Weight on the surface of a black hole ()

In summary, the conversation discusses the concept of black holes and how they are formed by extremely dense objects with a powerful gravitational pull. The problem at hand involves finding the limiting radius at which a mass becomes a black hole, and then using Newtonian mechanics to calculate the weight of an object on the surface of this super-dense sphere. The equations used in the solution are the universal gravitation law and the Schwarzschild radius, demonstrating the importance of precise values for the speed of light and the constant G in these calculations.
  • #1
lizzyb
168
0

Homework Statement



A black hole is an object so heavy that neither matter nor even light can escape the influence of its gravitational field. Since no light can escape from it, it appears black. Suppose a mass approximately size of the Earth's mass 4.38 X 10^24 kg is packed into a small uniform sphere of radius r.

Use: The speed of light c = 2.99792 X 10^8 m/s. The universal gravitation constant G = 6.67259 X 10^-11 N m^2/kg^2.

There were two parts:

a) Findthe limiting radius r_0 when this mass becomes a black hole - easy.

b) Using Newtonian mechanics, how much would a mass of 4.64 micro-g weight at the suface of this super-dense sphere? Answer in units of N.

Homework Equations



[tex]W = g m = \frac{G M_e m}{r^2} m[/tex]

The Attempt at a Solution



I did:

[tex] W = g M_o = \frac{G M_h M_o}{r^2} M_o = \frac{G M_h M_o^2}{r^2}[/tex]

Using for r the value I found by the solution of (a) above, M_h, the given value of the mass of the black hole, and M_o the given value of the object (converted to kilograms). The answer was counted as wrong.
 
Last edited:
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  • #2
U probably used a wrong equation
F = GMm/r^2,
that is it, there should not be any square of mass
 
  • #3
it's for calculating the weight, W = m g = m F = m GMm/r^2 - GMm^2/r^2
 
  • #4
lizzyb said:
it's for calculating the weight, W = m g = m F = m GMm/r^2 - GMm^2/r^2

Your equation is dimensionally incorrect. mg is a force. How can mg = m*F? The problem gave you a rather precise value for the speed of light as well as the constant G. Do you think the correct calculation for part a might use those quantities? Have you learned about the Schwarzschild radius? I think that is what you need to know about to do the first part of this problem. The second part can then be done using the universal gravitaion law.
 

1. What is the weight on the surface of a black hole?

The weight on the surface of a black hole, also known as the event horizon, cannot be measured in the traditional sense as it is not a solid surface. However, the immense gravitational pull of a black hole can cause objects to accelerate and gain weight as they get closer to the event horizon.

2. Can anything escape the gravitational pull of a black hole?

Once an object crosses the event horizon of a black hole, it is impossible for it to escape the gravitational pull. This is because the escape velocity, or the speed needed to break free from the gravitational pull, exceeds the speed of light at the event horizon.

3. How does the weight on the surface of a black hole affect time?

The immense gravitational force near a black hole can cause time to slow down significantly. This phenomenon, known as time dilation, occurs because the gravity of the black hole warps the fabric of space-time, affecting the passage of time in its vicinity.

4. Is the weight on the surface of a black hole constant?

No, the weight on the surface of a black hole can vary depending on the mass and size of the black hole. The more massive a black hole is, the stronger its gravitational pull and the greater the weight on its surface.

5. What would happen to an object's weight if it fell into a black hole?

If an object falls into a black hole, its weight would continue to increase as it gets closer to the event horizon. However, once it crosses the event horizon, it would be pulled towards the singularity at the center of the black hole where it would be crushed to an infinitely small point, known as a singularity, where weight and other physical properties cease to exist.

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