Question

Neutron stars, such as the one at the center of the Crab Nebula, have about the same mass as our sun but a much smaller diameter.Part AIf you weigh 685 N on the earth, what would be your weight on the surface of a neutron star that has the same mass as our sun and a diameter of 24.0 km ?Take the mass of the sun to be ms = 1.99×1030 kg , the gravitational constant to be G = 6.67×10−11 N⋅m2/kg2 , and the free-fall acceleration at the earth's surface to be g = 9.8 m/s2 .Express your weight wstar in newtons.View Available Hint(s)wstar =nothingN

Answer 1

Step-by-step explanation:

Given that,

A person weight on earth is

W = 685N

Weight is not constant it varies due to gravity, but mass is constant, let find the person mass in earth

Weight is given as

W = mg

Then, m = W / g

Given that gravity (g) on earth is 9.8m/s²

Then, m = 685 / 9.8

m = 69.9 kg

The mass of the person on earth is 69.9 kg and it is constant everywhere on the planet

We want to find the weight of the person on a neutron star

Then, we need to know the acceleration due to gravity on a neutron star

The local acceleration due to gravity near a body of mass M

is given by the formula:

g = GM / R²

Given that,

G = 6.67 × 10^-11 Nm²/kg²

M = 1.99 × 10^30 kg

Diameter = 24km = 24,000m

Then, radius = D/2

R = 24,000 / 2

R = 12,000

So,

g = GM / R²

g = 6.67 × 10^-11 × 1.99 × 10^30 / 12000²

g = 9.218 × 10¹¹ m/s²

Then, it weights on neutron star is

W = mg

W = 69.9 × 9.218 × 10¹¹

W = 6.443 × 10¹³ N

Wow, this is a very risky place to go.

This is over 10¹¹ times your weight on earth! You probably shouldn't venture there.