks of ice that orbit the planet. The inner radius of the rings is km, while the outer radius is km. Find the period of an orbiting chunk of ice at the outer radius. [The mass of Saturn is 5.69 x 1026 kg.] 9. Read the following information box and then answer the questions that follow: The National Academy of Science, in order to gather information on global deforestation, wishes to place a 500 kg infrared-sensing satellite in a polar orbit around the earth. The radius of the earth is approximately 6.38 x 103 km, and the acceleration of gravity at the orbital altitude of 160 km is very nearly the same as it is at the surface of the earth. a. Construct a force diagram (FBD) for the satellite described in the statement above.

3 b. What is the agent (cause) of the centripetal force for the satellite? c. How much work is done on the satellite during one complete orbit of the earth? Explain your answer. d. How long would you predict it to take for the satellite to make one complete revolution around the earth? 10. The earth's orbit around the sun is very nearly circular, with an average radius of 1.5 x 108 km. Assume the mass of the earth is 6 x 1024 kg. a. What is the average speed of the earth in its orbit around the sun? b. What is the magnitude of the earth's average acceleration in its orbit around the sun? Show your working. c. With what force does the sun attract the earth? Past HSC Questions The diagram shows four positions of a car on a roller coaster ride. At which point during this ride would the occupant experience maximum g force? (A) P (B) Q (C) R (D) S

4 5. The table contains information related to two planets orbiting a distant star. The orbital period of the planet Ba can be determined by using data selected from this table. What is the orbital period of the planet Ba? (A) 3.10 x10 7 s (C) 1.39 x10 8 s (B) 5.51 x10 7 s (D) 2.47 x10 8 s 2003 A satellite moves in uniform circular motion around Earth. The following table shows the symbols used in the diagrams below. These diagrams are NOT drawn to scale. Key: F net force on satellite v velocity of satellite Which diagram shows the direction of F and v at the position indicated? (A) (B) (C) (D)

5 For a satellite moving in uniform circular motion around Earth, the centripetal force is provided by the gravitational force. The mass of Earth is M E. The mass of the satellite is M S. The distance of the satellite from the centre of Earth is d. Which of the following equations should be used to calculate the speed of this satellite? (A) (B) (C) (D) Two planets, X and Y, travel around a star in the same direction, in circular orbits. Planet X completes one revolution about the star in time T. The radii of the orbits are in the ratio 1: 4. How many revolutions does planet Y make about the star in the same time T? (A) 1/8 revolution (B) 1/2 revolution (C) 2 revolutions (D) 8 revolutions Question 17 (6 marks) A satellite of mass 150 kg is launched from Earth s surface into a uniform circular orbit of radius 7.5 x 10 6 m. (a) Calculate the magnitude of the gravitational potential energy Ep of the satellite. (c) Discuss the effect of Earth s rotational motion on the launch of this satellite. (b) From this uniform circular orbit, the satellite can escape Earth s gravitational field when its kinetic energy is equal to the magnitude of the gravitational potential energy. Use this relationship to calculate the escape velocity of the satellite.

6 2004 Question 17 (6 marks) In July 1969 the Apollo 11 Command Module with Michael Collins on board orbited the Moon waiting for the Ascent Module to return from the Moon s surface. The mass of the Command Module was 9.98 x 10 3 kg, its period was 119 minutes, and the radius of its orbit from the Moon s centre was 1.85 x10 6 metres. (a) Assuming the Command Module was in circular orbit, calculate (i) the mass of the Moon; (2) (ii) the magnitude of the orbital velocity of the Command Module.(2) (b) The docking of the Ascent Module with the Command Module resulted in an increase in mass of the orbiting spacecraft. The spacecraft remained at the same altitude. This docking procedure made no difference to the orbital speed. Justify this statement Question 18 (4 marks) A car with a mass of 800 kg travels at a constant speed of 7.5 m.s 1 on a roundabout so that it follows a circular path with a radius of 16 m. Question 19 (6 marks) On 11 June 2003 the Mars Rover called Spirit was launched on a satellite from Earth when the planets were in the positions shown in the diagram below. The satellite arrived at Mars on 3 December A person observing this situation makes the following statement. There is no net force acting on the car because the speed is constant and the friction between the tyres and the road balances the centripetal force acting on the car. Assess this statement. Support your answer with an analysis of the horizontal forces acting on the car, using the numerical data provided above. (a) Indicate on the diagram the approximate positions of Earth and Mars on 3 December 2003 and show the satellite s trajectory to Mars. (b) Discuss the effect of Earth s motion on the launch and trajectory to Mars of this satellite.

7 Why would a satellite in low orbit around Earth eventually fall to Earth? (A) It is not in a geostationary orbit. (B) Gravity is too strong at low orbits. (C) The sun s solar wind pushes it out of orbit. (D) The upper atmosphere gradually slows it down. 3. The initial velocity required by a space probe to just escape the gravitational pull of a planet is called escape velocity. Which of the following quantities does NOT affect the magnitude of the escape velocity? (A) Mass of the planet (B) Mass of the space probe (C) Radius of the planet (D) Universal gravitational constant 4. A space probe, P, is in a stable orbit around a small, distant planet. The probe fires a forward-facing rocket that reduces its orbital speed by half. Which of the following best illustrates the subsequent motion of the probe? Question 16 (5 marks) 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, T Europa 2 x T Io T Ganymede 2 x T Europa The mass of Jupiter is kg, and the orbital radius of Io is km. (a) Use Kepler s Law of Periods to calculate Ganymede s orbital radius. (b) Calculate Ganymede s orbital speed.

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