Two neutron stars are separated by a distance of 10^13 m. They each have a mass of 10^30 kg and a radius of 10^5 m. They are initially at rest with respect to each other. (a) How fast are they moving when their separation has decreased to one-half its initial value? My answer is 3.652 x 10^3 m/s , and it is wrong again (sigh). here is my computations 1/2(mass)(final velocity)^2 - G(M1)(m2)/Final distance = 1/2(mass)(initial velocity)^2 - G(M1)(m2)/(initial radius) Since they are initially at rest, the vi term is zero, and that kinetic energy term vanishes. Then i plug in the values and solve for final velocity: 1/2(10^30)(final velocity)^2 - (6.67x10^-11)(10^30)^2/(5x10^12) = -(6.67x10^-11)(10^30)^2/(10^13) so I isolate for final velocity and i get (final velocity)^2 = 1.33 x 10^7 and i get final velocity = 3.652 x 10^3, when i input it it says it is wrong. Can someone help me, where did i go wrong? I did it multiple times already.
you have a 2 different ways to approach this problem 1. use reduced mass and the centrifugal force=gravitational force 2. use conservation of energy both with end up with the same answer
I used Potential Energy Final + Kinetic Energy final = Potential energy initial + kinetic energy initial
In this problem, are you are they are orbiting around each other? Cauase in part B they collide, so I assumed they are in a straight line path toward each other. WTF
part b? you didn't mention that.... even if they are moving in a straight line, both neutron stars are moving (with same speed).
Part A: Your equation is set up right, however you need to multiply the final kinetic energy by 2 since you have 2 neutron stars. final distance = 1/2 initial distance, subsitute that into the equation. Also you shouldn't really label r as the initial radius, because this part of the problem uses the distance (10^13m). Part B: uses the same equation, but the distance is now 2x the radius which would be the diameter. Should really work with variables first to simplify the equation, then start plugging in values. Also what school do you go to? I was working on this same problem a couple of hours ago.
ahhh, i see, i didn't realize i had to multiply the final kinetic energy by 2...i missed that key point. Ok leme try to do my computations , brb TY.