3. What is the change in the gravitational potential energy of the satellite in problem #1 as it is lifted from the earth's surface to its orbit?
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1 3. A 1.10 x io3 kg object is dropped from a distance of 2.00 x io5 m onto the surface of the moon. How fast is the object travelling when it hits the moon's surface? = 6.67x10- kg -3.2O x io8 J 3.20 x io8 J kg)(i.io x io3 kg ooxio5m+i.74xio m 1.74x10 m x io8 J = (1.10 xio3 kg)(uf2) -- (i.ioxio3 kg)(o) Vf Practice Problems: 2 2 = 7.62 x io2 m/s i. What is the gravitational potential energy of a 5.00 x io3 kg satellite that is in an orbit that has a radius of 9.90 x io6 m around the earth. (Use gravitational potential energy = o at r = oo.) (-2.0 x io11 J) 2. What is the work done against gravity on the satellite in the problem #1 in lifting it into its orbit? (l.ll x IO11 J) 3. What is the change in the gravitational potential energy of the satellite in problem #1 as it is lifted from the earth's surface to its orbit? (l.ll x IO11 J) Castle Rock Research 306 Copyright Protected Not for
2 What is the speed of a 1750 kg meteorite when it hits the surface of the moon? This meteorite had a velocity of i.oo x io3 m/s heading directly toward the moon when it was m above the moon's surface. (1.02 x io3 m/s) What is the gravitational potential energy of a 10.0 kg object when it is sitting on the surface of the earth? (Use gravitational potential energy = o at r = oo.~) (-6.25 x io8 J) 6. What is the change in the gravitational potential energy of a 2.50 x io3 kg satellite as it is lifted vertically into a circular orbit (radius = 6.90 x io6 m) around the earth? » * * * * * * * (1.18 x io10 J) -.11 Not for Reproduction 307 Physics 12 SNAP
3 PROBLEMS: LAUNCHING Formula: v = v = Practice Problems: l. What is the escape speed at the moon's surface? (r = 1.74 x io6 m, M = 5.98 x 1024kg.) (2.37 x io3 m/s) 2. What is the escape speed at Jupiter's surface? (r = 7.18 x 10? m, mass = 1.9 x io2? kg) (5.94 x io4 m/s) 3. What is the mass of a planet that has an escape speed of 9.0 x io3 m/s and a radius of 7.2 x io6 m? 4. What is the mass of a planet that has a radius of 2.57 x io6 m and an escape speed of 2.92 x io3 m/s? * * * * * * * * * * (I.64xio23kg) Not for Reproduction 309 Physics 12 SNAP
4 Practice Problems: i. Calculate the speed of the moon in its orbit around the earth. (Radius of moon's orbit = 3.84 x io8 m moon's mass = 7.35 x io22 kg) SUMMAR In this unit c equations: mu r (1.02 x io3 m/s) 2. Calculate the speed of a satellite orbiting the earth at a height of 4.4 x IQS m above the earth's surface. (Hint: remember to add the earth's radius of 6.38 x io6 m.) equal to 3. Calculate the orbital speed of a satellite 5.0 x io6 m above the surface of Jupiter, (rj = 7.18 x 10? m, mj = 1.90 x lo2? kg) (7.65 x io3 m/s) This was de force, i.e. th used this wi Again F (4.06 x io4 m/s) 4. Calculate the speed of earth in its orbit around the sun. (Radius of earth's orbit = 1.50 x io11 m,ms = 1.98 x io3 kg) (2.97 x io4 m/s) 5. Using T =., calculate the time of one revolution (length of a year) on Mars. (mm = 6.4 x io23 kg, ms = 2.0 x io3 kg, Radius of Mars' orbit = 2.3 x io11 m) (6.0 x io7 s or 1.9 years) Castle Rock Research 312 Copyright Protected Not for Repr
5 Launching: 16. You find yourself on a planet where the potential energy of a 2.60 kg mass with respect to the centre of the planet is 3.64 x io6 J. What is the escape velocity on this planet? Satellite. 19. \ (1.91 x io3 m/s) 17. What is the mass of an a planet (radius = 5.85 x 10? m) which has an escape velocity of 2.54 x ich m/s? 2O. JL (2.83xl026kg) 18. What is the escape velocity on a planet that has a mass of 3.18 x io23 kg and a radius of 2.43 x io6 m? 21. (4.18xlO3 m/s) Castle Rock Research 320 Copyright Protected Not for Rej
6 Satellites in Orbit: i respect anet? 19. What is the speed of an artificial satellite (mass = 625 kg) which is placed in an orbit i.oo x io6 m above the surface of a planet?(mp = 3.18 x io23 kg, rp = 2.43 x io6 m) i x io3 m/s) elocity of (2.49 x io3 m/s) 20 < An artificial satellite (mass = 572 kg) is put into a circular orbit about the earth (mass = 5.98 x io24 kg). If the radius of this orbit is 1.2 x io7 m, how long will it take to make one revolution? 2.83x10 kg) i radius of (1.3 x 1Q4 s) 21. An artificial satellite (mass = 611 kg) is put into a circular orbit around Jupiter (mass = 1.90 x lo2? kg, radius = 6.99 x 10? m). If this satellite has an orbital velocity of 3.12 x ich m/s, how far above Jupiter's surface is the satellite? 4.18xlO3 m/s) (6.03 x 10? m) yright Protected Not for Reproduction 321 Physics 12 SNAP
7 Gravitational Potential Energy: 22. What is the gravitational potential energy of the moon with respect to the earth? 1. (-7.63xio28J) 23. What is the change in the gravitational potential energy of a 10.0 kg object when it is lifted vertically to a height of 6.38 x io6 m above the surface of the earth? (3.13 x io8 J) ********** Castle Rock Research 322 Copyright Protected Not for I
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