Neutron stars consist only of neutrons and have unbelievably high densities. A typical mass and radius for a neutron star might be 3.4 multiplied by 1028 kg and 2.0 multiplied by 103 m.
(a) Find the density of such a star.
(b) If a dime (V = 2.0 multiplied by 10-7m3) were made from this material, how much would it weigh (in pounds)?
To find the density of the neutron star, we can use the formula:
Density = Mass / Volume
(a) Density of the neutron star:
Given:
Mass of the neutron star (m) = 3.4 x 10^28 kg
Radius of the neutron star (r) = 2.0 x 10^3 m
The volume of a sphere is given by the equation:
Volume = (4/3) x π x r^3
Substituting the given values into the equation:
Volume = (4/3) x π x (2.0 x 10^3)^3
Calculate the volume.
Next, we can calculate the density:
Density = (Mass of the neutron star) / (Volume of the neutron star)
Substitute the values we have:
Density = (3.4 x 10^28 kg) / (Volume of the neutron star)
This will give you the density in kg/m^3.
(b) To determine how much a dime made from this material would weigh in pounds, we need to know its volume. Given that the volume of the dime is V = 2.0 x 10^-7 m^3, we can use the density (which we calculated in part a) to find the weight:
Weight = (Volume of the dime) x (Density)
Substituting the values we have:
Weight = (2.0 x 10^-7 m^3) x (Density)
Finally, convert the weight from kg to pounds. Since 1 kg is approximately equal to 2.205 pounds, you can multiply the weight by this conversion factor to get the weight in pounds.
(a) density = (Mass)/(Volume)
= [3/(4 pi)]*Mass/(radius)^3
(b) Multiply the density that you get in (a) by the volume of a dime (2*10^-7 m^3). That will give you the mass in kg. Multiply that by 2.2 lb/kg for the weight in pounds. (They want you to assume that the dime is on the Earth, with acceleration of gravity 9.8 m/s^2.)
It would be so heavy that it would probably sink to the center of the Earth. You might want to compare the mass of the dime to the mass of the Earth.