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where to shrink Jupiter and put all of its mass into a small enough radius, you could form a black hole with mass equal to the mass of Jupiter. Calculate the radius at which Jupiter would become a black hole. r this problem in the following two questions below. tion 5 ou need find an equation for the escape velocity and then solve for the radius r. cape velocity is that at which the Kinetic Energy KE = mv²is equal to the Potential Energy PE = mgr (notice that you are used to see PE = mgh, since we usually measure potential energy relative to the surface, now we want to find the ial at the surface, so hr). though that the gravitational acceleration g is not constant if you change the radius r, we can find how g depends on r using Newton's Law of Gravitation and Newton's 2nd Law: g = 4 = GmM. GM mr? - PE and solve for r, what do you get? Remember to set g= CM 2GM tion 6 hat you have an equation for r, set the escape velocity to the speed light, i.e. v =c (that is how we define a black hole), and the mass M to the mass of Jupiter. Use the values below in the equation and calculate r. 10 m/s ational Constant - 6.7 x 1011 m kg s2 of Jupiter 2 x 10^27 kg pur answer in units of meters

where to shrink Jupiter and put all of its mass into a small enough radius, you could form a black hole with mass equal to the mass of Jupiter. Calculate the radius at which Jupiter would become a black hole. r this problem in the following two questions below. tion 5 ou need find an equation for the escape velocity and then solve for the radius r. cape velocity is that at which the Kinetic Energy KE = mv²is equal to the Potential Energy PE = mgr (notice that you are used to see PE = mgh, since we usually measure potential energy relative to the surface, now we want to find the ial at the surface, so hr). though that the gravitational acceleration g is not constant if you change the radius r, we can find how g depends on r using Newton's Law of Gravitation and Newton's 2nd Law: g = 4 = GmM. GM mr? - PE and solve for r, what do you get? Remember to set g= CM 2GM tion 6 hat you have an equation for r, set the escape velocity to the speed light, i.e. v =c (that is how we define a black hole), and the mass M to the mass of Jupiter. Use the values below in the equation and calculate r. 10 m/s ational Constant - 6.7 x 1011 m kg s2 of Jupiter 2 x 10^27 kg pur answer in units of meters

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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Please help with both questions 5 and 6 since they are related to one another and I need help with both. Thank you so much in advance!

If you where to shrink Jupiter and put all of its mass into a small enough radius, you could form a black hole with mass equal to the mass of Jupiter. Calculate the radius at which Jupiter would become a black hole. Answer this problem in the following two questions below. Question 5 First you need find an equation for the escape velocity and then solve for the radius r. The escape velocity is that at which the Kinetic Energy KE = mv² is equal to the Potential Energy PE = mgr (notice that you are used to see PE = mgh, since we usually measure potential energy relative to the surface, now we want to find the potential at the surface, so h = r). F, Notice though that the gravitational acceleration g is not constant if you change the radius r, we can find how g depends on r using Newton's Law of Gravitation and Newton's 2nd Law: g = GmM GM %3D mr2 Set KE = PE and solve for r, what do you get? GM HINT: Remember to set g = O r = Or = GM От- 2GM Or = 2GM Question 6 Now that you have an equation for r, set the escape velocity to the speed of light, i.e. v = c (that is how we define a black hole), and the mass M to the mass of Jupiter. Use the values below in the equation and calculate r. c = 3 x 108 m/s Gravitational Constant = 6.7 x 1011 m3 kg1 s2 Mass of Jupiter = 2 x 10^27 kg Give your answer in units of meters
Transcribed Image Text:If you where to shrink Jupiter and put all of its mass into a small enough radius, you could form a black hole with mass equal to the mass of Jupiter. Calculate the radius at which Jupiter would become a black hole. Answer this problem in the following two questions below. Question 5 First you need find an equation for the escape velocity and then solve for the radius r. The escape velocity is that at which the Kinetic Energy KE = mv² is equal to the Potential Energy PE = mgr (notice that you are used to see PE = mgh, since we usually measure potential energy relative to the surface, now we want to find the potential at the surface, so h = r). F, Notice though that the gravitational acceleration g is not constant if you change the radius r, we can find how g depends on r using Newton's Law of Gravitation and Newton's 2nd Law: g = GmM GM %3D mr2 Set KE = PE and solve for r, what do you get? GM HINT: Remember to set g = O r = Or = GM От- 2GM Or = 2GM Question 6 Now that you have an equation for r, set the escape velocity to the speed of light, i.e. v = c (that is how we define a black hole), and the mass M to the mass of Jupiter. Use the values below in the equation and calculate r. c = 3 x 108 m/s Gravitational Constant = 6.7 x 1011 m3 kg1 s2 Mass of Jupiter = 2 x 10^27 kg Give your answer in units of meters
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