Neutron stars consist only of neutrons and have unbelievably high densities. A typical mass and radius for a neutron star might be 6.3 x 1028 kg and 1.6 x 103 m. (a) Find the density of such a star. (b) If a dime (V = 2.0 x 10-7 m3) were made from this material, how much would it weight (in pounds)?
ρ= m/V= 6.3•10²⁸/1.6•10³=3.93 •10²⁵ kg/m³
m= ρV₁=3.93 •10²⁵•2 •10⁻⁷=7.875•10¹⁸ kg=17.4•10¹⁸ lb
^ That is wrong, V does not = 1.6*10^3
To find the density of a neutron star, we can use the formula:
Density = Mass / Volume
(a) Density of the neutron star:
Given:
Mass of the neutron star, M = 6.3 x 10^28 kg
Radius of the neutron star, R = 1.6 x 10^3 m
The volume of a sphere can be calculated using the formula:
Volume = (4/3) * π * R^3
Substituting the given values:
Volume = (4/3) * π * (1.6 x 10^3)^3 = 4.207 x 10^10 m^3
Now, we can calculate the density:
Density = Mass / Volume = (6.3 x 10^28 kg) / (4.207 x 10^10 m^3)
Density ≈ 1.5 x 10^18 kg/m^3
Thus, the density of the neutron star is approximately 1.5 x 10^18 kg/m^3.
(b) Weight of the dime made from this material:
Given:
Volume of the dime, V = 2.0 x 10^-7 m^3
We can calculate the mass of the dime using the density we found in part (a):
Mass = Density * Volume = (1.5 x 10^18 kg/m^3) * (2.0 x 10^-7 m^3)
Mass ≈ 3.0 x 10^11 kg
Now, we can convert the mass to pounds:
1 kg is approximately equal to 2.20462 pounds
So, the dime would weigh:
Weight = Mass * 2.20462 pounds/kg = (3.0 x 10^11 kg) * 2.20462 pounds/kg
Calculating the weight:
Weight ≈ 6.4 x 10^11 pounds
Therefore, the dime made from the material of a neutron star would weigh approximately 6.4 x 10^11 pounds.