Neutron stars are extremely dense objects that represent the final stage of life
ID: 1267086 • Letter: N
Question
Neutron stars are extremely dense objects that represent the final stage of life for some massive stars. Assume that a particular neutron star has a mass of 2.8x10Mkg (which is 1.4 times the Sun's mass) and a radius of 10km. A 2kg object falls from rest from a height of 5km above the neutron star's surface. What speed will the 2kg object have at the instant it hits the surface? (Our answer here is not entirely correct. With gravitational fields this strong and speeds this large (37% of the speed of light) we would have to use special and general relativity to obtain the correct answer. However, this answer is probably correct to within 10%.) Would a 3kg object (which would feel a larger gravitational attraction) hit the ground with a larger speed? Explain. What would be the weight of a 60kg person standing on the neutron star surface? (Considering that many neutron stars have surface temperatures of 100000 K this isn't a safe thing to do but....)Explanation / Answer
a) conservation of energy
-G M m/r = 1/2 mv^2 - G M m/r
notice m cancels
-6.67E-11*2.8E30/(10.0E3+5.0E3) = 0.5*v^2-6.67E-11*2.8E30/(10.0E3)
v=1.12E8 m/s
b) since m canceled same answer
v = 1.12E8 m/s
c) F = G M m/r^2 = 6.67E-11*2.8E30*60/(10.0E3)^2=1.12E14 N