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Categorize This example is a substitution problem. Use Equation 13.22 to find the escape speed: Evaluate the kinetic energy of the ïµesc 2 ï¨ 6.674 ï´10ï11 N ï m 2 kg 2 ï©ï¨ 5.97 ï´1024 kg ï© 2GM E ï½ ï½ RE 6.37 ï´106 m ï½ 1.12 ï´104 m s 2 K ï½ 12 mïµesc ï½ 1 2 ï¨ 5.00 ï´10 3 kg ï©ï¨1.12 ï´104 m s ï© 2 ï½ 3.13 ï´1011 J spacecraft from Equation 7.16: The calculated escape speed corresponds to about 25 000 mi/h. The kinetic energy of the spacecraft is equivalent to the energy released by the combustion of about 2 300 gal of gasoline. WHAT IF? What if you want to launch a 1 000-kg spacecraft at the escape speed? How much energy would that require? Answer In Equation 13.22, the mass of the object moving with the escape speed does not appear. Therefore, the escape speed for the 1 000-kg spacecraft is the same as that for the 5 000-kg spacecraft. The only change in the kinetic energy is due to the mass, so the 1 000-kg spacecraft requires one-fifth of the energy of the 5 000-kg spacecraft: K ï½ 15 ï¨ 3.13 ï´1011 J ï© ï½ 6.25 ï´1010 J Objective Questions 1. denotes answer available in Student Solutions Manual/Study Guide 1. A system consists of five particles. How many terms appear in the expression for the total gravitational potential energy of the system? (a) 4 (b) 5 (c) 10 (d) 20 (e) 25 2. Rank the following quantities of energy from largest to smallest. State if any are equal. (a) the absolute value of the average potential energy of the SunâEarth