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Unformatted text preview: Nguyen, Thanh – Homework 19 – Due: Nov 13 2007, 7:00 pm – Inst: D Weathers 1 This print-out should have 11 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. 001 (part 1 of 2) 10 points A black hole is an object so heavy that neither matter nor even light can escape the influence of its gravitational field. Since no light can escape from it, it appears black. Suppose a mass approximately the size of the Earth’s mass 6 . 93 × 10 24 kg is packed into a small uniform sphere of radius r . Use: The speed of light c = 2 . 99792 × 10 8 m / s . The universal gravitation constant G = 6 . 67259 × 10- 11 Nm 2 / kg 2 . Hint: The escape speed must be the speed of light. Based on Newtonian mechanics, determine the limiting radius r when this mass (approx- imately the size of the Earth’s mass) becomes a black hole. Correct answer: 0 . 01029 m. Explanation: Basic Concepts: Gravitational energy conservation E =- GmM r + K . At minimum escape velocity, E = 0 (the pro- jectile has just enough initial kinetic energy to overcome the gravitational potential). Solution: Technically speaking, in a region where gravity is extremely intense, Newton’s mechanics cannot be used. Rather, one needs to apply the “general theory of relativity” developed by Albert Einstein. Knowing this is the case, we still would like to see what Newtonian mechanics tells us. Setting v esc = c , the limiting radius is given by 1 2 mv 2 esc = 1 2 mc 2 = GmM r , or r = 2 GM c 2 ....
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This note was uploaded on 10/24/2011 for the course PHYS 1710 taught by Professor Weathers during the Winter '08 term at North Texas.
- Winter '08