Question

In: Physics

To get a better idea about tidal forces, Esperanza and Mika assume that the black hole...

To get a better idea about tidal forces, Esperanza and Mika assume that the black hole is about one solar mass, 2.0 ✕ 10³⁰ kg, and that the distance from its center to the person's feet is 3 km (the approximate Schwarzschild radius, the distance at which the escape speed from the body becomes c, the speed of light). They also assume that the person's mass is 60 kg and the person's height is 2 m. How can they use the equation for the tidal force,

F_tidal = GMm (1/d^2 - 1/ (d+h)^2) to find how many times greater this tidal force is than the weight of the person on Earth, approximately 600 N? (Choose the ratio of the tidal force to the weight of the person on Earth.)

Expert Solution

Given,

Mass of black hole .

Distance of the person's feet from center of black hole is .

Person's mass is .

Person's height is .

The tidal force on that person will be

is gravitational force on head.

is force on feet.

If we consider that the person's head is pointing towards the center of black hole.

Distance of person's head from the center of black hole is .

Distance of person's feet from the center of black hole is .

Then the tidal force on that person will be

G is gravitational constant

The tidal force on person is .

Weight of the person is given as approximately equal to .

The tidal force on person is

times the weight of the person on the earth.

times the weight of the person on the Earth.

Tidal force on person is times greater than his weight on the Earth.

genius_generous answered 1 year ago

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