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Q.44 - Excercises And Problems

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
Found in: Page 355

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Short Answer

The unexplored planet Alpha Centauri III has a radius of . A visiting astronaut drops a rock, from rest, into a -deep crevasse. She records that it takes for the rock to reach the bottom. What is the mass of Alpha Centauri III?

Mass of Alpha Centauri III

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Step by Step Solution

Step 1: Given information

radius of the planet

height of the stone traveled into crevasse

time taken to for stone reaching through the crevasse

Step 2: Explanation

The velocity of the stone

The initial mechanical energy of the stone, when it is located at height above the the planet, is just gravitational potential energy:

where

is the gravitational constant

is the mass of the planet

is the mass of the stone

is the radius of the planet

is the altitude of the stone

When the stone hits the ground, its mechanical energy will sum of potential energy and kinetic energy:

where

is the speed of the object at the ground

Since the mechanical energy is conserved, we can write

and solving for M, we find

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